| Title: | Extended Mixed Models Using Latent Classes and Latent Processes |
|---|---|
| Description: | Estimation of various extensions of the mixed models including latent class mixed models, joint latent class mixed models, mixed models for curvilinear outcomes, mixed models for multivariate longitudinal outcomes using a maximum likelihood estimation method (Proust-Lima, Philipps, Liquet (2017) <doi:10.18637/jss.v078.i02>). |
| Authors: | Cecile Proust-Lima [aut, cre], Viviane Philipps [aut], Amadou Diakite [ctb], Benoit Liquet [ctb] |
| Maintainer: | Cecile Proust-Lima <[email protected]> |
| License: | GPL (>= 2.0) |
| Version: | 2.1.0 |
| Built: | 2024-10-30 06:55:10 UTC |
| Source: | CRAN |
Functions for the estimation of latent class mixed models (LCMM), joint latent class mixed models for longitudinal and survival data (JLCM) and latent process mixed models (with or without latent classes of trajectory) for univariate and multivariate longitudinal outcomes of different types including curvilinear and ordinal outcomes. All the models are estimated in a maximum likelihood framework using an iterative algorithm. The package also provides various post fit functions.
| Package: | lcmm |
| Type: | Package |
| Version: | 2.1.0 |
| Date: | 2023-10-06 |
| License: | GPL (>=2.0) |
| LazyLoad: | yes |
The package includes for the moment the estimation of :
latent class mixed models for Gaussian longitudinal outcomes
using hlme function,
latent class mixed models for other
quantitative, bounded quantitative (curvilinear) and discrete (ordinal/binary) longitudinal
outcomes using lcmm function,
mixed models (with and without latent classes) for
multivariate longitudinal outcomes of different nature using
multlcmm function (this includes a longitudinal IRT model for homogeneous and heterogeneous data),
joint latent class mixed models for a
Gaussian (or curvilinear) longitudinal outcome and a right-censored
(potentially left-truncated and of multiple causes) time-to-event using
Jointlcmm function,
joint latent class mixed models for multivariate longitudinal outcomes
and a right-censored (potentially left-truncated and of multiple causes) time-to-event using
mpjlcmm function.
Please report any bug or comment regarding the package for future updates VIA GITHUB ONLY.
Cecile Proust-Lima, Viviane Philipps, Amadou Diakite and Benoit Liquet
Proust-Lima C, Philipps V, Liquet B (2017). Estimation of Extended Mixed Models Using Latent Classes and Latent Processes: The R Package lcmm. Journal of Statistical Software, 78(2), 1-56. doi:10.18637/jss.v078.i02
Lin, Turnbull, McCulloch and Slate (2002). Latent class models for joint analysis of longitudinal biomarker and event process data: application to longitudinal prostate-specific antigen readings and prostate cancer. Journal of the American Statistical Association 97, 53-65.
Muthen and Shedden (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics 55, 463-9
Proust and Jacqmin-Gadda (2005). Estimation of linear mixed models with a mixture of distribution for the random-effects. Comput Methods Programs Biomed 78:165-73
Proust, Jacqmin-Gadda, Taylor, Ganiayre, and Commenges (2006). A nonlinear model with latent process for cognitive evolution using multivariate longitudinal data. Biometrics 62, 1014-24.
Proust-Lima, Dartigues and Jacqmin-Gadda (2011). Misuse of the linear mixed model when evaluating risk factors of cognitive decline. Amer J Epidemiol 174(9), 1077-88
Proust-Lima and Taylor (2009). Development and validation of a dynamic prognostic tool for prostate cancer recurrence using repeated measures of post-treatment PSA: a joint modelling approach. Biostatistics 10, 535-49.
Proust-Lima, Sene, Taylor, Jacqmin-Gadda (2014). Joint latent class models for longitudinal and time-to-event data: a review. Statistical Methods in Medical Research 23, 74-90.
Proust-Lima, Amieva, Jacqmin-Gadda (2013). Analysis of multivariate mixed longitudinal data: A flexible latent process approach. Br J Math Stat Psychol 66(3), 470-87.
Proust-Lima, Philipps, Perrot, Blanchin, Sebille (2021). Modeling repeated self-reported outcome data: a continuous-time longitudinal Item Response Theory model. arXiv:210913064. http://arxiv.org/abs/2109.13064
Proust-Lima, Dartigues, Jacqmin-Gadda (2016). Joint modeling of repeated multivariate cognitive measures and competing risks of dementia and death: a latent process and latent class approach. Stat Med;35(3):382-98
Proust-Lima, Philipps, Dartigues, Bennett, Glymour, Jacqmin-Gadda, et al (2019). Are latent variable models preferable to composite score approaches when assessing risk factors of change? Evaluation of type-I error and statistical power in longitudinal cognitive studies. Stat Methods Med Res;28(7):1942-57
Verbeke and Lesaffre (1996). A linear mixed-effects model with heterogeneity in the random-effects population. Journal of the American Statistical Association 91, 217-21
This function computes the predicted cumulative incidence of each cause of event according to a profile of covariates from a joint latent class model. Confidence bands can be computed by a Monte-Carlo method.
cuminc(x, time, draws = FALSE, ndraws = 2000, integrateOptions = NULL, ...)cuminc(x, time, draws = FALSE, ndraws = 2000, integrateOptions = NULL, ...)
x |
an object inheriting from class |
time |
a vector of times at which the cumulative incidence is calculated |
draws |
optional boolean specifying whether a Monte Carlo approximation of the posterior distribution of the cumulative incidence is computed and the median, 2.5% and 97.5% percentiles are given. Otherwise, the predicted cumulative incidence is computed at the point estimate. By default, draws=FALSE. |
ndraws |
if draws=TRUE, ndraws specifies the number of draws that should be generated to approximate the posterior distribution of the predicted cumulative incidence. By default, ndraws=2000. |
integrateOptions |
optional list specifying the subdivisions, rel.tol and stop.on.error options (see ?integrate). |
... |
further arguments, in particular values of the covariates specified in the survival part of the joint model. |
An object of class cuminc containing as many matrices as
profiles defined by the covariates values. Each of these matrices contains
the event-specific cumulative incidences in each latent class at the
different times specified.
Viviane Philipps and Cecile Proust-Lima
Jointlcmm, plot.Jointlcmm, plot.cuminc
m2 <- Jointlcmm(fixed= Ydep1~Time*X1,mixture=~Time,random=~Time, classmb=~X3,subject='ID',survival = Surv(Tevent,Event)~X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",ng=2,data=data_lcmm, B=c(0.64,-0.62,0,0,0.52,0.81,0.41,0.78,0.1,0.77,-0.05,10.43,11.3,-2.6, -0.52,1.41,-0.05,0.91,0.05,0.21,1.5)) par(mfrow=c(1,2)) plot(cuminc(m2,time=seq(0,20),X1=0,X2=0), ylim=c(0,1)) plot(cuminc(m2,time=seq(0,20),X1=0,X2=1), ylim=c(0,1))m2 <- Jointlcmm(fixed= Ydep1~Time*X1,mixture=~Time,random=~Time, classmb=~X3,subject='ID',survival = Surv(Tevent,Event)~X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",ng=2,data=data_lcmm, B=c(0.64,-0.62,0,0,0.52,0.81,0.41,0.78,0.1,0.77,-0.05,10.43,11.3,-2.6, -0.52,1.41,-0.05,0.91,0.05,0.21,1.5)) par(mfrow=c(1,2)) plot(cuminc(m2,time=seq(0,20),X1=0,X2=0), ylim=c(0,1)) plot(cuminc(m2,time=seq(0,20),X1=0,X2=1), ylim=c(0,1))
The data were simulated from a 3-latent class linear mixed model. Repeated data for 100 subjects were simulated. The three latent classes are predicted by X2 and X3. In each latent class, Y follows a linear mixed model including intercept and time both with correlated random-effects and class-specific fixed effects. In addition, X1 and X1*time have a common impact over classes on the Y trajectory.
A data frame with 326 observations on the following 9 variables.
subject identification number
longitudinal outcome
time of measurement
binary covariate
binary covariate
binary covariate
hlme, postprob,
summary.lcmm, plot.predict
The data were simulated from a joint latent class mixed model with 3 classes. Repeated data of 3 longitudinal outcomes (Ydep1, Ydep2, Ydep3) and censored time of event (Tevent, Event) with delayed entry (Tentry) were simulated for a total of 300 subjects. The three latent classes were predicted by the continuous covariate X3. In each latent class, the longitudinal outcome Ydep1 followed a linear mixed model including intercept, time and squared time both with correlated random-effects and class-specific fixed effects. In addition, the binary covariate X1 and its interaction with time X1:Time had a common impact (over classes) on the Ydep1 trajectory. The longitudinal ordinal outcomes Ydep2 and Ydep3 were generated from Ydep1 using threshold models with respectively 30 and 10 thresholds. In each latent class, the time of event followed a class-specific Weibull hazard with a common proportional effect of the binary covariate X2. Both time of entry Tentry and time of censoring had a uniform distribution
A data frame with 1678 observations over 300 different subjects and 22 variables.
subject identification number
longitudinal continuous outcome
longitudinal ordinal outcome with 31 levels
longitudinal ordinal outcome with 11 levels
delayed entry for the time-to-event
observed time-to-event: either censoring time or time of event
indicator that Tevent is the time of event
time of measurement
binary covariate
binary covariate
continuous covariate
categorical covariate
Jointlcmm
This function computes the difference of 2 EPOCE estimates (CVPOL or MPOL)
and its 95% tracking interval between two joint latent class models
estimated using Jointlcmm and evaluated using epoce function.
Difference in CVPOL is computed when the EPOCE was previously estimated on
the same dataset as used for estimation (using an approximated
cross-validation), and difference in MPOL is computed when the EPOCE was
previously estimated on an external dataset.
Diffepoce(epoceM1, epoceM2)Diffepoce(epoceM1, epoceM2)
epoceM1 |
a first object inheriting from class |
epoceM2 |
a second object inheriting from class |
This function does not apply for the moment with multiple causes of event (competing risks).
From the EPOCE estimates and the individual contributions to the prognostic
observed log-likelihood obtained with epoce function on the same
dataset from two different estimated joint latent class models, the
difference of CVPOL (or MPOL) and its 95% tracking interval is computed.
The 95% tracking interval is:
Delta(MPOL) +/- qnorm(0.975)*sqrt(VARIANCE) for an external dataset
Delta(CVPOL) +/- qnorm(0.975)*sqrt(VARIANCE) for the dataset used in
Jointlcmm
where Delta(CVPOL) (or Delta(MPOL)) is the difference of CVPOL (or MPOL) of the two joint latent class models, and VARIANCE is the empirical variance of the difference of individual contributions to the prognostic observed log-likelihoods of the two joint latent class models.
See Commenges et al. (2012) and Proust-Lima et al. (2012) for further details.
call.Jointlcmm1 |
the |
call.Jointlcmm2 |
the |
call |
the matched call |
DiffEPOCE |
Dataframe containing, for each prediction time s, the difference in either MPOL or CVPOL depending on the dataset used, and the 95% tracking bands (TIinf and TIsup) |
new.data |
a boolean for internal use only, which is FALSE if
computation is done on the same data as for |
Cecile Proust-Lima and Amadou Diakite
Commenges, Liquet and Proust-Lima (2012). Choice of prognostic estimators in joint models by estimating differences of expected conditional Kullback-Leibler risks. Biometrics 68(2), 380-7.
Proust-Lima, Sene, Taylor, Jacqmin-Gadda (2014). Joint latent class models for longitudinal and time-to-event data: a review. Statistical Methods in Medical Research 23, 74-90.
Jointlcmm, epoce, summary.Diffepoce
## Not run: #### estimation with 2 latent classes (ng=2) m2 <- Jointlcmm(fixed= Ydep1~Time*X1,random=~Time,mixture=~Time,subject='ID' ,survival = Surv(Tevent,Event)~ X1+X2 ,hazard="Weibull" ,hazardtype="PH",ng=2,data=data_lcmm, B=c( 0.7608, -9.4974, 1.0242, 1.4331, 0.1063 , 0.6714, 10.4679, 11.3178, -2.5671, -0.5386, 1.4616, -0.0605, 0.9489, 0.1020, 0.2079, 1.5045),logscale=TRUE) m1 <- Jointlcmm(fixed= Ydep1~Time*X1,random=~Time,subject='ID' ,survival = Surv(Tevent,Event)~ X1+X2 ,hazard="Weibull" ,hazardtype="PH",ng=1,data=data_lcmm, B=c(-7.6634, 0.9136, 0.1002, 0.6641, 10.5675, -1.6589, 1.4767, -0.0806, 0.9240,0.5643, 1.2277, 1.5004)) ## EPOCE computation for predictions times from 1 to 6 on the dataset used ## for estimation of m. VecTime <- c(1,3,5,7,9,11,13,15) cvpol1 <- epoce(m1,var.time="Time",pred.times=VecTime) cvpol1 cvpol2 <- epoce(m2,var.time="Time",pred.times=VecTime) cvpol2 DeltaEPOCE <- Diffepoce(cvpol1,cvpol2) summary(DeltaEPOCE) plot(DeltaEPOCE,bty="l") ## End(Not run)## Not run: #### estimation with 2 latent classes (ng=2) m2 <- Jointlcmm(fixed= Ydep1~Time*X1,random=~Time,mixture=~Time,subject='ID' ,survival = Surv(Tevent,Event)~ X1+X2 ,hazard="Weibull" ,hazardtype="PH",ng=2,data=data_lcmm, B=c( 0.7608, -9.4974, 1.0242, 1.4331, 0.1063 , 0.6714, 10.4679, 11.3178, -2.5671, -0.5386, 1.4616, -0.0605, 0.9489, 0.1020, 0.2079, 1.5045),logscale=TRUE) m1 <- Jointlcmm(fixed= Ydep1~Time*X1,random=~Time,subject='ID' ,survival = Surv(Tevent,Event)~ X1+X2 ,hazard="Weibull" ,hazardtype="PH",ng=1,data=data_lcmm, B=c(-7.6634, 0.9136, 0.1002, 0.6641, 10.5675, -1.6589, 1.4767, -0.0806, 0.9240,0.5643, 1.2277, 1.5004)) ## EPOCE computation for predictions times from 1 to 6 on the dataset used ## for estimation of m. VecTime <- c(1,3,5,7,9,11,13,15) cvpol1 <- epoce(m1,var.time="Time",pred.times=VecTime) cvpol1 cvpol2 <- epoce(m2,var.time="Time",pred.times=VecTime) cvpol2 DeltaEPOCE <- Diffepoce(cvpol1,cvpol2) summary(DeltaEPOCE) plot(DeltaEPOCE,bty="l") ## End(Not run)
This function computes individual dynamic predictions and 95% confidence bands. Given a joint latent class model, a landmark time s, a horizon time t and measurements until time s, the predicted probability of event in the window [s,s+t] is calculated. Confidence bands can be provided using a Monte Carlo method.
dynpred( model, newdata, event = 1, landmark, horizon, var.time, fun.time = identity, na.action = 1, draws = FALSE, ndraws = 2000 )dynpred( model, newdata, event = 1, landmark, horizon, var.time, fun.time = identity, na.action = 1, draws = FALSE, ndraws = 2000 )
model |
an object inheriting from class |
newdata |
a data frame containing the data from which predictions are computed. This data frame must contain all the model's covariates, the observations of the longitudinal and survival outcomes, the subject identifier and if necessary the variables specified in prior and TimeDepVar argumentsfrom Jointlcmm. |
event |
integer giving the event for which the prediction is to be calculated |
landmark |
a numeric vector containing the landmark times. |
horizon |
a numeric vector containing the horizon times. |
var.time |
a character indicating the time variable in |
fun.time |
an optional function. This is only required if the time
scales in the longitudinal part of the model and the survival part are
different. In that case, |
na.action |
Integer indicating how NAs are managed. The default is 1 for 'na.omit'. The alternative is 2 for 'na.fail'. Other options such as 'na.pass' or 'na.exclude' are not implemented in the current version. |
draws |
optional boolean specifying whether median and confidence bands of the predicted values should be computed (TRUE). IF TRUE, a Monte Carlo approximation of the posterior distribution of the predicted values is computed and the median, 2.5% and 97.5% percentiles are given. Otherwise, the predicted values are computed at the point estimate. By default, draws=FALSE. |
ndraws |
if draws=TRUE, ndraws specifies the number of draws that should be generated to approximate the posterior distribution of the predicted values. By default, ndraws=2000. |
A list containing :
pred |
a matrix with 4 columns if draws=FALSE and 6 columns if draws=TRUE, containing the subjects identifier, the landmark times, the horizon times, the predicted probability (if draws=FALSE) or the median, 2.5% and 97.5 % percentiles of the 'ndraws' probabilities calculated (if draws=TRUE). If a subject has no measurement before time s or if the event has already occured at time s, his probability is NA. |
newdata |
a data frame obtained from argument newdata containing time measurements and longitudinal observations used to compute the predictions |
Cecile Proust-Lima, Viviane Philipps
Proust-Lima, Sene, Taylor and Jacqmin-Gadda (2014). Joint latent class models of longitudinal and time-to-event data: a review. Statistical Methods in Medical Research 23, 74-90.
plot.dynpred, Jointlcmm, predictY, plot.predict
## Joint latent class model with 2 classes : m32 <- Jointlcmm(Ydep1~Time*X1,mixture=~Time,random=~Time,subject="ID", classmb=~X3,ng=2,survival=Surv(Tevent,Event)~X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",data=data_lcmm, B = c(0.641, -0.6217, 0, 0, 0.5045, 0.8115, -0.4316, 0.7798, 0.1027, 0.7704, -0.0479, 10.4257, 11.2972, -2.5955, -0.5234, 1.4147, -0.05, 0.9124, 0.0501, 0.2138, 1.5027)) ## Predictions at landmark 10 and 12 for horizon 3, 5 and 10 for two subjects : dynpred(m32,landmark=c(10,12),horizon=c(3,5,10),var.time="Time", fun.time=function(x){10*x},newdata=data_lcmm[1:8,]) ## Not run: dynpred(m32,landmark=c(10,12),horizon=c(3,5,10),var.time="Time", fun.time=function(x){10*x},newdata=data_lcmm[1:8,],draws=TRUE,ndraws=2000) ## End(Not run)## Joint latent class model with 2 classes : m32 <- Jointlcmm(Ydep1~Time*X1,mixture=~Time,random=~Time,subject="ID", classmb=~X3,ng=2,survival=Surv(Tevent,Event)~X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",data=data_lcmm, B = c(0.641, -0.6217, 0, 0, 0.5045, 0.8115, -0.4316, 0.7798, 0.1027, 0.7704, -0.0479, 10.4257, 11.2972, -2.5955, -0.5234, 1.4147, -0.05, 0.9124, 0.0501, 0.2138, 1.5027)) ## Predictions at landmark 10 and 12 for horizon 3, 5 and 10 for two subjects : dynpred(m32,landmark=c(10,12),horizon=c(3,5,10),var.time="Time", fun.time=function(x){10*x},newdata=data_lcmm[1:8,]) ## Not run: dynpred(m32,landmark=c(10,12),horizon=c(3,5,10),var.time="Time", fun.time=function(x){10*x},newdata=data_lcmm[1:8,],draws=TRUE,ndraws=2000) ## End(Not run)
Jointlcmm
This function computes estimators of the Expected Prognostic Observed
Cross-Entropy (EPOCE) for evaluating the predictive accuracy of joint latent
class models estimated using Jointlcmm. On the same data as used for
estimation of the Jointlcmm object, this function computes both the
Mean Prognostic Observed Log-Likelihood (MPOL) and the Cross-Validated
Observed Log-Likelihood (CVPOL), two estimators of EPOCE. The latter
corrects the MPOL estimate for over-optimism by approximated
cross-validation. On external data, this function only computes the Mean
Prognostic Observed Log-Likelihood (MPOL).
epoce( model, pred.times, var.time, fun.time = identity, newdata = NULL, subset = NULL, na.action = 1 )epoce( model, pred.times, var.time, fun.time = identity, newdata = NULL, subset = NULL, na.action = 1 )
model |
an object inheriting from class |
pred.times |
Vector of times of prediction, from which predictive accuracy is evaluated (only subjects still at risk at the time of prediction are included in the computation, and only information before the time of prediction is considered. |
var.time |
Name of the variable indicating time in the dataset |
fun.time |
an optional function. This is only required if the time
scales in the longitudinal part of the model and the survival part are
different. In that case, |
newdata |
optional. When missing, the data used for estimating the
|
subset |
a specification of the rows to be used: defaults to all rows. This can be any valid indexing vector for the rows of data or if that is not supplied, a data frame made up of the variable used in formula. |
na.action |
Integer indicating how NAs are managed. The default is 1 for 'na.omit'. The alternative is 2 for 'na.fail'. Other options such as 'na.pass' or 'na.exclude' are not implemented in the current version. |
This function does not apply for the moment with multiple causes of event (competing risks).
EPOCE assesses the prognostic information of a joint latent class model. It relies on information theory.
MPOL computed at time s equals minus the mean individual contribution to the conditional log-likelihood of the time to event given the longitudinal data up to the time of prediction s and given the subject is still at risk of event in s.
CVPOL computed at time s equals MPOL at time s plus a penalty term that corrects for over-optimism when computing predictive accuracy measures on the same dataset as used for estimation. This penalty term is computed from the inverse of the Hessian of the joint log-likelihood and the product of the gradients of the contributions to respectively the joint log-likelihood and the conditional log-likelihood.
The theory of EPOCE and its estimators MPOL and CVPOL is given in Commenges et al. (2012), and further detailed and illustrated for joint models in Proust-Lima et al. (2013).
call.Jointlcmm |
the |
call.epoce |
the matched call |
EPOCE |
Dataframe containing, for
each prediction time s, the number of subjects still at risk at s (and with
at least one measure before s), the number of events after time s, the MPOL,
and the CVPOL when computation is done on the dataset used for
|
IndivContrib |
Individual contributions to the prognostic observed log-likelihood at each time of prediction. Used for computing tracking intervals of EPOCE differences between models. |
new.data |
a boolean for internal use only, which is FALSE if
computation is done on the same data as for |
Cecile Proust-Lima and Amadou Diakite
Commenges, Liquet and Proust-Lima (2012). Choice of prognostic estimators in joint models by estimating differences of expected conditional Kullback-Leibler risks. Biometrics 68(2), 380-7.
Proust-Lima, Sene, Taylor and Jacqmin-Gadda (2014). Joint latent class models of longitudinal and time-to-event data: a review. Statistical Methods in Medical Research 23, 74-90.
Jointlcmm, print.epoce, summary.epoce, plot.epoce
## Not run: ## estimation of a joint latent class model with 2 latent classes (ng=2) # (see the example section of Jointlcmm for details about # the model specification) m <- Jointlcmm(fixed= Ydep1~Time*X1,random=~Time,mixture=~Time,subject='ID' ,survival = Surv(Tevent,Event)~ X1+X2 ,hazard="Weibull" ,hazardtype="PH",ng=2,data=data_lcmm,logscale=TRUE, B=c(0.7608, -9.4974 , 1.0242, 1.4331 , 0.1063 , 0.6714, 10.4679, 11.3178, -2.5671, -0.5386, 1.4616, -0.0605, 0.9489, 0.1020 , 0.2079, 1.5045)) summary(m) ## Computation of the EPOCE on the same dataset as used for # estimation of m with times at predictions from 1 to 15 VecTime <- c(1,3,5,7,9,11,13,15) cvpl <- epoce(m,var.time="Time",pred.times=VecTime) summary(cvpl) plot(cvpl,bty="l",ylim=c(0,2)) ## End(Not run)## Not run: ## estimation of a joint latent class model with 2 latent classes (ng=2) # (see the example section of Jointlcmm for details about # the model specification) m <- Jointlcmm(fixed= Ydep1~Time*X1,random=~Time,mixture=~Time,subject='ID' ,survival = Surv(Tevent,Event)~ X1+X2 ,hazard="Weibull" ,hazardtype="PH",ng=2,data=data_lcmm,logscale=TRUE, B=c(0.7608, -9.4974 , 1.0242, 1.4331 , 0.1063 , 0.6714, 10.4679, 11.3178, -2.5671, -0.5386, 1.4616, -0.0605, 0.9489, 0.1020 , 0.2079, 1.5045)) summary(m) ## Computation of the EPOCE on the same dataset as used for # estimation of m with times at predictions from 1 to 15 VecTime <- c(1,3,5,7,9,11,13,15) cvpl <- epoce(m,var.time="Time",pred.times=VecTime) summary(cvpl) plot(cvpl,bty="l",ylim=c(0,2)) ## End(Not run)
This function provides the vector of maximum likelihood estimates of a model
estimated with hlme, lcmm, multlcmm,
Jointlcmm, mpjlcmm, externSurv, or externX.
estimates(x, cholesky = TRUE)estimates(x, cholesky = TRUE)
x |
an object of class |
cholesky |
optional logical indicating if the parameters of variance-covariance of the random effets should be displayed instead of their cholesky transformations used in the estimation process. |
a vector with all estimates of the model.
Cecile Proust-Lima, Viviane Philipps
VarCov, hlme, lcmm,
multlcmm, Jointlcmm
This function fits regression models to relate a latent class structure (stemmed
from a latent class model estimated within lcmm package) with either an external
outcome or external class predictors.
Two inference techniques are implemented to account for the classification error:
- a 2-stage estimation of the joint likelihood of the primary latent class model and the secondary/ external regression;
- a regression between the posterior latent class assignment and the external variable which internally corrects for the assignment misclassification.
It returns an object from one of the lcmm package classes.
externVar( model, fixed, mixture, random, subject, classmb, survival, hazard = "Weibull", hazardtype = "Specific", hazardnodes = NULL, TimeDepVar = NULL, logscale = FALSE, idiag = FALSE, nwg = FALSE, randomY = NULL, link = NULL, intnodes = NULL, epsY = NULL, cor = NULL, nsim = NULL, range = NULL, data, longitudinal, method, varest, M = 200, B, convB = 1e-04, convL = 1e-04, convG = 1e-04, maxiter = 100, posfix, partialH = FALSE, verbose = FALSE, nproc = 1 )externVar( model, fixed, mixture, random, subject, classmb, survival, hazard = "Weibull", hazardtype = "Specific", hazardnodes = NULL, TimeDepVar = NULL, logscale = FALSE, idiag = FALSE, nwg = FALSE, randomY = NULL, link = NULL, intnodes = NULL, epsY = NULL, cor = NULL, nsim = NULL, range = NULL, data, longitudinal, method, varest, M = 200, B, convB = 1e-04, convL = 1e-04, convG = 1e-04, maxiter = 100, posfix, partialH = FALSE, verbose = FALSE, nproc = 1 )
model |
an object inheriting from class |
fixed |
optional two sided linear formula object for specifying the
fixed-effects in the secondary model with an external outcome variable.
The response outcome is on the left of |
mixture |
optional one-sided formula object for the class-specific fixed effects
in the model for the external outcome. Among the list of covariates included in fixed,
the covariates with class-specific regression parameters are entered in
mixture separated by |
random |
optional one-sided linear formula object for specifying the random-effects on external outcome in the secondary model, if appropriate. By default, no random effect is included. |
subject |
name of the covariate representing the grouping structure. Even in the absence of a hierarchical structure. |
classmb |
optional one-sided formula specifying the external predictors of
latent class membership to be modelled in the secondary class-membership multinomial
logistic model. Covariates are separated by |
survival |
optional two-sided formula specifying the external survival part of the model. |
hazard |
optional family of hazard function assumed for the survival model (Weibull, piecewise or splines) |
hazardtype |
optional indicator for the type of baseline risk function (Specific, PH or Common) |
hazardnodes |
optional vector containing interior nodes if |
TimeDepVar |
optional vector specifying the name of the time-depending covariate in the survival model |
logscale |
optional boolean indicating whether an exponential (logscale=TRUE) or a square (logscale=FALSE -by default) transformation is used to ensure positivity of parameters in the baseline risk functions |
idiag |
if appropriate, optional logical for the structure of the variance-covariance
matrix of the random-effects in the secondary model.
If |
nwg |
if appropriate, optional logical indicating if the variance-covariance of the
random-effects in the secondary model is class-specific. If |
randomY |
optional logical for including an outcome-specific random intercept. If FALSE no outcome-specific random intercept is added (default). If TRUE independent outcome-specific random intercept with parameterized variance are included |
link |
optional family of parameterized link functions for the external outcome if appropriate. Defaults to NULL, corresponding to continuous Gaussian distribution (hlme function). |
intnodes |
optional vector of interior nodes. This argument is only required for a I-splines link function with nodes entered manually. |
epsY |
optional definite positive real used to rescale the marker in (0,1) when the beta link function is used. By default, epsY=0.5. |
cor |
optional indicator for inclusion of an auto correlated Gaussian process in the latent process linear (latent process) mixed model. Option "BM" indicates a brownian motion with parameterized variance. Option "AR" specifies an autoregressive process of order 1 with parameterized variance and correlation intensity. Each option should be followed by the time variable in brackets as codecor=BM(time). By default, no autocorrelated Gaussian process is added. |
nsim |
number of points to be used in the estimated link function. By default, nsom=100. |
range |
optional vector indicating the range of the outcomes (that is the minimum and maximum). By default, the range is defined according to the minimum and maximum observed values of the outcome. The option should be used only for Beta and Splines transformations. |
data |
Data frame containing the variables named in
|
longitudinal |
only with |
method |
character indicating the inference technique to be used:
|
varest |
optional character indicating the method to be used to compute the
variance of the regression estimates. |
M |
option integer indicating the number of draws for the parametric boostrap
when |
B |
optional vector of initial parameter values for the secondary model.
If external outcome, the vector has the same structure as a latent class model
estimated in the other functions of |
convB |
optional threshold for the convergence criterion based on the parameter stability. By default, convB=0.0001. |
convL |
optional threshold for the convergence criterion based on the log-likelihood stability. By default, convL=0.0001. |
convG |
optional threshold for the convergence criterion based on the derivatives. By default, convG=0.0001. |
maxiter |
optional maximum number of iterations for the secondary model estimation using Marquardt iterative algorithm. Defaults to 100 |
posfix |
optional vector specifying indices in parameter vector B the secondary model that should not be estimated. Default to NULL, all the parameters of the secondary regression are estimated. |
partialH |
optional logical for Piecewise and Splines baseline risk functions and Splines link functions only. Indicates whether the parameters of the baseline risk or link functions can be dropped from the Hessian matrix to define convergence criteria (can solve non convergence due to estimates at the boundary of the parameter space - usually 0). |
verbose |
logical indicating whether information about computation should be reported. Default to FALSE. |
nproc |
the number cores for parallel computation. Default to 1 (sequential mode). |
A. DATA STRUCTURE
The data argument must follow specific structure for individual variables,
i.e. variables with a unique constant value for each subject. For an individual variable
given as external outcome, data value must be present only once per subject,
independently of any time variable used in the primary latent class.
For an individual variable given as external class predictor,
data values must be given for every row of every individual (as usual)
B. VARIANCE ESTIMATION
Not taking into account first stage variance with specifing "none" may lead to
underestimation of the final variance. When possible, Method "Hessian"
which relies on the combination of Hessians from the primary and secondary
model is recommended. However, it may become numerically intensive in the event
of very high number of parameters in the primary latent class model. As an
alternative, especially in situations with a complex primary model but rather
parcimonious secondary model, method "paramBoot" which implements a
parametric bootstrap can be used.
an object of class externVar and
externSurv for external survival outcomes,
externX for external class predictors, and
hlme, lcmm, or multlcmm for external longitudinal or cross-sectional outcomes.
## Not run: ###### Estimation of the primary latent class model ###### set.seed(1234) PrimMod <- hlme(Ydep1~Time,random=~Time,subject='ID',ng=1,data=data_lcmm) PrimMod2 <- hlme(Ydep1~Time,mixture=~Time,random=~Time,subject='ID', ng=2,data=data_lcmm,B=random(PrimMod)) ###### Example 1: Relationship between a latent class structure and # # external class predictors ###### # estimation of the secondary multinomial logistic model with total variance # computed with the Hessian XextHess <- externVar(PrimMod2, classmb = ~X1 + X2 + X3 + X4, subject = "ID", data = data_lcmm, method = "twoStageJoint") summary(XextHess) # estimation of a secondary multinomial logistic model with total variance # computed with parametric Bootstrap (much longer). When using the bootstrap # estimator, we recommend running first the analysis with option varest = "none" # which is faster but which underestimates the variance. And then use these values # as initial values when running the model with varest = "paramBoot" to obtain # a valid variance of the parameters. XextNone <- externVar(PrimMod2, classmb = ~X1 + X2 + X3 + X4, subject = "ID", data = data_lcmm, varest = "none", method = "twoStageJoint") XextBoot <- externVar(PrimMod2, classmb = ~X1 + X2 + X3 + X4, subject = "ID", data = data_lcmm, varest = "paramBoot", method = "twoStageJoint", B = XextNone$best) summary(XextBoot) ###### Example 2: Relationship between a latent class structure and # # external outcome (repeatedly measured over time) ###### # estimation of the secondary linear mixed model with total variance # computed with the Hessian YextHess = externVar(PrimMod2, #primary model fixed = Ydep2 ~ Time*X1, #secondary model random = ~Time, #secondary model mixture = ~Time, #secondary model subject="ID", data=data_lcmm, method = "twoStageJoint") # estimation of a secondary linear mixed model with total variance # computed with parametric Bootstrap (much longer). When using the bootstrap # estimator, we recommend running first the analysis with option varest = "none" # which is faster but which underestimates the variance. And then use these values # as initial values when running the model with varest = "paramBoot" to obtain # a valid variance of the parameters. YextNone = externVar(PrimMod2, #primary model fixed = Ydep2 ~ Time*X1, #secondary model random = ~Time, #secondary model mixture = ~Time, #secondary model subject="ID", data=data_lcmm, varest = "none", method = "twoStageJoint") YextBoot = externVar(PrimMod2, #primary model fixed = Ydep2 ~ Time*X1, #secondary model random = ~Time, #secondary model mixture = ~Time, #secondary model subject="ID", data=data_lcmm, method = "twoStageJoint", B = YextNone$best, varest= "paramBoot") summary(YextBoot) ###### Example 3: Relationship between a latent class structure and # # external outcome (survival) ###### # estimation of the secondary survival model with total variance # computed with the Hessian YextHess = externVar(PrimMod2, #primary model survival = Surv(Tevent,Event)~ X1+mixture(X2), #secondary model hazard="3-quant-splines", #secondary model hazardtype="PH", #secondary model subject="ID", data=data_lcmm, method = "twoStageJoint") summary(YextHess) # estimation of a secondary survival model with total variance # computed with parametric Bootstrap (much longer). When using the bootstrap # estimator, we recommend running first the analysis with option varest = "none" # which is faster but which underestimates the variance. And then use these values # as initial values when running the model with varest = "paramBoot" to obtain # a valid variance of the parameters. YextNone = externVar(PrimMod2, #primary model survival = Surv(Tevent,Event)~ X1+mixture(X2), #secondary model hazard="3-quant-splines", #secondary model hazardtype="PH", #secondary model subject="ID", data=data_lcmm, varest = "none", method = "twoStageJoint") YextBoot = externVar(PrimMod2, #primary model survival = Surv(Tevent,Event)~ X1+mixture(X2), #secondary model hazard="3-quant-splines", #secondary model hazardtype="PH", #secondary model subject="ID", data=data_lcmm, method = "twoStageJoint", B = YextNone$best, varest= "paramBoot") summary(YextBoot) ## End(Not run)## Not run: ###### Estimation of the primary latent class model ###### set.seed(1234) PrimMod <- hlme(Ydep1~Time,random=~Time,subject='ID',ng=1,data=data_lcmm) PrimMod2 <- hlme(Ydep1~Time,mixture=~Time,random=~Time,subject='ID', ng=2,data=data_lcmm,B=random(PrimMod)) ###### Example 1: Relationship between a latent class structure and # # external class predictors ###### # estimation of the secondary multinomial logistic model with total variance # computed with the Hessian XextHess <- externVar(PrimMod2, classmb = ~X1 + X2 + X3 + X4, subject = "ID", data = data_lcmm, method = "twoStageJoint") summary(XextHess) # estimation of a secondary multinomial logistic model with total variance # computed with parametric Bootstrap (much longer). When using the bootstrap # estimator, we recommend running first the analysis with option varest = "none" # which is faster but which underestimates the variance. And then use these values # as initial values when running the model with varest = "paramBoot" to obtain # a valid variance of the parameters. XextNone <- externVar(PrimMod2, classmb = ~X1 + X2 + X3 + X4, subject = "ID", data = data_lcmm, varest = "none", method = "twoStageJoint") XextBoot <- externVar(PrimMod2, classmb = ~X1 + X2 + X3 + X4, subject = "ID", data = data_lcmm, varest = "paramBoot", method = "twoStageJoint", B = XextNone$best) summary(XextBoot) ###### Example 2: Relationship between a latent class structure and # # external outcome (repeatedly measured over time) ###### # estimation of the secondary linear mixed model with total variance # computed with the Hessian YextHess = externVar(PrimMod2, #primary model fixed = Ydep2 ~ Time*X1, #secondary model random = ~Time, #secondary model mixture = ~Time, #secondary model subject="ID", data=data_lcmm, method = "twoStageJoint") # estimation of a secondary linear mixed model with total variance # computed with parametric Bootstrap (much longer). When using the bootstrap # estimator, we recommend running first the analysis with option varest = "none" # which is faster but which underestimates the variance. And then use these values # as initial values when running the model with varest = "paramBoot" to obtain # a valid variance of the parameters. YextNone = externVar(PrimMod2, #primary model fixed = Ydep2 ~ Time*X1, #secondary model random = ~Time, #secondary model mixture = ~Time, #secondary model subject="ID", data=data_lcmm, varest = "none", method = "twoStageJoint") YextBoot = externVar(PrimMod2, #primary model fixed = Ydep2 ~ Time*X1, #secondary model random = ~Time, #secondary model mixture = ~Time, #secondary model subject="ID", data=data_lcmm, method = "twoStageJoint", B = YextNone$best, varest= "paramBoot") summary(YextBoot) ###### Example 3: Relationship between a latent class structure and # # external outcome (survival) ###### # estimation of the secondary survival model with total variance # computed with the Hessian YextHess = externVar(PrimMod2, #primary model survival = Surv(Tevent,Event)~ X1+mixture(X2), #secondary model hazard="3-quant-splines", #secondary model hazardtype="PH", #secondary model subject="ID", data=data_lcmm, method = "twoStageJoint") summary(YextHess) # estimation of a secondary survival model with total variance # computed with parametric Bootstrap (much longer). When using the bootstrap # estimator, we recommend running first the analysis with option varest = "none" # which is faster but which underestimates the variance. And then use these values # as initial values when running the model with varest = "paramBoot" to obtain # a valid variance of the parameters. YextNone = externVar(PrimMod2, #primary model survival = Surv(Tevent,Event)~ X1+mixture(X2), #secondary model hazard="3-quant-splines", #secondary model hazardtype="PH", #secondary model subject="ID", data=data_lcmm, varest = "none", method = "twoStageJoint") YextBoot = externVar(PrimMod2, #primary model survival = Surv(Tevent,Event)~ X1+mixture(X2), #secondary model hazard="3-quant-splines", #secondary model hazardtype="PH", #secondary model subject="ID", data=data_lcmm, method = "twoStageJoint", B = YextNone$best, varest= "paramBoot") summary(YextBoot) ## End(Not run)
lcmm, Jointlcmm or multlcmm objectsThe function computes the marginal predictions of the longitudinal
outcome(s) in their natural scale on the individual data used for the
estimation from lcmm, Jointlcmm or multlcmm objects.
fitY(x)fitY(x)
x |
an object inheriting from classes |
For lcmm and Jointlcmm objects, returns a matrix with
ng+1 columns containing the subject identifier and the ng class-specific
marginal predicted values.
For multlcmm objects, returns a matrix with ng+2 columns containing
the subject identifier, the outcome indicator and the ng class-specific
predicted values.
Cecile Proust-Lima, Viviane Philipps
This function provides an automatic grid search for latent class mixed
models estimated with hlme, lcmm, multlcmm and
Jointlcmm functions.
gridsearch(m, rep, maxiter, minit, cl = NULL)gridsearch(m, rep, maxiter, minit, cl = NULL)
m |
a call of |
rep |
the number of departures from random initial values |
maxiter |
the number of iterations in the optimization algorithm |
minit |
an object of class |
cl |
a cluster created by makeCluster from package parallel or an integer specifying the number of cores to use for parallel computation |
The function permits the estimation of a model from a grid of random initial values to reduce the odds of a convergence towards a local maximum.
The function was inspired by the emEM technique described in Biernacki et al. (2003). It consists in:
1. randomly generating rep sets of initial values for m from
the estimates of minit (this is done internally using option
B=random(minit) rep times)
2. running the optimization algorithm for the model specified in m
from the rep sets of initial values with a maximum number of
iterations of maxit each time.
3. retaining the estimates of the random initialization that provides the
best log-likelihood after maxiter iterations.
4. running the optimization algorithm from these estimates for the final estimation.
an object of class hlme, lcmm, multlcmm,
Jointlcmm or mpjlcmm corresponding to the call specified in m.
Cecile Proust-Lima and Viviane Philipps
Biernacki C, Celeux G, Govaert G (2003). Choosing Starting Values for the EM Algorithm for Getting the Highest Likelihood in Multivariate Gaussian Mixture models. Computational Statistics and Data Analysis, 41(3-4), 561-575.
## Not run: # initial model with ng=1 for the random initial values m1 <- hlme(Y ~ Time * X1, random =~ Time, subject = 'ID', ng = 1, data = data_hlme) # gridsearch with 10 iterations from 50 random departures m2d <- gridsearch(rep = 50, maxiter = 10, minit = m1, hlme(Y ~ Time * X1, mixture =~ Time, random =~ Time, classmb =~ X2 + X3, subject = 'ID', ng = 2, data = data_hlme)) ## End(Not run)## Not run: # initial model with ng=1 for the random initial values m1 <- hlme(Y ~ Time * X1, random =~ Time, subject = 'ID', ng = 1, data = data_hlme) # gridsearch with 10 iterations from 50 random departures m2d <- gridsearch(rep = 50, maxiter = 10, minit = m1, hlme(Y ~ Time * X1, mixture =~ Time, random =~ Time, classmb =~ X2 + X3, subject = 'ID', ng = 2, data = data_hlme)) ## End(Not run)
This function fits linear mixed models and latent class linear mixed models
(LCLMM) also known as growth mixture models or heterogeneous linear mixed
models. The LCLMM consists in assuming that the population is divided in a
finite number of latent classes. Each latent class is characterised by a
specific trajectory modelled by a class-specific linear mixed model. Both
the latent class membership and the trajectory can be explained according to
covariates. This function is limited to a mixture of Gaussian outcomes. For
other types of outcomes, please see function lcmm. For multivariate
longitudinal outcomes, please see multlcmm.
hlme( fixed, mixture, random, subject, classmb, ng = 1, idiag = FALSE, nwg = FALSE, cor = NULL, data, B, convB = 1e-04, convL = 1e-04, convG = 1e-04, prior, pprior = NULL, maxiter = 500, subset = NULL, na.action = 1, posfix = NULL, verbose = FALSE, returndata = FALSE, var.time = NULL, partialH = FALSE, nproc = 1, clustertype = NULL )hlme( fixed, mixture, random, subject, classmb, ng = 1, idiag = FALSE, nwg = FALSE, cor = NULL, data, B, convB = 1e-04, convL = 1e-04, convG = 1e-04, prior, pprior = NULL, maxiter = 500, subset = NULL, na.action = 1, posfix = NULL, verbose = FALSE, returndata = FALSE, var.time = NULL, partialH = FALSE, nproc = 1, clustertype = NULL )
fixed |
two-sided linear formula object for the fixed-effects in the
linear mixed model. The response outcome is on the left of |
mixture |
one-sided formula object for the class-specific fixed effects
in the linear mixed model (to specify only for a number of latent classes
greater than 1). Among the list of covariates included in |
random |
optional one-sided formula for the random-effects in the
linear mixed model. Covariates with a random-effect are separated by
|
subject |
name of the covariate representing the grouping structure specified with ”. |
classmb |
optional one-sided formula describing the covariates in the
class-membership multinomial logistic model. Covariates included are
separated by |
ng |
optional number of latent classes considered. If |
idiag |
optional logical for the structure of the variance-covariance
matrix of the random-effects. If |
nwg |
optional logical indicating if the variance-covariance of the
random-effects is class-specific. If |
cor |
optional brownian motion or autoregressive process modeling the correlation between the observations. "BM" or "AR" should be specified, followed by the time variable between brackets. By default, no correlation is added. |
data |
optional data frame containing the variables named in
|
B |
optional specification for the initial values for the parameters.
Three options are allowed: (1) a vector of initial values is entered (the
order in which the parameters are included is detailed in |
convB |
optional threshold for the convergence criterion based on the parameter stability. By default, convB=0.0001. |
convL |
optional threshold for the convergence criterion based on the log-likelihood stability. By default, convL=0.0001. |
convG |
optional threshold for the convergence criterion based on the derivatives. By default, convG=0.0001. |
prior |
optional name of a covariate containing a prior information about the latent class membership. The covariate should be an integer with values in 0,1,...,ng. Value 0 indicates no prior for the subject while a value in 1,...,ng indicates that the subject belongs to the corresponding latent class. |
pprior |
optional vector specifying the names of the covariates containing the prior probabilities to belong to each latent class. These probabilities should be between 0 and 1 and should sum up to 1 for each subject. |
maxiter |
optional maximum number of iterations for the Marquardt iterative algorithm. By default, maxiter=500. |
subset |
a specification of the rows to be used: defaults to all rows. This can be any valid indexing vector for the rows of data or if that is not supplied, a data frame made up of the variable used in formula. |
na.action |
Integer indicating how NAs are managed. The default is 1 for 'na.omit'. The alternative is 2 for 'na.fail'. Other options such as 'na.pass' or 'na.exclude' are not implemented in the current version. |
posfix |
Optional vector specifying the indices in vector B of the parameters that should not be estimated. Default to NULL, all parameters are estimated. |
verbose |
logical indicating if information about computation should be reported. Default to TRUE. |
returndata |
logical indicating if data used for computation should be returned. Default to FALSE, data are not returned. |
var.time |
optional character indicating the name of the time variable. |
partialH |
optional logical indicating if parameters can be dropped from the Hessian matrix to define convergence criteria. |
nproc |
the number cores for parallel computation. Default to 1 (sequential mode). |
clustertype |
optional character indicating the type of cluster for parallel computation. |
A. THE VECTOR OF PARAMETERS B
The parameters in the vector of initial values B or equivalently in
the vector of maximum likelihood estimates best are included in the
following order:
(1) ng-1 parameters are required for intercepts in the latent class
membership model, and when covariates are included in classmb, ng-1
paramaters should be entered for each covariate;
(2) for all covariates in fixed, one parameter is required if the
covariate is not in mixture, ng paramaters are required if the
covariate is also in mixture;
(3) the variance of each random-effect specified in random (including
the intercept) when idiag=TRUE, or the inferior triangular
variance-covariance matrix of all the random-effects when
idiag=FALSE;
(4) only when nwg=TRUE, ng-1 parameters are required for the ng-1
class-specific proportional coefficients in the variance covariance matrix
of the random-effects;
(5) when cor is specified, 1 parameter corresponding to the variance
of the Brownian motion should be entered with cor=BM and 2 parameters
corresponding to the correlation and the variance parameters of the
autoregressive process should be entered
(6) the standard error of the residual error.
B. CAUTIONS
Some caution should be made when using the program:
(1) As the log-likelihood of a latent class model can have multiple maxima,
a careful choice of the initial values is crucial for ensuring convergence
toward the global maximum. The program can be run without entering the
vector of initial values (see point 2). However, we recommend to
systematically enter initial values in B and try different sets of
initial values.
(2) The automatic choice of initial values we provide requires the
estimation of a preliminary linear mixed model. The user should be aware
that first, this preliminary analysis can take time for large datatsets and
second, that the generated initial values can be very not likely and even
may converge slowly to a local maximum. This is the reason why several
alternatives exist. The vector of initial values can be directly specified
in B the initial values can be generated (automatically or randomly)
from a model with ng=. Finally, function gridsearch performs
an automatic grid search.
(3) Convergence criteria are very strict as they are based on the derivatives of the log-likelihood in addition to the parameter stability and log-likelihood stability. In some cases, the program may not converge and reach the maximum number of iterations fixed at 100. In this case, the user should check that parameter estimates at the last iteration are not on the boundaries of the parameter space. If the parameters are on the boundaries of the parameter space, the identifiability of the model is critical. This may happen especially with splines parameters that may be too close to 0 (lower boundary) or classmb parameters that are too high or low (perfect classification). When identifiability of some parameters is suspected, the program can be run again from the former estimates by fixing the suspected parameters to their value with option posfix. This usually solves the problem. An alternative is to remove the parameters of the Beta of Splines link function from the inverse of the Hessian with option partialH. If not, the program should be run again with other initial values, with a higher maximum number of iterations or less strict convergence tolerances.
The list returned is:
ns |
number of grouping units in the dataset |
ng |
number of latent classes |
loglik |
log-likelihood of the model |
\
itembestvector of parameter estimates in the same order as
specified in B and detailed in section details
V |
if the model converged (conv=1 or 3), vector containing the upper triangle
matrix of variance-covariance estimates of |
gconv |
vector of convergence criteria: 1. on the parameters, 2. on the likelihood, 3. on the derivatives |
conv |
status of convergence: =1 if the convergence criteria were satisfied, =2 if the maximum number of iterations was reached, =3 if the convergence criteria were satisfied with a partial Hessian matrix, =4 or 5 if a problem occured during optimisation |
call |
the matched call |
niter |
number of Marquardt iterations |
N |
internal information used in related functions |
idiag |
internal information used in related functions |
pred |
table of individual predictions and residuals; it
includes marginal predictions (pred_m), marginal residuals (resid_m),
subject-specific predictions (pred_ss) and subject-specific residuals
(resid_ss) averaged over classes, the observation (obs) and finally the
class-specific marginal and subject-specific predictions (with the number of
the latent class: pred_m_1,pred_m_2,...,pred_ss_1,pred_ss_2,...). If |
pprob |
table of posterior classification and posterior individual class-membership probabilities |
Xnames |
list of covariates included in the model |
predRE |
table containing individual predictions of the random-effects : a column per random-effect, a line per subject |
cholesky |
vector containing the estimates of the Cholesky transformed parameters of the variance-covariance matrix of the random-effects |
data |
the original data set (if returndata is TRUE) |
Cecile Proust-Lima, Benoit Liquet and Viviane Philipps
Proust-Lima C, Philipps V, Liquet B (2017). Estimation of Extended Mixed Models Using Latent Classes and Latent Processes: The R Package lcmm. Journal of Statistical Software, 78(2), 1-56. doi:10.18637/jss.v078.i02
Verbeke G and Lesaffre E (1996). A linear mixed-effects model with heterogeneity in the random-effects population. Journal of the American Statistical Association 91, 217-21
Muthen B and Shedden K (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics 55, 463-9
Proust C and Jacqmin-Gadda H (2005). Estimation of linear mixed models with a mixture of distribution for the random-effects. Computer Methods Programs Biomedicine 78, 165-73
postprob, plot.hlme,
summary, predictY
##### Example of a latent class model estimated for a varying number # of latent classes: # The model includes a subject- (ID) and class-specific linear # trend (intercept and Time in fixed, random and mixture components) # and a common effect of X1 and its interaction with time over classes # (in fixed). # The variance of the random intercept and slope are assumed to be equal # over classes (nwg=F). # The covariate X3 predicts the class membership (in classmb). # # !CAUTION: initialization of mixed models with latent classes is # of most importance because of the problem of multimodality of the likelihood. # Calls m2a-m2d illustrate the different implementations for the # initial values. ### homogeneous linear mixed model (standard linear mixed model) ### with correlated random-effects m1<-hlme(Y~Time*X1,random=~Time,subject='ID',ng=1,data=data_hlme) summary(m1) ### latent class linear mixed model with 2 classes # a. automatic specification from G=1 model estimates: m2a<-hlme(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3,subject='ID', ng=2,data=data_hlme,B=m1) # b. vector of initial values provided by the user: m2b<-hlme(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3,subject='ID', ng=2,data=data_hlme,B=c(0.11,-0.74,-0.07,20.71, 29.39,-1,0.13,2.45,-0.29,4.5,0.36,0.79,0.97)) # c. random draws from G = 1 model estimates: m2c<-hlme(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3,subject='ID', ng=2,data=data_hlme,B=random(m1)) # d. gridsearch with 50 departures and 10 iterations of the algorithm # (see function gridsearch for details) ## Not run: m2d <- gridsearch(rep = 50, maxiter = 10, minit = m1, hlme(Y ~ Time * X1, mixture =~ Time, random =~ Time, classmb =~ X2 + X3, subject = 'ID', ng = 2, data = data_hlme)) ## End(Not run) # summary of the estimation process summarytable(m1, m2a, m2b, m2c) # summary of m2a summary(m2a) # posterior classification postprob(m2a) # plot of predicted trajectories using some newdata newdata<-data.frame(Time=seq(0,5,length=100), X1=rep(0,100),X2=rep(0,100),X3=rep(0,100)) plot(predictY(m2a,newdata,var.time="Time"),legend.loc="right",bty="l")##### Example of a latent class model estimated for a varying number # of latent classes: # The model includes a subject- (ID) and class-specific linear # trend (intercept and Time in fixed, random and mixture components) # and a common effect of X1 and its interaction with time over classes # (in fixed). # The variance of the random intercept and slope are assumed to be equal # over classes (nwg=F). # The covariate X3 predicts the class membership (in classmb). # # !CAUTION: initialization of mixed models with latent classes is # of most importance because of the problem of multimodality of the likelihood. # Calls m2a-m2d illustrate the different implementations for the # initial values. ### homogeneous linear mixed model (standard linear mixed model) ### with correlated random-effects m1<-hlme(Y~Time*X1,random=~Time,subject='ID',ng=1,data=data_hlme) summary(m1) ### latent class linear mixed model with 2 classes # a. automatic specification from G=1 model estimates: m2a<-hlme(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3,subject='ID', ng=2,data=data_hlme,B=m1) # b. vector of initial values provided by the user: m2b<-hlme(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3,subject='ID', ng=2,data=data_hlme,B=c(0.11,-0.74,-0.07,20.71, 29.39,-1,0.13,2.45,-0.29,4.5,0.36,0.79,0.97)) # c. random draws from G = 1 model estimates: m2c<-hlme(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3,subject='ID', ng=2,data=data_hlme,B=random(m1)) # d. gridsearch with 50 departures and 10 iterations of the algorithm # (see function gridsearch for details) ## Not run: m2d <- gridsearch(rep = 50, maxiter = 10, minit = m1, hlme(Y ~ Time * X1, mixture =~ Time, random =~ Time, classmb =~ X2 + X3, subject = 'ID', ng = 2, data = data_hlme)) ## End(Not run) # summary of the estimation process summarytable(m1, m2a, m2b, m2c) # summary of m2a summary(m2a) # posterior classification postprob(m2a) # plot of predicted trajectories using some newdata newdata<-data.frame(Time=seq(0,5,length=100), X1=rep(0,100),X2=rep(0,100),X3=rep(0,100)) plot(predictY(m2a,newdata,var.time="Time"),legend.loc="right",bty="l")
lcmm or multlcmm
object with ordinal outcomes.The function computes the conditional probability and information function of each level of each ordinal outcome and the information function at the item level. Confidence bands (and median) can be computed by a Monte Carlo approximation.
ItemInfo( x, lprocess, condRE_Y = FALSE, nsim = 200, draws = FALSE, ndraws = 2000, ... )ItemInfo( x, lprocess, condRE_Y = FALSE, nsim = 200, draws = FALSE, ndraws = 2000, ... )
x |
an object inheriting from class |
lprocess |
numeric vector containing the latent process values at which the predictions should be computed. |
condRE_Y |
for multlcmm objects only, logical indicating if the predictions are conditional to the outcome-specific random-effects or not. Default to FALSE= the predictions are marginal to these random effects. |
nsim |
number of points used in the numerical integration (Monte-Carlo) with splines or Beta link functions. nsim should be relatively important (nsim=200 by default). |
draws |
optional boolean specifying whether median and confidence bands of the predicted values should be computed (TRUE). A Monte Carlo approximation of the posterior distribution of the predicted values is computed and the median, 2.5% and 97.5% percentiles are given. Otherwise, the predicted values are computed at the point estimate. By default, draws=FALSE. |
ndraws |
if draws=TRUE, ndraws specifies the number of draws that should be generated to approximate the posterior distribution of the predicted values. By default, ndraws=2000. |
... |
further arguments to be passed to or from other methods. They are ignored in this function. |
An object of class ItemInfo with values :
- ItemInfo:
If draws=FALSE, returns a matrix with 3 columns: the first column indicates the
name of the outcome, the second indicates the latent process value and the last
is the computed Fisher information.
If draws=TRUE, returns a matrix with 5 columns: the name of the outcome, the
latent process value and the 50%, 2.5% and 97.5% percentiles of the approximated
posterior distribution of information.
- LevelInfo:
If draws=FALSE, returns a matrix with 5 columns: the first column indicates the
name of the outcome, the second indicates the outcome's level, the third indicates the
latent process value and the two last contain the probability and Fisher information.
If draws=TRUE, returns a matrix with 5 columns: the name of the outcome,
the outcome's level, the latent process value and the 50%, 2.5% and 97.5%
percentiles of the approximated posterior distribution of the probability and information.
- object: the model from which the computations are done.
- IC: indicator specifying if confidence intervals are computed.
Cecile Proust-Lima, Viviane Philipps
## Not run: ## This is a toy example to illustrate the information functions. ## The binary outcomes are arbitrarily created, please do not ## consider them as relevent indicators. data_lcmm$Yord1 <- as.numeric(data_lcmm$Ydep1>10) data_lcmm$Yord2 <- as.numeric(data_lcmm$Ydep2>25) m <- multlcmm(Yord1+Yord2~Time+I(Time^2),random=~Time,subject='ID',ng=1, data=data_lcmm,link="thresholds") info <- ItemInfo(m,lprocess=seq(-4,4,length.out=100),draws=TRUE) plot(info) par(mfrow=c(1,2)) plot(info, which="LevelInfo", outcome="Yord1") plot(info, which="LevelInfo", outcome="Yord2") plot(info, which="LevelProb", outcome="Yord1") plot(info, which="LevelProb", outcome="Yord2") ## End(Not run)## Not run: ## This is a toy example to illustrate the information functions. ## The binary outcomes are arbitrarily created, please do not ## consider them as relevent indicators. data_lcmm$Yord1 <- as.numeric(data_lcmm$Ydep1>10) data_lcmm$Yord2 <- as.numeric(data_lcmm$Ydep2>25) m <- multlcmm(Yord1+Yord2~Time+I(Time^2),random=~Time,subject='ID',ng=1, data=data_lcmm,link="thresholds") info <- ItemInfo(m,lprocess=seq(-4,4,length.out=100),draws=TRUE) plot(info) par(mfrow=c(1,2)) plot(info, which="LevelInfo", outcome="Yord1") plot(info, which="LevelInfo", outcome="Yord2") plot(info, which="LevelProb", outcome="Yord1") plot(info, which="LevelProb", outcome="Yord2") ## End(Not run)
This function fits joint latent class mixed models for a longitudinal
outcome and a right-censored (possibly left-truncated) time-to-event. The
function handles competing risks and Gaussian or non Gaussian (curvilinear)
longitudinal outcomes. For curvilinear longitudinal outcomes, normalizing
continuous functions (splines or Beta CDF) can be specified as in
lcmm.
Jointlcmm( fixed, mixture, random, subject, classmb, ng = 1, idiag = FALSE, nwg = FALSE, survival, hazard = "Weibull", hazardtype = "Specific", hazardnodes = NULL, hazardrange = NULL, TimeDepVar = NULL, link = NULL, intnodes = NULL, epsY = 0.5, range = NULL, cor = NULL, data, B, convB = 1e-04, convL = 1e-04, convG = 1e-04, maxiter = 100, nsim = 100, prior = NULL, pprior = NULL, logscale = FALSE, subset = NULL, na.action = 1, posfix = NULL, partialH = FALSE, verbose = FALSE, returndata = FALSE, var.time = NULL, nproc = 1, clustertype = NULL ) jlcmm( fixed, mixture, random, subject, classmb, ng = 1, idiag = FALSE, nwg = FALSE, survival, hazard = "Weibull", hazardtype = "Specific", hazardnodes = NULL, hazardrange = NULL, TimeDepVar = NULL, link = NULL, intnodes = NULL, epsY = 0.5, range = NULL, cor = NULL, data, B, convB = 1e-04, convL = 1e-04, convG = 1e-04, maxiter = 100, nsim = 100, prior = NULL, pprior = NULL, logscale = FALSE, subset = NULL, na.action = 1, posfix = NULL, partialH = FALSE, verbose = FALSE, returndata = FALSE, var.time = NULL, nproc = 1, clustertype = NULL )Jointlcmm( fixed, mixture, random, subject, classmb, ng = 1, idiag = FALSE, nwg = FALSE, survival, hazard = "Weibull", hazardtype = "Specific", hazardnodes = NULL, hazardrange = NULL, TimeDepVar = NULL, link = NULL, intnodes = NULL, epsY = 0.5, range = NULL, cor = NULL, data, B, convB = 1e-04, convL = 1e-04, convG = 1e-04, maxiter = 100, nsim = 100, prior = NULL, pprior = NULL, logscale = FALSE, subset = NULL, na.action = 1, posfix = NULL, partialH = FALSE, verbose = FALSE, returndata = FALSE, var.time = NULL, nproc = 1, clustertype = NULL ) jlcmm( fixed, mixture, random, subject, classmb, ng = 1, idiag = FALSE, nwg = FALSE, survival, hazard = "Weibull", hazardtype = "Specific", hazardnodes = NULL, hazardrange = NULL, TimeDepVar = NULL, link = NULL, intnodes = NULL, epsY = 0.5, range = NULL, cor = NULL, data, B, convB = 1e-04, convL = 1e-04, convG = 1e-04, maxiter = 100, nsim = 100, prior = NULL, pprior = NULL, logscale = FALSE, subset = NULL, na.action = 1, posfix = NULL, partialH = FALSE, verbose = FALSE, returndata = FALSE, var.time = NULL, nproc = 1, clustertype = NULL )
fixed |
two-sided linear formula object for the fixed-effects in the
linear mixed model. The response outcome is on the left of |
mixture |
one-sided formula object for the class-specific fixed effects
in the linear mixed model (to specify only for a number of latent classes
greater than 1). Among the list of covariates included in |
random |
optional one-sided formula for the random-effects in the
linear mixed model. Covariates with a random-effect are separated by
|
subject |
name of the covariate representing the grouping structure (called subject identifier) specified with ”. |
classmb |
optional one-sided formula describing the covariates in the
class-membership multinomial logistic model. Covariates included are
separated by |
ng |
optional number of latent classes considered. If |
idiag |
optional logical for the structure of the variance-covariance
matrix of the random-effects. If |
nwg |
optional logical indicating if the variance-covariance of the
random-effects is class-specific. If |
survival |
two-sided formula object. The left side of the formula
corresponds to a |
hazard |
optional family of hazard function assumed for the survival
model. By default, "Weibull" specifies a Weibull baseline risk function.
Other possibilities are "piecewise" for a piecewise constant risk function
or "splines" for a cubic M-splines baseline risk function. For these two
latter families, the number of nodes and the location of the nodes should be
specified as well, separated by |
hazardtype |
optional indicator for the type of baseline risk function when ng>1. By default "Specific" indicates a class-specific baseline risk function. Other possibilities are "PH" for a baseline risk function proportional in each latent class, and "Common" for a baseline risk function that is common over classes. In the presence of competing events, a vector of hazardtypes should be given. |
hazardnodes |
optional vector containing interior nodes if
|
hazardrange |
optional vector indicating the range of the survival times (that is the minimum and maximum). By default, the range is defined according to the minimum and maximum observed values of the survival times. The option should be used only for piecewise constant and Splines hazard functions. |
TimeDepVar |
optional vector containing an intermediate time corresponding to a change in the risk of event. This time-dependent covariate can only take the form of a time variable with the assumption that there is no effect on the risk before this time and a constant effect on the risk of event after this time (example: initiation of a treatment to account for). |
link |
optional family of link functions to estimate. By default,
"linear" option specifies a linear link function leading to a standard
linear mixed model (homogeneous or heterogeneous as estimated in
|
intnodes |
optional vector of interior nodes. This argument is only required for a I-splines link function with nodes entered manually. |
epsY |
optional definite positive real used to rescale the marker in (0,1) when the beta link function is used. By default, epsY=0.5. |
range |
optional vector indicating the range of the outcome (that is the minimum and maximum). By default, the range is defined according to the minimum and maximum observed values of the outcome. The option should be used only for Beta and Splines transformations. |
cor |
optional brownian motion or autoregressive process modeling the correlation between the observations. "BM" or "AR" should be specified, followed by the time variable between brackets. By default, no correlation is added. |
data |
optional data frame containing the variables named in
|
B |
optional specification for the initial values for the parameters.
Three options are allowed: (1) a vector of initial values is entered (the
order in which the parameters are included is detailed in |
convB |
optional threshold for the convergence criterion based on the parameter stability. By default, convB=0.0001. |
convL |
optional threshold for the convergence criterion based on the log-likelihood stability. By default, convL=0.0001. |
convG |
optional threshold for the convergence criterion based on the derivatives. By default, convG=0.0001. |
maxiter |
optional maximum number of iterations for the Marquardt iterative algorithm. By default, maxiter=150. |
nsim |
optional number of points for the predicted survival curves and predicted baseline risk curves. By default, nsim=100. |
prior |
optional name of a covariate containing a prior information about the latent class membership. The covariate should be an integer with values in 0,1,...,ng. Value O indicates no prior for the subject while a value in 1,...,ng indicates that the subject belongs to the corresponding latent class. |
pprior |
optional vector specifying the names of the covariates containing the prior probabilities to belong to each latent class. These probabilities should be between 0 and 1 and should sum up to 1 for each subject. |
logscale |
optional boolean indicating whether an exponential (logscale=TRUE) or a square (logscale=FALSE -by default) transformation is used to ensure positivity of parameters in the baseline risk functions. See details section |
subset |
a specification of the rows to be used: defaults to all rows. This can be any valid indexing vector for the rows of data or if that is not supplied, a data frame made up of the variable used in formula. |
na.action |
Integer indicating how NAs are managed. The default is 1 for 'na.omit'. The alternative is 2 for 'na.fail'. Other options such as 'na.pass' or 'na.exclude' are not implemented in the current version. |
posfix |
Optional vector specifying the indices in vector B of the parameters that should not be estimated. Default to NULL, all parameters are estimated. |
partialH |
optional logical for Piecewise and Splines baseline risk functions and Splines link functions only. Indicates whether the parameters of the baseline risk or link functions can be dropped from the Hessian matrix to define convergence criteria. |
verbose |
logical indicating if information about computation should be reported. Default to TRUE. |
returndata |
logical indicating if data used for computation should be returned. Default to FALSE, data are not returned. |
var.time |
optional character indicating the name of the time variable. |
nproc |
the number cores for parallel computation. Default to 1 (sequential mode). |
clustertype |
optional character indicating the type of cluster for parallel computation. |
A. BASELINE RISK FUNCTIONS
For the baseline risk functions, the following parameterizations were considered. Be careful, parametrisations changed in lcmm_V1.5:
1. With the "Weibull" function: 2 parameters are necessary w_1 and w_2 so that the baseline risk function a_0(t) = w_1^2*w_2^2*(w_1^2*t)^(w_2^2-1) if logscale=FALSE and a_0(t) = exp(w_1)*exp(w_2)(t)^(exp(w_2)-1) if logscale=TRUE.
2. with the "piecewise" step function and nz nodes (y_1,...y_nz), nz-1 parameters are necesssary p_1,...p_nz-1 so that the baseline risk function a_0(t) = p_j^2 for y_j < t =< y_j+1 if logscale=FALSE and a_0(t) = exp(p_j) for y_j < t =< y_j+1 if logscale=TRUE.
3. with the "splines" function and nz nodes (y_1,...y_nz), nz+2 parameters are necessary s_1,...s_nz+2 so that the baseline risk function a_0(t) = sum_j s_j^2 M_j(t) if logscale=FALSE and a_0(t) = sum_j exp(s_j) M_j(t) if logscale=TRUE where M_j is the basis of cubic M-splines.
Two parametrizations of the baseline risk function are proposed (logscale=TRUE or FALSE) because in some cases, especially when the instantaneous risks are very close to 0, some convergence problems may appear with one parameterization or the other. As a consequence, we recommend to try the alternative parameterization (changing logscale option) when a joint latent class model does not converge (maximum number of iterations reached) where as convergence criteria based on the parameters and likelihood are small.
B. THE VECTOR OF PARAMETERS B
The parameters in the vector of initial values B or in the vector of
maximum likelihood estimates best are included in the following
order: (1) ng-1 parameters are required for intercepts in the latent class
membership model, and if covariates are included in classmb, ng-1
parameters should be entered for each one; (2) parameters for the baseline
risk function: 2 parameters for each Weibull, nz-1 for each piecewise
constant risk and nz+2 for each splines risk; this number should be
multiplied by ng if specific hazard is specified; otherwise, ng-1 additional
proportional effects are expected if PH hazard is specified; otherwise
nothing is added if common hazard is specified. In the presence of competing
events, the number of parameters should be adapted to the number of causes
of event; (3) for all covariates in survival, ng parameters are
required if the covariate is inside a mixture(), otherwise 1
parameter is required. Covariates parameters should be included in the same
order as in survival. In the presence of cause-specific effects, the
number of parameters should be multiplied by the number of causes; (4) for
all covariates in fixed, one parameter is required if the covariate
is not in mixture, ng parameters are required if the covariate is
also in mixture. Parameters should be included in the same order as
in fixed; (5) the variance of each random-effect specified in
random (including the intercept) if idiag=TRUE and the
inferior triangular variance-covariance matrix of all the random-effects if
idiag=FALSE; (6) only if nwg=TRUE, ng-1 parameters for
class-specific proportional coefficients for the variance covariance matrix
of the random-effects; (7) the variance of the residual error.
C. CAUTION
Some caution should be made when using the program:
(1) As the log-likelihood of a latent class model can have multiple maxima,
a careful choice of the initial values is crucial for ensuring convergence
toward the global maximum. The program can be run without entering the
vector of initial values (see point 2). However, we recommend to
systematically enter initial values in B and try different sets of
initial values.
(2) The automatic choice of initial values that we provide requires the
estimation of a preliminary linear mixed model. The user should be aware
that first, this preliminary analysis can take time for large datatsets and
second, that the generated initial values can be very not likely and even
may converge slowly to a local maximum. This is a reason why several
alternatives exist. The vector of initial values can be directly specified
in B the initial values can be generated (automatically or randomly)
from a model with ng=. Finally, function gridsearch performs
an automatic grid search.
(3) Convergence criteria are very strict as they are based on derivatives of the log-likelihood in addition to the parameter and log-likelihood stability. In some cases, the program may not converge and reach the maximum number of iterations fixed at 150. In this case, the user should check that parameter estimates at the last iteration are not on the boundaries of the parameter space. If the parameters are on the boundaries of the parameter space, the identifiability of the model is critical. This may happen especially when baseline risk functions involve splines (value close to the lower boundary - 0 with logscale=F -infinity with logscale=F) or classmb parameters that are too high or low (perfect classification) or linkfunction parameters. When identifiability of some parameters is suspected, the program can be run again from the former estimates by fixing the suspected parameters to their value with option posfix. This usually solves the problem. An alternative is to remove the parameters of the Beta of Splines link function from the inverse of the Hessian with option partialH. If not, the program should be run again with other initial values. Some problems of convergence may happen when the instantaneous risks of event are very low and "piecewise" or "splines" baseline risk functions are specified. In this case, changing the parameterization of the baseline risk functions with option logscale is recommended (see paragraph A for details).
The list returned is:
loglik |
log-likelihood of the model |
best |
vector of parameter estimates in the same order as specified in
|
V |
if the model converged (conv=1 or 3), vector containing
the upper triangle matrix of variance-covariance estimates of |
gconv |
vector of convergence criteria: 1. on the parameters, 2. on the likelihood, 3. on the derivatives |
conv |
status of convergence: =1 if the convergence criteria were satisfied, =2 if the maximum number of iterations was reached, =4 or 5 if a problem occured during optimisation |
call |
the matched call |
niter |
number of Marquardt iterations |
pred |
table of
individual predictions and residuals; it includes marginal predictions
(pred_m), marginal residuals (resid_m), subject-specific predictions
(pred_ss) and subject-specific residuals (resid_ss) averaged over classes,
the observation (obs) and finally the class-specific marginal and
subject-specific predictions (with the number of the latent class:
pred_m_1,pred_m_2,...,pred_ss_1,pred_ss_2,...). If |
pprob |
table of posterior classification and posterior individual class-membership probabilities based on the longitudinal data and the time-to-event data |
pprobY |
table of posterior classification and posterior individual class-membership probabilities based only on the longitudinal data |
predRE |
table containing individual predictions of the random-effects: a column per random-effect, a line per subject |
cholesky |
vector containing the estimates of the Cholesky transformed parameters of the variance-covariance matrix of the random-effects |
scoretest |
Statistic of the Score Test for the conditional independence assumption of the longitudinal and survival data given the latent class structure. Under the null hypothesis, the statistics is a Chi-square with p degrees of freedom where p indicates the number of random-effects in the longitudinal mixed model. See Jacqmin-Gadda and Proust-Lima (2009) for more details. |
predSurv |
table of predictions giving for the window of times to event (called "time"), the predicted baseline risk function in each latent class (called "RiskFct") and the predicted cumulative baseline risk function in each latent class (called "CumRiskFct"). |
hazard |
internal information about the hazard specification used in related functions |
data |
the original data set (if returndata is TRUE) |
Cecile Proust Lima, Amadou Diakite and Viviane Philipps
Proust-Lima C, Philipps V, Liquet B (2017). Estimation of Extended Mixed Models Using Latent Classes and Latent Processes: The R Package lcmm. Journal of Statistical Software, 78(2), 1-56. doi:10.18637/jss.v078.i02
Lin, H., Turnbull, B. W., McCulloch, C. E. and Slate, E. H. (2002). Latent class models for joint analysis of longitudinal biomarker and event process data: application to longitudinal prostate-specific antigen readings and prostate cancer. Journal of the American Statistical Association 97, 53-65.
Proust-Lima, C. and Taylor, J. (2009). Development and validation of a dynamic prognostic tool for prostate cancer recurrence using repeated measures of post-treatment PSA: a joint modelling approach. Biostatistics 10, 535-49.
Jacqmin-Gadda, H. and Proust-Lima, C. (2010). Score test for conditional independence between longitudinal outcome and time-to-event given the classes in the joint latent class model. Biometrics 66(1), 11-9
Proust-Lima, Sene, Taylor and Jacqmin-Gadda (2014). Joint latent class models of longitudinal and time-to-event data: a review. Statistical Methods in Medical Research 23, 74-90.
postprob, plot.Jointlcmm,
plot.predict, epoce
#### Example of a joint latent class model estimated for a varying number # of latent classes: # The linear mixed model includes a subject- (ID) and class-specific # linear trend (intercept and Time in fixed, random and mixture components) # and a common effect of X1 and its interaction with time over classes # (in fixed). # The variance of the random intercept and slopes are assumed to be equal # over classes (nwg=F). # The covariate X3 predicts the class membership (in classmb). # The baseline hazard function is modelled with cubic M-splines -3 # nodes at the quantiles- (in hazard) and a proportional hazard over # classes is assumed (in hazardtype). Covariates X1 and X2 predict the # risk of event (in survival) with a common effect over classes for X1 # and a class-specific effect of X2. # !CAUTION: for illustration, only default initial values where used but # other sets of initial values should be tried to ensure convergence # towards the global maximum. ## Not run: #### estimation with 1 latent class (ng=1): independent models for the # longitudinal outcome and the time of event m1 <- Jointlcmm(fixed= Ydep1~X1*Time,random=~Time,subject='ID' ,survival = Surv(Tevent,Event)~ X1+X2 ,hazard="3-quant-splines" ,hazardtype="PH",ng=1,data=data_lcmm) summary(m1) #Goodness-of-fit statistics for m1: # maximum log-likelihood: -3944.77 ; AIC: 7919.54 ; BIC: 7975.09 ## End(Not run) #### estimation with 2 latent classes (ng=2) m2 <- Jointlcmm(fixed= Ydep1~Time*X1,mixture=~Time,random=~Time, classmb=~X3,subject='ID',survival = Surv(Tevent,Event)~X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",ng=2,data=data_lcmm, B=c(0.64,-0.62,0,0,0.52,0.81,0.41,0.78,0.1,0.77,-0.05,10.43,11.3,-2.6, -0.52,1.41,-0.05,0.91,0.05,0.21,1.5)) summary(m2) #Goodness-of-fit statistics for m2: # maximum log-likelihood: -3921.27; AIC: 7884.54; BIC: 7962.32 ## Not run: #### estimation with 3 latent classes (ng=3) m3 <- Jointlcmm(fixed= Ydep1~Time*X1,mixture=~Time,random=~Time, classmb=~X3,subject='ID',survival = Surv(Tevent,Event)~ X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",ng=3,data=data_lcmm, B=c(0.77,0.4,-0.82,-0.27,0,0,0,0.3,0.62,2.62,5.31,-0.03,1.36,0.82, -13.5,10.17,10.24,11.51,-2.62,-0.43,-0.61,1.47,-0.04,0.85,0.04,0.26,1.5)) summary(m3) #Goodness-of-fit statistics for m3: # maximum log-likelihood: -3890.26 ; AIC: 7834.53; BIC: 7934.53 #### estimation with 4 latent classes (ng=4) m4 <- Jointlcmm(fixed= Ydep1~Time*X1,mixture=~Time,random=~Time, classmb=~X3,subject='ID',survival = Surv(Tevent,Event)~ X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",ng=4,data=data_lcmm, B=c(0.54,-0.42,0.36,-0.94,-0.64,-0.28,0,0,0,0.34,0.59,2.6,2.56,5.26, -0.1,1.27,1.34,0.7,-5.72,10.54,9.02,10.2,11.58,-2.47,-2.78,-0.28,-0.57, 1.48,-0.06,0.61,-0.07,0.31,1.5)) summary(m4) #Goodness-of-fit statistics for m4: # maximum log-likelihood: -3886.93 ; AIC: 7839.86; BIC: 7962.09 ##### The model with 3 latent classes is retained according to the BIC ##### and the conditional independence assumption is not rejected at ##### the 5% level. # posterior classification plot(m3,which="postprob") # Class-specific predicted baseline risk & survival functions in the # 3-class model retained (for the reference value of the covariates) plot(m3,which="baselinerisk",bty="l") plot(m3,which="baselinerisk",ylim=c(0,5),bty="l") plot(m3,which="survival",bty="l") # class-specific predicted trajectories in the 3-class model retained # (with characteristics of subject ID=193) data <- data_lcmm[data_lcmm$ID==193,] plot(predictY(m3,var.time="Time",newdata=data,bty="l") # predictive accuracy of the model evaluated with EPOCE vect <- 1:15 cvpl <- epoce(m3,var.time="Time",pred.times=vect) summary(cvpl) plot(cvpl,bty="l",ylim=c(0,2)) ############## end of example ############## ## End(Not run)#### Example of a joint latent class model estimated for a varying number # of latent classes: # The linear mixed model includes a subject- (ID) and class-specific # linear trend (intercept and Time in fixed, random and mixture components) # and a common effect of X1 and its interaction with time over classes # (in fixed). # The variance of the random intercept and slopes are assumed to be equal # over classes (nwg=F). # The covariate X3 predicts the class membership (in classmb). # The baseline hazard function is modelled with cubic M-splines -3 # nodes at the quantiles- (in hazard) and a proportional hazard over # classes is assumed (in hazardtype). Covariates X1 and X2 predict the # risk of event (in survival) with a common effect over classes for X1 # and a class-specific effect of X2. # !CAUTION: for illustration, only default initial values where used but # other sets of initial values should be tried to ensure convergence # towards the global maximum. ## Not run: #### estimation with 1 latent class (ng=1): independent models for the # longitudinal outcome and the time of event m1 <- Jointlcmm(fixed= Ydep1~X1*Time,random=~Time,subject='ID' ,survival = Surv(Tevent,Event)~ X1+X2 ,hazard="3-quant-splines" ,hazardtype="PH",ng=1,data=data_lcmm) summary(m1) #Goodness-of-fit statistics for m1: # maximum log-likelihood: -3944.77 ; AIC: 7919.54 ; BIC: 7975.09 ## End(Not run) #### estimation with 2 latent classes (ng=2) m2 <- Jointlcmm(fixed= Ydep1~Time*X1,mixture=~Time,random=~Time, classmb=~X3,subject='ID',survival = Surv(Tevent,Event)~X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",ng=2,data=data_lcmm, B=c(0.64,-0.62,0,0,0.52,0.81,0.41,0.78,0.1,0.77,-0.05,10.43,11.3,-2.6, -0.52,1.41,-0.05,0.91,0.05,0.21,1.5)) summary(m2) #Goodness-of-fit statistics for m2: # maximum log-likelihood: -3921.27; AIC: 7884.54; BIC: 7962.32 ## Not run: #### estimation with 3 latent classes (ng=3) m3 <- Jointlcmm(fixed= Ydep1~Time*X1,mixture=~Time,random=~Time, classmb=~X3,subject='ID',survival = Surv(Tevent,Event)~ X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",ng=3,data=data_lcmm, B=c(0.77,0.4,-0.82,-0.27,0,0,0,0.3,0.62,2.62,5.31,-0.03,1.36,0.82, -13.5,10.17,10.24,11.51,-2.62,-0.43,-0.61,1.47,-0.04,0.85,0.04,0.26,1.5)) summary(m3) #Goodness-of-fit statistics for m3: # maximum log-likelihood: -3890.26 ; AIC: 7834.53; BIC: 7934.53 #### estimation with 4 latent classes (ng=4) m4 <- Jointlcmm(fixed= Ydep1~Time*X1,mixture=~Time,random=~Time, classmb=~X3,subject='ID',survival = Surv(Tevent,Event)~ X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",ng=4,data=data_lcmm, B=c(0.54,-0.42,0.36,-0.94,-0.64,-0.28,0,0,0,0.34,0.59,2.6,2.56,5.26, -0.1,1.27,1.34,0.7,-5.72,10.54,9.02,10.2,11.58,-2.47,-2.78,-0.28,-0.57, 1.48,-0.06,0.61,-0.07,0.31,1.5)) summary(m4) #Goodness-of-fit statistics for m4: # maximum log-likelihood: -3886.93 ; AIC: 7839.86; BIC: 7962.09 ##### The model with 3 latent classes is retained according to the BIC ##### and the conditional independence assumption is not rejected at ##### the 5% level. # posterior classification plot(m3,which="postprob") # Class-specific predicted baseline risk & survival functions in the # 3-class model retained (for the reference value of the covariates) plot(m3,which="baselinerisk",bty="l") plot(m3,which="baselinerisk",ylim=c(0,5),bty="l") plot(m3,which="survival",bty="l") # class-specific predicted trajectories in the 3-class model retained # (with characteristics of subject ID=193) data <- data_lcmm[data_lcmm$ID==193,] plot(predictY(m3,var.time="Time",newdata=data,bty="l") # predictive accuracy of the model evaluated with EPOCE vect <- 1:15 cvpl <- epoce(m3,var.time="Time",pred.times=vect) summary(cvpl) plot(cvpl,bty="l",ylim=c(0,2)) ############## end of example ############## ## End(Not run)
This function fits mixed models and latent class mixed models for different
types of outcomes. It handles continuous longitudinal outcomes (Gaussian or
non-Gaussian) as well as bounded quantitative, discrete and ordinal
longitudinal outcomes. The different types of outcomes are taken into
account using parameterized nonlinear link functions between the observed
outcome and the underlying latent process of interest it measures. At the
latent process level, the model estimates a standard linear mixed model or a
latent class linear mixed model when heterogeneity in the population is
investigated (in the same way as in function hlme). It should be
noted that the program also works when no random-effect is included.
Parameters of the nonlinear link function and of the latent process mixed
model are estimated simultaneously using a maximum likelihood method.
lcmm( fixed, mixture, random, subject, classmb, ng = 1, idiag = FALSE, nwg = FALSE, link = "linear", intnodes = NULL, epsY = 0.5, cor = NULL, data, B, convB = 1e-04, convL = 1e-04, convG = 1e-04, maxiter = 100, nsim = 100, prior, pprior = NULL, range = NULL, subset = NULL, na.action = 1, posfix = NULL, partialH = FALSE, verbose = FALSE, returndata = FALSE, var.time = NULL, nproc = 1, clustertype = NULL, computeDiscrete = NULL )lcmm( fixed, mixture, random, subject, classmb, ng = 1, idiag = FALSE, nwg = FALSE, link = "linear", intnodes = NULL, epsY = 0.5, cor = NULL, data, B, convB = 1e-04, convL = 1e-04, convG = 1e-04, maxiter = 100, nsim = 100, prior, pprior = NULL, range = NULL, subset = NULL, na.action = 1, posfix = NULL, partialH = FALSE, verbose = FALSE, returndata = FALSE, var.time = NULL, nproc = 1, clustertype = NULL, computeDiscrete = NULL )
fixed |
a two-sided linear formula object for specifying the
fixed-effects in the linear mixed model at the latent process level. The
response outcome is on the left of |
mixture |
a one-sided formula object for the class-specific fixed
effects in the latent process mixed model (to specify only for a number of
latent classes greater than 1). Among the list of covariates included in
|
random |
an optional one-sided formula for the random-effects in the
latent process mixed model. Covariates with a random-effect are separated by
|
subject |
name of the covariate representing the grouping structure. |
classmb |
an optional one-sided formula describing the covariates in
the class-membership multinomial logistic model. Covariates included are
separated by |
ng |
number of latent classes considered. If |
idiag |
optional logical for the variance-covariance structure of the
random-effects. If |
nwg |
optional logical of class-specific variance-covariance of the
random-effects. If |
link |
optional family of link functions to estimate. By default,
"linear" option specifies a linear link function leading to a standard
linear mixed model (homogeneous or heterogeneous as estimated in
|
intnodes |
optional vector of interior nodes. This argument is only required for a I-splines link function with nodes entered manually. |
epsY |
optional definite positive real used to rescale the marker in (0,1) when the beta link function is used. By default, epsY=0.5. |
cor |
optional brownian motion or autoregressive process modeling the correlation between the observations. "BM" or "AR" should be specified, followed by the time variable between brackets. By default, no correlation is added. |
data |
optional data frame containing the variables named in
|
B |
optional specification for the initial values for the parameters.
Three options are allowed: (1) a vector of initial values is entered (the
order in which the parameters are included is detailed in |
convB |
optional threshold for the convergence criterion based on the parameter stability. By default, convB=0.0001. |
convL |
optional threshold for the convergence criterion based on the log-likelihood stability. By default, convL=0.0001. |
convG |
optional threshold for the convergence criterion based on the derivatives. By default, convG=0.0001. |
maxiter |
optional maximum number of iterations for the Marquardt iterative algorithm. By default, maxiter=100. |
nsim |
number of points used to plot the estimated link function. By default, nsim=100. |
prior |
name of the covariate containing the prior on the latent class membership. The covariate should be an integer with values in 0,1,...,ng. When there is no prior, the value should be 0. When there is a prior for the subject, the value should be the number of the latent class (in 1,...,ng). |
pprior |
optional vector specifying the names of the covariates containing the prior probabilities to belong to each latent class. These probabilities should be between 0 and 1 and should sum up to 1 for each subject. |
range |
optional vector indicating the range of the outcome (that is the minimum and maximum). By default, the range is defined according to the minimum and maximum observed values of the outcome. The option should be used only for Beta and Splines transformations. |
subset |
optional vector giving the subset of observations in
|
na.action |
Integer indicating how NAs are managed. The default is 1 for 'na.omit'. The alternative is 2 for 'na.fail'. Other options such as 'na.pass' or 'na.exclude' are not implemented in the current version. |
posfix |
Optional vector specifying the indices in vector B of the parameters that should not be estimated. Default to NULL, all parameters are estimated. |
partialH |
optional logical for Splines link functions only. Indicates whether the parameters of the link functions can be dropped from the Hessian matrix to define convergence criteria. |
verbose |
logical indicating if information about computation should be reported. Default to TRUE. |
returndata |
logical indicating if data used for computation should be returned. Default to FALSE, data are not returned. |
var.time |
optional character indicating the name of the time variable. |
nproc |
the number cores for parallel computation. Default to 1 (sequential mode). |
clustertype |
optional character indicating the type of cluster for parallel computation. |
computeDiscrete |
optional logical indicating if a dscrete likelihood and UACV should be computed. By default, if the outcome only consists of integers computeDiscrete=TRUE. |
A. THE PARAMETERIZED LINK FUNCTIONS
lcmm function estimates mixed models and latent class mixed models
for different types of outcomes by assuming a parameterized link function
for linking the outcome Y(t) with the underlying latent process L(t) it
measures. To fix the latent process dimension, we chose to constrain the
(first) intercept of the latent class mixed model at the latent process
level at 0 and the standard error of the gaussian error of measurement at 1.
These two parameters are replaced by additional parameters in the
parameterized link function :
1. With the "linear" link function, 2 parameters are required that correspond directly to the intercept and the standard error: (Y - b1)/b2 = L(t).
2. With the "beta" link function, 4 parameters are required for the following transformation: [ h(Y(t)',b1,b2) - b3]/b4 where h is the Beta CDF with canonical parameters c1 and c2 that can be derived from b1 and b2 as c1=exp(b1)/[exp(b2)*(1+exp(b1))] and c2=1/[exp(b2)*(1+exp(b1))], and Y(t)' is the rescaled outcome i.e. Y(t)'= [ Y(t) - min(Y(t)) + epsY ] / [ max(Y(t)) - min(Y(t)) +2*epsY ].
3. With the "splines" link function, n+2 parameters are required for the following transformation b_1 + b_2*I_1(Y(t)) + ... + b_n+2 I_n+1(Y(t)), where I_1,...,I_n+1 is the basis of quadratic I-splines. To constraint the parameters to be positive, except for b_1, the program estimates b_k^* (for k=2,...,n+2) so that b_k=(b_k^*)^2.
4. With the "thresholds" link function for an ordinal outcome in levels 0,...,C. A maximumn of C parameters are required for the following transformation: Y(t)=c <=> b_c < L(t) <= b_c+1 with b_0 = - infinity and b_C+1=+infinity. The number of parameters is reduced if some levels do not have any information. For example, if a level c is not observed in the dataset, the corresponding threshold b_c+1 is constrained to be the same as the previous one b_c. The number of parameters in the link function is reduced by 1.
To constraint the parameters to be increasing, except for the first parameter b_1, the program estimates b_k^* (for k=2,...C) so that b_k=b_k-1+(b_k^*)^2.
Details of these parameterized link functions can be found in the referred papers.
B. THE VECTOR OF PARAMETERS B
The parameters in the vector of initial values B or in the vector of
maximum likelihood estimates best are included in the following
order: (1) ng-1 parameters are required for intercepts in the latent class
membership model, and if covariates are included in classmb, ng-1
paramaters should be entered for each one; (2) for all covariates in
fixed, one parameter is required if the covariate is not in
mixture, ng paramaters are required if the covariate is also in
mixture; When ng=1, the intercept is not estimated and no parameter
should be specified in B. When ng>1, the first intercept is not
estimated and only ng-1 parameters should be specified in B; (3) the
variance of each random-effect specified in random (including the
intercept) if idiag=TRUE and the inferior triangular
variance-covariance matrix of all the random-effects if idiag=FALSE;
(4) only if nwg=TRUE, ng-1 parameters for class-specific proportional
coefficients for the variance covariance matrix of the random-effects; (5)
In contrast with hlme, due to identifiability purposes, the standard error
of the Gaussian error is not estimated (fixed at 1), and should not be
specified in B; (6) The parameters of the link function: 2 for
"linear", 4 for "beta", n+2 for "splines" with n nodes and the number of
levels minus one for "thresholds".
C. CAUTIONS REGARDING THE USE OF THE PROGRAM
Some caution should be made when using the program. convergence criteria are very strict as they are based on derivatives of the log-likelihood in addition to the parameter and log-likelihood stability. In some cases, the program may not converge and reach the maximum number of iterations fixed at 100. In this case, the user should check that parameter estimates at the last iteration are not on the boundaries of the parameter space. If the parameters are on the boundaries of the parameter space, the identifiability of the model is critical. This may happen especially with splines parameters that may be too close to 0 (lower boundary) or classmb parameters that are too high or low (perfect classification). When identifiability of some parameters is suspected, the program can be run again from the former estimates by fixing the suspected parameters to their value with option posfix. This usually solves the problem. An alternative is to remove the parameters of the Beta of Splines link function from the inverse of the Hessian with option partialH. If not, the program should be run again with other initial values, with a higher maximum number of iterations or less strict convergence tolerances.
Specifically when investigating heterogeneity (that is with ng>1): (1) As
the log-likelihood of a latent class model can have multiple maxima, a
careful choice of the initial values is crucial for ensuring convergence
toward the global maximum. The program can be run without entering the
vector of initial values (see point 2). However, we recommend to
systematically enter initial values in B and try different sets of
initial values. (2) The automatic choice of initial values we provide
requires the estimation of a preliminary linear mixed model. The user should
be aware that first, this preliminary analysis can take time for large
datatsets and second, that the generated initial values can be very not
likely and even may converge slowly to a local maximum. This is the reason
why several alternatives exist. The vector of initial values can be directly
specified in B the initial values can be generated (automatically or
randomly) from a model with ng=. Finally, function gridsearch
performs an automatic grid search.
D. NUMERICAL INTEGRATION WITH THE THRESHOLD LINK FUNCTION
With exception for the threshold link function, maximum likelihood estimation implemented in lcmm does not require any numerical integration over the random-effects so that the estimation procedure is relatively fast. See Proust et al. (2006) for more details on the estimation procedure.
However, with the threshold link function and when at least one random-effect is specified, a numerical integration over the random-effects distribution is required in each computation of the individual contribution to the likelihood which complicates greatly the estimation procedure. For the moment, we do not allow any option regarding the numerical integration technics used. 1. When a single random-effect is specified, we use a standard non-adaptive Gaussian quadrature with 30 points. 2. When at least two random-effects are specified, we use a multivariate non-adaptive Gaussian quadrature implemented by Genz (1996) in HRMSYM Fortran subroutine.
Further developments should allow for adaptive technics and more options regarding the numerical integration technic.
E. POSTERIOR DISCRETE LIKELIHOOD
Models involving nonlinear continuous link functions assume the continuous data while the model with a threshold model assumes discrete data. As a consequence, comparing likelihoods or criteria based on the likelihood (as AIC) for these models is not possible as the former are based on a Lebesgue measure and the latter on a counting measure. To make the comparison possible, we compute the posterior discrete likelihood for all the models with a nonlinear continuous link function. This posterior likelihood considers the data as discrete; it is computed at the MLE (maximum likelihood estimates) using the counting measure so that models with threshold or continuous link functions become comparable. Further details can be found in Proust-Lima, Amieva, Jacqmin-Gadda (2012).
In addition to the Akaike information criterion based on the discrete posterior likelihood, we also compute a universal approximate cross-validation criterion to compare models based on a different measure. See Commenges, Proust-Lima, Samieri, Liquet (2015) for further details.
The list returned is:
ns |
number of grouping units in the dataset |
ng |
number of latent classes |
loglik |
log-likelihood of the model |
best |
vector of parameter estimates in the same order as
specified in |
V |
if the model converged (conv=1 or 3), vector containing the upper triangle
matrix of variance-covariance estimates of |
gconv |
vector of convergence criteria: 1. on the parameters, 2. on the likelihood, 3. on the derivatives |
conv |
status of convergence: =1 if the convergence criteria were satisfied, =2 if the maximum number of iterations was reached, =4 or 5 if a problem occured during optimisation |
call |
the matched call |
niter |
number of Marquardt iterations |
dataset |
dataset |
N |
internal information used in related functions |
idiag |
internal information used in related functions |
pred |
table of individual predictions and residuals in the
underlying latent process scale; it includes marginal predictions (pred_m),
marginal residuals (resid_m), subject-specific predictions (pred_ss) and
subject-specific residuals (resid_ss) averaged over classes, the transformed
observations in the latent process scale (obs) and finally the
class-specific marginal and subject-specific predictions (with the number of
the latent class: pred_m_1,pred_m_2,...,pred_ss_1,pred_ss_2,...). If |
pprob |
table of posterior classification and posterior individual class-membership probabilities |
Xnames |
list of covariates included in the model |
predRE |
table containing individual predictions of the random-effects : a column per random-effect, a line per subject. This output is not available yet when specifying a thresholds transformation. |
cholesky |
vector containing the estimates of the Cholesky transformed parameters of the variance-covariance matrix of the random-effects |
estimlink |
table containing the simulated values of the marker and corresponding estimated link function |
epsY |
definite positive real used to rescale the marker in (0,1) when the beta link function is used. By default, epsY=0.5. |
linktype |
indicator of link function type: 0 for linear, 1 for beta, 2 for splines and 3 for thresholds |
linknodes |
vector of nodes useful only for the 'splines' link function |
data |
the original data set (if returndata is TRUE) |
Cecile Proust-Lima, Amadou Diakite, Benoit Liquet and Viviane Philipps
Proust-Lima C, Philipps V, Liquet B (2017). Estimation of Extended Mixed Models Using Latent Classes and Latent Processes: The R Package lcmm. Journal of Statistical Software, 78(2), 1-56. doi:10.18637/jss.v078.i02
Genz and Keister (1996). Fully symmetric interpolatory rules for multiple integrals over infinite regions with gaussian weight. Journal of Computational and Applied Mathematics 71: 299-309.
Proust and Jacqmin-Gadda (2005). Estimation of linear mixed models with a mixture of distribution for the random-effects. Comput Methods Programs Biomed 78: 165-73.
Proust, Jacqmin-Gadda, Taylor, Ganiayre, and Commenges (2006). A nonlinear model with latent process for cognitive evolution using multivariate longitudinal data. Biometrics 62: 1014-24.
Proust-Lima, Dartigues and Jacqmin-Gadda (2011). Misuse of the linear mixed model when evaluating risk factors of cognitive decline. Amer J Epidemiol 174(9): 1077-88.
Proust-Lima, Amieva and Jacqmin-Gadda (2013). Analysis of multivariate mixed longitudinal data : a flexible latent process approach, British Journal of Mathematical and Statistical Psychology 66(3): 470-87.
Commenges, Proust-Lima, Samieri, Liquet (2015). A universal approximate cross-validation criterion for regular risk functions. Int J Biostat. 2015 May;11(1):51-67
postprob, plot.lcmm, plot.predict,
hlme
## Not run: #### Estimation of homogeneous mixed models with different assumed link #### functions, a quadratic mean trajectory for the latent process and #### correlated random intercept and slope (the random quadratic slope #### was removed as it did not improve the fit of the data). #### -- comparison of linear, Beta and 3 different splines link functions -- # linear link function m10<-lcmm(Ydep2~Time+I(Time^2),random=~Time,subject='ID',ng=1, data=data_lcmm,link="linear") summary(m10) # Beta link function m11<-lcmm(Ydep2~Time+I(Time^2),random=~Time,subject='ID',ng=1, data=data_lcmm,link="beta") summary(m11) plot(m11,which="linkfunction",bty="l") # I-splines with 3 equidistant nodes m12<-lcmm(Ydep2~Time+I(Time^2),random=~Time,subject='ID',ng=1, data=data_lcmm,link="3-equi-splines") summary(m12) # I-splines with 5 nodes at quantiles m13<-lcmm(Ydep2~Time+I(Time^2),random=~Time,subject='ID',ng=1, data=data_lcmm,link="5-quant-splines") summary(m13) # I-splines with 5 nodes, and interior nodes entered manually m14<-lcmm(Ydep2~Time+I(Time^2),random=~Time,subject='ID',ng=1, data=data_lcmm,link="5-manual-splines",intnodes=c(10,20,25)) summary(m14) plot(m14,which="linkfunction",bty="l") # Thresholds # Especially for the threshold link function, we recommend to estimate # models with increasing complexity and use estimates of previous ones # to specify plausible initial values (we remind that estimation of # models with threshold link function involves a computationally demanding # numerical integration -here of size 3) m15<-lcmm(Ydep2~Time+I(Time^2),random=~Time,subject='ID',ng=1 ,data=data_lcmm,link="thresholds",maxiter=100, B=c(-0.8379, -0.1103, 0.3832, 0.3788 , 0.4524, -7.3180, 0.5917, 0.7364, 0.6530, 0.4038, 0.4290, 0.6099, 0.6014 , 0.5354 , 0.5029 , 0.5463, 0.5310 , 0.5352, 0.6498, 0.6653, 0.5851, 0.6525, 0.6701 , 0.6670 , 0.6767 , 0.7394 , 0.7426, 0.7153, 0.7702, 0.6421)) summary(m15) plot(m15,which="linkfunction",bty="l") #### Plot of estimated different link functions: #### (applicable for models that only differ in the "link function" used. #### Otherwise, the latent process scale is different and a rescaling #### is necessary) plot(m10,which="linkfunction",col=1,xlab="latent process",ylab="marker", bty="l",xlim=c(-10,5),legend=NULL) plot(m11,which="linkfunction",add=TRUE,col=2,legend=NULL) plot(m12,which="linkfunction",add=TRUE,col=3,legend=NULL) plot(m13,which="linkfunction",add=TRUE,col=4,legend=NULL) plot(m14,which="linkfunction",add=TRUE,col=5,legend=NULL) plot(m15,which="linkfunction",add=TRUE,col=6,legend=NULL) legend(x="bottomright",legend=c("linear","beta","spl_3e","spl_5q","spl_5m","thresholds"), col=1:6,lty=1,inset=.02,box.lty=0) #### Estimation of 2-latent class mixed models with different assumed link #### functions with individual and class specific linear trend #### for illustration, only default initial values where used but other #### sets of initial values should also be tried to ensure convergence #### towards the golbal maximum # Linear link function m20<-lcmm(Ydep2~Time,random=~Time,subject='ID',mixture=~Time,ng=2, idiag=TRUE,data=data_lcmm,link="linear",B=c(-0.98,0.79,-2.09, -0.81,0.19,0.55,24.49,2.24)) summary(m20) postprob(m20) # Beta link function m21<-lcmm(Ydep2~Time,random=~Time,subject='ID',mixture=~Time,ng=2, idiag=TRUE,data=data_lcmm,link="beta",B=c(-0.1,-0.56,-0.4,-1.77, 0.53,0.14,0.6,-0.83,0.73,0.09)) summary(m21) postprob(m21) # I-splines link function (and 5 nodes at quantiles) m22<-lcmm(Ydep2~Time,random=~Time,subject='ID',mixture=~Time,ng=2, idiag=TRUE,data=data_lcmm,link="5-quant-splines",B=c(0.12,0.63, -1.76,-0.39,0.51,0.13,-7.37,1.05,1.28,1.96,1.3,0.93,1.05)) summary(m22) postprob(m22) data <- data_lcmm[data_lcmm$ID==193,] plot(predictL(m22,var.time="Time",newdata=data,bty="l") ## End(Not run)## Not run: #### Estimation of homogeneous mixed models with different assumed link #### functions, a quadratic mean trajectory for the latent process and #### correlated random intercept and slope (the random quadratic slope #### was removed as it did not improve the fit of the data). #### -- comparison of linear, Beta and 3 different splines link functions -- # linear link function m10<-lcmm(Ydep2~Time+I(Time^2),random=~Time,subject='ID',ng=1, data=data_lcmm,link="linear") summary(m10) # Beta link function m11<-lcmm(Ydep2~Time+I(Time^2),random=~Time,subject='ID',ng=1, data=data_lcmm,link="beta") summary(m11) plot(m11,which="linkfunction",bty="l") # I-splines with 3 equidistant nodes m12<-lcmm(Ydep2~Time+I(Time^2),random=~Time,subject='ID',ng=1, data=data_lcmm,link="3-equi-splines") summary(m12) # I-splines with 5 nodes at quantiles m13<-lcmm(Ydep2~Time+I(Time^2),random=~Time,subject='ID',ng=1, data=data_lcmm,link="5-quant-splines") summary(m13) # I-splines with 5 nodes, and interior nodes entered manually m14<-lcmm(Ydep2~Time+I(Time^2),random=~Time,subject='ID',ng=1, data=data_lcmm,link="5-manual-splines",intnodes=c(10,20,25)) summary(m14) plot(m14,which="linkfunction",bty="l") # Thresholds # Especially for the threshold link function, we recommend to estimate # models with increasing complexity and use estimates of previous ones # to specify plausible initial values (we remind that estimation of # models with threshold link function involves a computationally demanding # numerical integration -here of size 3) m15<-lcmm(Ydep2~Time+I(Time^2),random=~Time,subject='ID',ng=1 ,data=data_lcmm,link="thresholds",maxiter=100, B=c(-0.8379, -0.1103, 0.3832, 0.3788 , 0.4524, -7.3180, 0.5917, 0.7364, 0.6530, 0.4038, 0.4290, 0.6099, 0.6014 , 0.5354 , 0.5029 , 0.5463, 0.5310 , 0.5352, 0.6498, 0.6653, 0.5851, 0.6525, 0.6701 , 0.6670 , 0.6767 , 0.7394 , 0.7426, 0.7153, 0.7702, 0.6421)) summary(m15) plot(m15,which="linkfunction",bty="l") #### Plot of estimated different link functions: #### (applicable for models that only differ in the "link function" used. #### Otherwise, the latent process scale is different and a rescaling #### is necessary) plot(m10,which="linkfunction",col=1,xlab="latent process",ylab="marker", bty="l",xlim=c(-10,5),legend=NULL) plot(m11,which="linkfunction",add=TRUE,col=2,legend=NULL) plot(m12,which="linkfunction",add=TRUE,col=3,legend=NULL) plot(m13,which="linkfunction",add=TRUE,col=4,legend=NULL) plot(m14,which="linkfunction",add=TRUE,col=5,legend=NULL) plot(m15,which="linkfunction",add=TRUE,col=6,legend=NULL) legend(x="bottomright",legend=c("linear","beta","spl_3e","spl_5q","spl_5m","thresholds"), col=1:6,lty=1,inset=.02,box.lty=0) #### Estimation of 2-latent class mixed models with different assumed link #### functions with individual and class specific linear trend #### for illustration, only default initial values where used but other #### sets of initial values should also be tried to ensure convergence #### towards the golbal maximum # Linear link function m20<-lcmm(Ydep2~Time,random=~Time,subject='ID',mixture=~Time,ng=2, idiag=TRUE,data=data_lcmm,link="linear",B=c(-0.98,0.79,-2.09, -0.81,0.19,0.55,24.49,2.24)) summary(m20) postprob(m20) # Beta link function m21<-lcmm(Ydep2~Time,random=~Time,subject='ID',mixture=~Time,ng=2, idiag=TRUE,data=data_lcmm,link="beta",B=c(-0.1,-0.56,-0.4,-1.77, 0.53,0.14,0.6,-0.83,0.73,0.09)) summary(m21) postprob(m21) # I-splines link function (and 5 nodes at quantiles) m22<-lcmm(Ydep2~Time,random=~Time,subject='ID',mixture=~Time,ng=2, idiag=TRUE,data=data_lcmm,link="5-quant-splines",B=c(0.12,0.63, -1.76,-0.39,0.51,0.13,-7.37,1.05,1.28,1.96,1.3,0.93,1.05)) summary(m22) postprob(m22) data <- data_lcmm[data_lcmm$ID==193,] plot(predictL(m22,var.time="Time",newdata=data,bty="l") ## End(Not run)
Log-likelihood of hlme, lcmm, multlcmm, Jointlcmm and mpjlcmm models. The argument's specification is not straightforward, so these functions are usually not directly used.
loglikhlme( b, Y0, X0, prior0, pprior0, idprob0, idea0, idg0, idcor0, ns0, ng0, nv0, nobs0, nea0, nmes0, idiag0, nwg0, ncor0, npm0, fix0, nfix0, bfix0 ) logliklcmm( b, Y0, X0, prior0, pprior0, idprob0, idea0, idg0, idcor0, ns0, ng0, nv0, nobs0, nea0, nmes0, idiag0, nwg0, ncor0, npm0, epsY0, idlink0, nbzitr0, zitr0, minY0, maxY0, ide0, fix0, nfix0, bfix0 ) loglikmultlcmm( b, Y0, X0, prior0, pprior0, idprob0, idea0, idg0, idcor0, idcontr0, ny0, ns0, ng0, nv0, nobs0, nea0, nmes0, idiag0, nwg0, ncor0, nalea0, npm0, epsY0, idlink0, nbzitr0, zitr0, uniqueY0, indiceY0, nvalSPLORD0, fix0, nfix0, bfix0, methInteg0, nMC0, dimMC0, seqMC0, chol0 ) loglikJointlcmm( b, Y0, X0, prior0, pprior0, tentr0, tevt0, devt0, ind_survint0, idprob0, idea0, idg0, idcor0, idcom0, idspecif0, idtdv0, idlink0, epsY0, nbzitr0, zitr0, uniqueY0, nvalSPL0, indiceY0, typrisq0, risqcom0, nz0, zi0, ns0, ng0, nv0, nobs0, nmes0, nbevt0, nea0, nwg0, ncor0, idiag0, idtrunc0, logspecif0, npm0, fix0, nfix0, bfix0 ) loglikmpjlcmm( b, K0, ny0, nbevt0, ng0, ns0, Y0, nobs0, X0, nv0, Xns0, nv20, prior0, Tentr0, Tevt0, Devt0, ind_survint0, idnv0, idnv20, idspecif0, idlink0, epsY0, nbzitr0, zitr0, uniqueY0, nvalSPL0, indiceY0, typrisq0, risqcom0, nz0, zi0, nmes0, nea0, nw0, ncor0, nalea0, idiag0, idtrunc0, logspecif0, npm0, fix0, contrainte0, nfix0, bfix0 )loglikhlme( b, Y0, X0, prior0, pprior0, idprob0, idea0, idg0, idcor0, ns0, ng0, nv0, nobs0, nea0, nmes0, idiag0, nwg0, ncor0, npm0, fix0, nfix0, bfix0 ) logliklcmm( b, Y0, X0, prior0, pprior0, idprob0, idea0, idg0, idcor0, ns0, ng0, nv0, nobs0, nea0, nmes0, idiag0, nwg0, ncor0, npm0, epsY0, idlink0, nbzitr0, zitr0, minY0, maxY0, ide0, fix0, nfix0, bfix0 ) loglikmultlcmm( b, Y0, X0, prior0, pprior0, idprob0, idea0, idg0, idcor0, idcontr0, ny0, ns0, ng0, nv0, nobs0, nea0, nmes0, idiag0, nwg0, ncor0, nalea0, npm0, epsY0, idlink0, nbzitr0, zitr0, uniqueY0, indiceY0, nvalSPLORD0, fix0, nfix0, bfix0, methInteg0, nMC0, dimMC0, seqMC0, chol0 ) loglikJointlcmm( b, Y0, X0, prior0, pprior0, tentr0, tevt0, devt0, ind_survint0, idprob0, idea0, idg0, idcor0, idcom0, idspecif0, idtdv0, idlink0, epsY0, nbzitr0, zitr0, uniqueY0, nvalSPL0, indiceY0, typrisq0, risqcom0, nz0, zi0, ns0, ng0, nv0, nobs0, nmes0, nbevt0, nea0, nwg0, ncor0, idiag0, idtrunc0, logspecif0, npm0, fix0, nfix0, bfix0 ) loglikmpjlcmm( b, K0, ny0, nbevt0, ng0, ns0, Y0, nobs0, X0, nv0, Xns0, nv20, prior0, Tentr0, Tevt0, Devt0, ind_survint0, idnv0, idnv20, idspecif0, idlink0, epsY0, nbzitr0, zitr0, uniqueY0, nvalSPL0, indiceY0, typrisq0, risqcom0, nz0, zi0, nmes0, nea0, nw0, ncor0, nalea0, idiag0, idtrunc0, logspecif0, npm0, fix0, contrainte0, nfix0, bfix0 )
b |
the vector of estimated parameters (length npm0) |
Y0 |
the observed values of the outcome(s) (length nobs0) |
X0 |
the observed values of all covariates included in the model (dim nob0 * nv0) |
prior0 |
the prior latent class (length ns0) |
pprior0 |
the prior probabilty of each latent class (dim ns0 * ng0) |
idprob0 |
indicator of presence in the class membership submodel (length nv0) |
idea0 |
indicator of presence in the random part of the longitudinal submodel (length nv0) |
idg0 |
indicator of presence in the fixed part of the longitudinal submodel (length nv0) |
idcor0 |
indicator of presence in the correlation part of the longitudinal submodel (length nv0) |
ns0 |
number of subjects |
ng0 |
number of latent classes |
nv0 |
number of covariates |
nobs0 |
number of observations |
nea0 |
number of random effects |
nmes0 |
number of mesures for each subject (length ns0 or dom ns0*ny0) |
idiag0 |
indicator of diagonal variance matrix of the random effects |
nwg0 |
number of parameters for proportional random effects over latent classes |
ncor0 |
number of parameters for the correlation |
npm0 |
total number of parameters |
fix0 |
indicator of non estimated parameter (length npm0+nfix0) |
nfix0 |
number of non estimated parameters |
bfix0 |
vector of non estimated parameters |
epsY0 |
epsY values for Beta transformations |
idlink0 |
type of transformation |
nbzitr0 |
number of nodes for the transformations |
zitr0 |
nodes for the transformations |
minY0 |
minimum value for the longitudinal outcome |
maxY0 |
maximum value for the longitudinal outcome |
ide0 |
indicator of observed values for ordinal outcomes |
idcontr0 |
indicator of presence as contrast in the fixed part of the longitudinal submodel (length nv0) |
ny0 |
number of longitudinal outcomes |
nalea0 |
number of parameters f the outcome specific random effect |
uniqueY0 |
unique values of the longitudinal outcomes |
indiceY0 |
correspondance between Y0 and uniqueY0 |
nvalSPLORD0 |
number of unique values for outcomes modeled with splines transformations or as ordinal outcome |
methInteg0 |
type of integration |
nMC0 |
number of nodes for Monte Carlo integration |
dimMC0 |
dimension of the integration |
seqMC0 |
sequence of integration nodes |
chol0 |
indicator of Cholesky parameterization |
tentr0 |
entry time for the survival submodel |
tevt0 |
event time for the survival submodel |
devt0 |
indicator of event for the survival submodel |
ind_survint0 |
indicator of risk change |
idcom0 |
indicator of presence in the survival submodel with common effect |
idspecif0 |
indicator of presence in the survival submodel with cause-specific or class specific effect |
idtdv0 |
indicator of 'TimeDepVar' covariate |
nvalSPL0 |
number of unique values for outcomes modeled with splines transformations |
typrisq0 |
type of baseline risk |
risqcom0 |
specification of baseline risk across latent classes |
nz0 |
number of nodes for the baseline |
zi0 |
nodes for the baseline |
nbevt0 |
number of events |
idtrunc0 |
indicator of left truncation |
logspecif0 |
indicator of logarithm parameterization |
K0 |
number of latent processes |
Xns0 |
the observed values of the covariates included in the survival submodel (dim ns0*nv20) |
nv20 |
number of covariates in Xns0 |
Tentr0 |
entry time for the survival submodel (length ns0) |
Tevt0 |
event time for the survival submodel (length ns0) |
Devt0 |
indicator of event for the survival submodel (length ns0) |
idnv0 |
indicator of presence in each subpart of the longitudinal models (length 4*sum(nv0)) |
idnv20 |
indicator of presence in each subpart of the survival models (length 3*nv20) |
nw0 |
number of parameters for proportional random effects over latent classes |
contrainte0 |
type of identifiability constraints |
the log-likelihood
Cecile Proust-Lima, Viviane Philipps
This function fits joint latent class models for multivariate longitudinal markers and competing causes of event. It is a multivariate extension of the Jointlcmm function. It defines each longitudinal dimension as a latent process (mp in mpjlcmm is for multivariate processes), possibly measured by sereval continuous markers (Gaussian or curvilinear). For the moment, theses processes are assumed independent given the latent classes. The (optional) survival part handles competing risks, right censoring and left truncation. The specification of the function is similar to other estimating functions of the package.
mpjlcmm( longitudinal, subject, classmb, ng, survival, hazard = "Weibull", hazardtype = "Specific", hazardnodes = NULL, TimeDepVar = NULL, data, B, convB = 1e-04, convL = 1e-04, convG = 1e-04, maxiter = 100, nsim = 100, prior, logscale = FALSE, subset = NULL, na.action = 1, posfix = NULL, partialH = FALSE, verbose = FALSE, nproc = 1, clustertype = NULL )mpjlcmm( longitudinal, subject, classmb, ng, survival, hazard = "Weibull", hazardtype = "Specific", hazardnodes = NULL, TimeDepVar = NULL, data, B, convB = 1e-04, convL = 1e-04, convG = 1e-04, maxiter = 100, nsim = 100, prior, logscale = FALSE, subset = NULL, na.action = 1, posfix = NULL, partialH = FALSE, verbose = FALSE, nproc = 1, clustertype = NULL )
longitudinal |
list of longitudinal models of type hlme, lcmm or multlcmm. Each model defines the structure of one latent process. |
subject |
name of the covariate representing the grouping structure (called subject identifier) |
classmb |
optional one-sided formula describing the covariates in the class-membership multinomial logistic model |
ng |
number of latent classes considered |
survival |
two-sided formula object specifying the survival part of the model |
hazard |
optional family of hazard function assumed for the survival model (Weibull, piecewise or splines) |
hazardtype |
optional indicator for the type of baseline risk function (Specific, PH or Common) |
hazardnodes |
optional vector containing interior nodes if
|
TimeDepVar |
optional vector specifying the name of the time-depending covariate in the survival model |
data |
data frame containing all the variables used in the model |
B |
optional specification for the initial values of the parameters.
Three options are allowed: (1) a vector of initial values is entered (the
order in which the parameters are included is detailed in |
convB |
optional threshold for the convergence criterion based on the parameter stability |
convL |
optional threshold for the convergence criterion based on the log-likelihood stability |
convG |
optional threshold for the convergence criterion based on the derivatives |
maxiter |
optional maximum number of iterations for the Marquardt iterative algorithm |
nsim |
optional number of points for the predicted survival curves and predicted baseline risk curves |
prior |
optional name of a covariate containing a prior information about the latent class membership |
logscale |
optional boolean indicating whether an exponential (logscale=TRUE) or a square (logscale=FALSE -by default) transformation is used to ensure positivity of parameters in the baseline risk functions |
subset |
a specification of the rows to be used: defaults to all rows. This can be any valid indexing vector for the rows of data or if that is not supplied, a data frame made up of the variable used in formula. |
na.action |
Integer indicating how NAs are managed. The default is 1 for 'na.omit'. The alternative is 2 for 'na.fail'. Other options such as 'na.pass' or 'na.exclude' are not implemented in the current version. |
posfix |
Optional vector specifying the indices in vector B of the parameters that should not be estimated. Default to NULL, all parameters are estimated |
partialH |
optional logical for Piecewise and Splines baseline risk functions and Splines link functions only. Indicates whether the parameters of the baseline risk or link functions can be dropped from the Hessian matrix to define convergence criteria (can solve non convergence due to estimates at the boundary of the parameter space - usually 0). |
verbose |
logical indicating whether information about computation should be reported. Default to FALSE. |
nproc |
the number cores for parallel computation. Default to 1 (sequential mode). |
clustertype |
optional character indicating the type of cluster for parallel computation. |
Cecile Proust Lima and Viviane Philipps
## Not run: paquid$age65 <- (paquid$age-65)/10 ############################################################################## ### EXAMPLE 1 : ### ###two outcomes measuring the same latent process along with dementia onset### ############################################################################## ## multlcmm model for MMSE and BVRT for 1 class mult1 <- multlcmm(MMSE+BVRT~age65+I(age65^2)+CEP+male,random=~age65+I(age65^2), subject="ID",link=c("5-quant-splines","4-quant-splines"),data=paquid) summary(mult1) ## joint model for 1 class m1S <- mpjlcmm(longitudinal=list(mult1),subject="ID",ng=1,data=paquid, survival=Surv(age_init,agedem,dem)~1) summary(m1S) ##### joint model for 2 classes ##### ## specify longitudinal model for 2 classes, without estimation mult2 <- multlcmm(MMSE+BVRT~age65+I(age65^2)+CEP+male,random=~age65+I(age65^2), subject="ID",link=c("5-quant-splines","4-quant-splines"),ng=2, mixture=~age65+I(age65^2),data=paquid,B=random(mult1),maxiter=0) ## estimation of the associated joint model m2S <- mpjlcmm(longitudinal=list(mult2),subject="ID",ng=2,data=paquid, survival=Surv(age_init,agedem,dem)~1) ## estimation by a grid search with 50 replicates, initial values ## randomly generated from m1S m2S_b <- gridsearch(mpjlcmm(longitudinal=list(mult2),subject="ID",ng=2, data=paquid,survival=Surv(age_init,agedem,dem)~1), minit=m1S, rep=50, maxiter=30) ##### joint model for 3 classes ##### mult3 <- multlcmm(MMSE+BVRT~age65+I(age65^2)+CEP+male,random=~age65+I(age65^2), subject="ID",link=c("5-quant-splines","4-quant-splines"),ng=3, mixture=~age65+I(age65^2),data=paquid,B=random(mult1),maxiter=0) m3S <- mpjlcmm(longitudinal=list(mult3),subject="ID",ng=3,data=paquid, survival=Surv(age_init,agedem,dem)~1) m3S_b <- gridsearch(mpjlcmm(longitudinal=list(mult3),subject="ID",ng=3, data=paquid,survival=Surv(age_init,agedem,dem)~1), minit=m1S, rep=50, maxiter=30) ##### summary of the models ##### summarytable(m1S,m2S,m2S_b,m3S,m3S_b) ##### post-fit ##### ## update longitudinal models : mod2 <- update(m2S) mult2_post <- mod2[[1]] ## -> use the available functions for multlcmm on the mult2_post object ## fit of the longitudinal trajectories par(mfrow=c(2,2)) plot(mult2_post,"fit","age65",marg=TRUE,shades=TRUE,outcome=1) plot(mult2_post,"fit","age65",marg=TRUE,shades=TRUE,outcome=2) plot(mult2_post,"fit","age65",marg=FALSE,shades=TRUE,outcome=1) plot(mult2_post,"fit","age65",marg=FALSE,shades=TRUE,outcome=2) ## predicted trajectories dpred <- data.frame(age65=seq(0,3,0.1),male=0,CEP=0) predL <- predictL(mult2_post,newdata=dpred,var.time="age65",confint=TRUE) plot(predL,shades=TRUE) # in the latent process scale predY <- predictY(mult2_post,newdata=dpred,var.time="age65",draws=TRUE) plot(predY,shades=TRUE,ylim=c(0,30),main="MMSE") #in the 0-30 scale for MMSE plot(predY,shades=TRUE,ylim=c(0,15),outcome=2,main="BVRT") #in 0-15 for BVRT ## baseline hazard and survival curves : plot(m2S,"hazard") plot(m2S,"survival") ## posteriori probabilities and classification : postprob(m2S) #################################################################################### ### EXAMPLE 2 : ### ### two latent processes measured each by one outcome along with dementia onset ### #################################################################################### ## define the two longitudinal models mMMSE1 <- lcmm(MMSE~age65+I(age65^2)+CEP,random=~age65+I(age65^2),subject="ID", link="5-quant-splines",data=paquid) mCESD1 <- lcmm(CESD~age65+I(age65^2)+male,random=~age65+I(age65^2),subject="ID", link="5-quant-splines",data=paquid) ## joint estimation mm1S <- mpjlcmm(longitudinal=list(mMMSE1,mCESD1),subject="ID",ng=1,data=paquid, survival=Surv(age_init,agedem,dem)~CEP+male) ## with 2 latent classes mMMSE2 <- lcmm(MMSE~age65+I(age65^2)+CEP,random=~age65+I(age65^2),subject="ID", link="5-quant-splines",data=paquid,ng=2,mixture=~age65+I(age65^2), B=random(mMMSE1),maxiter=0) mCESD2 <- lcmm(CESD~age65+I(age65^2)+male,random=~age65+I(age65^2),subject="ID", link="5-quant-splines",data=paquid,ng=2,mixture=~age65+I(age65^2), B=random(mCESD1),maxiter=0) mm2S <- mpjlcmm(longitudinal=list(mMMSE2,mCESD2),subject="ID",ng=2,data=paquid, survival=Surv(age_init,agedem,dem)~CEP+mixture(male),classmb=~CEP+male) mm2S_b <- gridsearch(mpjlcmm(longitudinal=list(mMMSE2,mCESD2),subject="ID",ng=2, data=paquid,survival=Surv(age_init,agedem,dem)~CEP+mixture(male), classmb=~CEP+male),minit=mm1S,rep=50,maxiter=50) summarytable(mm1S,mm2S,mm2S_b) mod1_biv <- update(mm1S) mod2_biv <- update(mm2S) ## -> use post-fit functions as in exemple 1 ## End(Not run)## Not run: paquid$age65 <- (paquid$age-65)/10 ############################################################################## ### EXAMPLE 1 : ### ###two outcomes measuring the same latent process along with dementia onset### ############################################################################## ## multlcmm model for MMSE and BVRT for 1 class mult1 <- multlcmm(MMSE+BVRT~age65+I(age65^2)+CEP+male,random=~age65+I(age65^2), subject="ID",link=c("5-quant-splines","4-quant-splines"),data=paquid) summary(mult1) ## joint model for 1 class m1S <- mpjlcmm(longitudinal=list(mult1),subject="ID",ng=1,data=paquid, survival=Surv(age_init,agedem,dem)~1) summary(m1S) ##### joint model for 2 classes ##### ## specify longitudinal model for 2 classes, without estimation mult2 <- multlcmm(MMSE+BVRT~age65+I(age65^2)+CEP+male,random=~age65+I(age65^2), subject="ID",link=c("5-quant-splines","4-quant-splines"),ng=2, mixture=~age65+I(age65^2),data=paquid,B=random(mult1),maxiter=0) ## estimation of the associated joint model m2S <- mpjlcmm(longitudinal=list(mult2),subject="ID",ng=2,data=paquid, survival=Surv(age_init,agedem,dem)~1) ## estimation by a grid search with 50 replicates, initial values ## randomly generated from m1S m2S_b <- gridsearch(mpjlcmm(longitudinal=list(mult2),subject="ID",ng=2, data=paquid,survival=Surv(age_init,agedem,dem)~1), minit=m1S, rep=50, maxiter=30) ##### joint model for 3 classes ##### mult3 <- multlcmm(MMSE+BVRT~age65+I(age65^2)+CEP+male,random=~age65+I(age65^2), subject="ID",link=c("5-quant-splines","4-quant-splines"),ng=3, mixture=~age65+I(age65^2),data=paquid,B=random(mult1),maxiter=0) m3S <- mpjlcmm(longitudinal=list(mult3),subject="ID",ng=3,data=paquid, survival=Surv(age_init,agedem,dem)~1) m3S_b <- gridsearch(mpjlcmm(longitudinal=list(mult3),subject="ID",ng=3, data=paquid,survival=Surv(age_init,agedem,dem)~1), minit=m1S, rep=50, maxiter=30) ##### summary of the models ##### summarytable(m1S,m2S,m2S_b,m3S,m3S_b) ##### post-fit ##### ## update longitudinal models : mod2 <- update(m2S) mult2_post <- mod2[[1]] ## -> use the available functions for multlcmm on the mult2_post object ## fit of the longitudinal trajectories par(mfrow=c(2,2)) plot(mult2_post,"fit","age65",marg=TRUE,shades=TRUE,outcome=1) plot(mult2_post,"fit","age65",marg=TRUE,shades=TRUE,outcome=2) plot(mult2_post,"fit","age65",marg=FALSE,shades=TRUE,outcome=1) plot(mult2_post,"fit","age65",marg=FALSE,shades=TRUE,outcome=2) ## predicted trajectories dpred <- data.frame(age65=seq(0,3,0.1),male=0,CEP=0) predL <- predictL(mult2_post,newdata=dpred,var.time="age65",confint=TRUE) plot(predL,shades=TRUE) # in the latent process scale predY <- predictY(mult2_post,newdata=dpred,var.time="age65",draws=TRUE) plot(predY,shades=TRUE,ylim=c(0,30),main="MMSE") #in the 0-30 scale for MMSE plot(predY,shades=TRUE,ylim=c(0,15),outcome=2,main="BVRT") #in 0-15 for BVRT ## baseline hazard and survival curves : plot(m2S,"hazard") plot(m2S,"survival") ## posteriori probabilities and classification : postprob(m2S) #################################################################################### ### EXAMPLE 2 : ### ### two latent processes measured each by one outcome along with dementia onset ### #################################################################################### ## define the two longitudinal models mMMSE1 <- lcmm(MMSE~age65+I(age65^2)+CEP,random=~age65+I(age65^2),subject="ID", link="5-quant-splines",data=paquid) mCESD1 <- lcmm(CESD~age65+I(age65^2)+male,random=~age65+I(age65^2),subject="ID", link="5-quant-splines",data=paquid) ## joint estimation mm1S <- mpjlcmm(longitudinal=list(mMMSE1,mCESD1),subject="ID",ng=1,data=paquid, survival=Surv(age_init,agedem,dem)~CEP+male) ## with 2 latent classes mMMSE2 <- lcmm(MMSE~age65+I(age65^2)+CEP,random=~age65+I(age65^2),subject="ID", link="5-quant-splines",data=paquid,ng=2,mixture=~age65+I(age65^2), B=random(mMMSE1),maxiter=0) mCESD2 <- lcmm(CESD~age65+I(age65^2)+male,random=~age65+I(age65^2),subject="ID", link="5-quant-splines",data=paquid,ng=2,mixture=~age65+I(age65^2), B=random(mCESD1),maxiter=0) mm2S <- mpjlcmm(longitudinal=list(mMMSE2,mCESD2),subject="ID",ng=2,data=paquid, survival=Surv(age_init,agedem,dem)~CEP+mixture(male),classmb=~CEP+male) mm2S_b <- gridsearch(mpjlcmm(longitudinal=list(mMMSE2,mCESD2),subject="ID",ng=2, data=paquid,survival=Surv(age_init,agedem,dem)~CEP+mixture(male), classmb=~CEP+male),minit=mm1S,rep=50,maxiter=50) summarytable(mm1S,mm2S,mm2S_b) mod1_biv <- update(mm1S) mod2_biv <- update(mm2S) ## -> use post-fit functions as in exemple 1 ## End(Not run)
This function constitutes a multivariate extension of function lcmm.
It fits multivariate mixed models and multivariate latent class mixed models
for multivariate longitudinal outcomes of different types. It handles
continuous longitudinal outcomes (Gaussian or non-Gaussian, curvilinear) as
well as ordinal longitudinal outcomes (with cumulative probit measurement model).
The model assumes that all the outcomes measure the same underlying latent process
defined as their common factor, and each outcome is related to this latent common
factor by a specific parameterized link function. At the latent process level, the
model estimates a standard linear mixed model or a latent class linear mixed
model when heterogeneity in the population is investigated (in the same way
as in functions hlme and lcmm). Parameters of the nonlinear link
functions and of the latent process mixed model are estimated simultaneously
using a maximum likelihood method.
multlcmm( fixed, mixture, random, subject, classmb, ng = 1, idiag = FALSE, nwg = FALSE, randomY = FALSE, link = "linear", intnodes = NULL, epsY = 0.5, cor = NULL, data, B, convB = 1e-04, convL = 1e-04, convG = 1e-04, maxiter = 100, nsim = 100, prior, pprior = NULL, range = NULL, subset = NULL, na.action = 1, posfix = NULL, partialH = FALSE, verbose = FALSE, returndata = FALSE, methInteg = "QMC", nMC = NULL, var.time = NULL, nproc = 1, clustertype = NULL ) mlcmm( fixed, mixture, random, subject, classmb, ng = 1, idiag = FALSE, nwg = FALSE, randomY = FALSE, link = "linear", intnodes = NULL, epsY = 0.5, cor = NULL, data, B, convB = 1e-04, convL = 1e-04, convG = 1e-04, maxiter = 100, nsim = 100, prior, pprior = NULL, range = NULL, subset = NULL, na.action = 1, posfix = NULL, partialH = FALSE, verbose = FALSE, returndata = FALSE, methInteg = "QMC", nMC = NULL, var.time = NULL, nproc = 1, clustertype = NULL )multlcmm( fixed, mixture, random, subject, classmb, ng = 1, idiag = FALSE, nwg = FALSE, randomY = FALSE, link = "linear", intnodes = NULL, epsY = 0.5, cor = NULL, data, B, convB = 1e-04, convL = 1e-04, convG = 1e-04, maxiter = 100, nsim = 100, prior, pprior = NULL, range = NULL, subset = NULL, na.action = 1, posfix = NULL, partialH = FALSE, verbose = FALSE, returndata = FALSE, methInteg = "QMC", nMC = NULL, var.time = NULL, nproc = 1, clustertype = NULL ) mlcmm( fixed, mixture, random, subject, classmb, ng = 1, idiag = FALSE, nwg = FALSE, randomY = FALSE, link = "linear", intnodes = NULL, epsY = 0.5, cor = NULL, data, B, convB = 1e-04, convL = 1e-04, convG = 1e-04, maxiter = 100, nsim = 100, prior, pprior = NULL, range = NULL, subset = NULL, na.action = 1, posfix = NULL, partialH = FALSE, verbose = FALSE, returndata = FALSE, methInteg = "QMC", nMC = NULL, var.time = NULL, nproc = 1, clustertype = NULL )
fixed |
a two-sided linear formula object for specifying the
fixed-effects in the linear mixed model at the latent process level. The
response outcomes are separated by |
mixture |
a one-sided formula object for the class-specific fixed
effects in the latent process mixed model (to specify only for a number of
latent classes greater than 1). Among the list of covariates included in
|
random |
an optional one-sided formula for the random-effects in the
latent process mixed model. At least one random effect should be included
for identifiability purposes. Covariates with a random-effect are separated
by |
subject |
name of the covariate representing the grouping structure. |
classmb |
an optional one-sided formula describing the covariates in
the class-membership multinomial logistic model. Covariates included are
separated by |
ng |
number of latent classes considered. If |
idiag |
optional logical for the variance-covariance structure of the
random-effects. If |
nwg |
optional logical of class-specific variance-covariance of the
random-effects. If |
randomY |
optional logical for including an outcome-specific random
intercept. If |
link |
optional vector of families of parameterized link functions to
estimate (one by outcome). Option "linear" (by default) specifies a linear
link function. Other possibilities include "beta" for estimating a link
function from the family of Beta cumulative distribution functions,
"thresholds" for using a threshold model to describe the correspondence
between each level of an ordinal outcome and the underlying latent process and
"Splines" for approximating the link function by I-splines. For this latter
case, the number of nodes and the nodes location should be also specified.
The number of nodes is first entered followed by |
intnodes |
optional vector of interior nodes. This argument is only required for a I-splines link function with nodes entered manually. |
epsY |
optional definite positive real used to rescale the marker in (0,1) when the beta link function is used. By default, epsY=0.5. |
cor |
optional indicator for inclusion of an autocorrelated Gaussian
process in the latent process linear (latent process) mixed model. Option
"BM" indicates a brownian motion with parameterized variance. Option "AR"
specifies an autoregressive process of order 1 with parameterized variance
and correlation intensity. Each option should be followed by the time
variable in brackets as |
data |
data frame containing the variables named in |
B |
optional specification for the initial values for the parameters.
Three options are allowed: (1) a vector of initial values is entered (the
order in which the parameters are included is detailed in |
convB |
optional threshold for the convergence criterion based on the parameter stability. By default, convB=0.0001. |
convL |
optional threshold for the convergence criterion based on the log-likelihood stability. By default, convL=0.0001. |
convG |
optional threshold for the convergence criterion based on the derivatives. By default, convG=0.0001. |
maxiter |
optional maximum number of iterations for the Marquardt iterative algorithm. By default, maxiter=100. |
nsim |
number of points used to plot the estimated link functions. By default, nsim=100. |
prior |
name of the covariate containing the prior on the latent class membership. The covariate should be an integer with values in 0,1,...,ng. When there is no prior, the value should be 0. When there is a prior for the subject, the value should be the number of the latent class (in 1,...,ng). |
pprior |
optional vector specifying the names of the covariates containing the prior probabilities to belong to each latent class. These probabilities should be between 0 and 1 and should sum up to 1 for each subject. |
range |
optional vector indicating the range of the outcomes (that is the minimum and maximum). By default, the range is defined according to the minimum and maximum observed values of the outcome. The option should be used only for Beta and Splines transformations. |
subset |
optional vector giving the subset of observations in
|
na.action |
Integer indicating how NAs are managed. The default is 1 for 'na.omit'. The alternative is 2 for 'na.fail'. Other options such as 'na.pass' or 'na.exclude' are not implemented in the current version. |
posfix |
Optional vector giving the indices in vector B of the parameters that should not be estimated. Default to NULL, all parameters are estimated. |
partialH |
optional logical for Splines link functions only. Indicates whether the parameters of the link functions can be dropped from the Hessian matrix to define convergence criteria. |
verbose |
logical indicating if information about computation should be reported. Default to TRUE. |
returndata |
logical indicating if data used for computation should be returned. Default to FALSE, data are not returned. |
methInteg |
character indicating the type of integration if ordinal outcomes are considered. 'MCO' for ordinary Monte Carlo, 'MCA' for antithetic Monte Carlo, 'QMC' for quasi Monte Carlo. Default to "QMC". |
nMC |
integer, number of Monte Carlo simulations. By default, 1000 points are used if at least one threshold link is specified. |
var.time |
optional character indicating the name of the time variable. |
nproc |
the number cores for parallel computation. Default to 1 (sequential mode). |
clustertype |
optional character indicating the type of cluster for parallel computation. |
A. THE PARAMETERIZED LINK FUNCTIONS
multlcmm function estimates multivariate latent class mixed models
for different types of outcomes by assuming a parameterized link function
for linking each outcome Y_k(t) with the underlying latent common factor
L(t) they measure. To fix the latent process dimension, we chose to
constrain at the latent process level the (first) intercept of the latent
class mixed model at 0 and the standard error of the first random effect at
1.
1. With the "linear" link function, 2 parameters are required for the following transformation (Y(t) - b1)/b2
2. With the "beta" link function, 4 parameters are required for the following transformation: [ h(Y(t)',b1,b2) - b3]/b4 where h is the Beta CDF with canonical parameters c1 and c2 that can be derived from b1 and b2 as c1=exp(b1)/[exp(b2)*(1+exp(b1))] and c2=1/[exp(b2)*(1+exp(b1))], and Y(t)' is the rescaled outcome i.e. Y(t)'= [ Y(t) - min(Y(t)) + epsY ] / [ max(Y(t)) - min(Y(t)) +2*epsY ].
3. With the "splines" link function, n+2 parameters are required for the following transformation b_1 + b_2*I_1(Y(t)) + ... + b_n+2 I_n+1(Y(t)), where I_1,...,I_n+1 is the basis of quadratic I-splines. To constraint the parameters to be positive, except for b_1, the program estimates b_k^* (for k=2,...,n+2) so that b_k=(b_k^*)^2. This parameterization may lead in some cases to problems of convergence that we are currently addressing.
4. With the "thresholds" link function for an ordinal outcome with levels 0,...,C, C-1 parameters are required for the following transformation: Y(t)=c <=> b_c < L(t) <= b_c+1 with b_0 = - infinity and b_C+1=+infinity. To constraint the parameters to be increasing, except for the first parameter b_1, the program estimates b_k^* (for k=2,...C-1) so that b_k=b_k-1+(b_k^*)^2.
Details of these parameterized link functions can be found in the papers: Proust-Lima et al. (Biometrics 2006), Proust-Lima et al. (BJMSP 2013), Proust-Lima et al. (arxiv 2021 - https://arxiv.org/abs/2109.13064)
B. THE VECTOR OF PARAMETERS B
The parameters in the vector of initial values B or in the vector of
maximum likelihood estimates best are included in the following
order: (1) ng-1 parameters are required for intercepts in the latent class
membership model, and if covariates are included in classmb, ng-1
paramaters should be entered for each one; (2) for all covariates in
fixed, one parameter is required if the covariate is not in
mixture, ng paramaters are required if the covariate is also in
mixture; When ng=1, the intercept is not estimated and no parameter
should be specified in B. When ng>1, the first intercept is not
estimated and only ng-1 parameters should be specified in B; (3) for
all covariates included with contrast() in fixed, one
supplementary parameter per outcome is required excepted for the last
outcome for which the parameter is not estimated but deduced from the
others; (4) if idiag=TRUE, the variance of each random-effect
specified in random is required excepted the first one (usually the
intercept) which is constrained to 1. (5) if idiag=FALSE, the
inferior triangular variance-covariance matrix of all the random-effects is
required excepted the first variance (usually the intercept) which is
constrained to 1. (5) only if nwg=TRUE and ng>1, ng-1
parameters for class-specific proportional coefficients for the variance
covariance matrix of the random-effects; (6) if cor is specified, the
standard error of the Brownian motion or the standard error and the
correlation parameter of the autoregressive process; (7) the standard error
of the outcome-specific Gaussian errors (one per outcome); (8) if
randomY=TRUE, the standard error of the outcome-specific random
intercept (one per outcome); (9) the parameters of each parameterized link
function: 2 for "linear", 4 for "beta", n+2 for "splines" with n nodes.
C. CAUTIONS REGARDING THE USE OF THE PROGRAM
Some caution should be made when using the program. Convergence criteria are very strict as they are based on the derivatives of the log-likelihood in addition to the parameter and log-likelihood stability. In some cases, the program may not converge and reach the maximum number of iterations fixed at 100. In this case, the user should check that parameter estimates at the last iteration are not on the boundaries of the parameter space.
If the parameters are on the boundaries of the parameter space, the identifiability of the model is critical. This may happen especially with splines parameters that may be too close to 0 (lower boundary) or classmb parameters that are too high or low (perfect classification). When identifiability of some parameters is suspected, the program can be run again from the former estimates by fixing the suspected parameters to their value with option posfix. This usually solves the problem. An alternative is to remove the parameters of the Beta or Splines link function from the inverse of the Hessian with option partialH.
If not, the program should be run again with other initial values, with a higher maximum number of iterations or less strict convergence tolerances.
Specifically when investigating heterogeneity (that is with ng>1): (1) As
the log-likelihood of a latent class model can have multiple maxima, a
careful choice of the initial values is crucial for ensuring convergence
toward the global maximum. The program can be run without entering the
vector of initial values (see point 2). However, we recommend to
systematically enter initial values in B and try different sets of
initial values. (2) The automatic choice of initial values we provide
requires the estimation of a preliminary linear mixed model. The user should
be aware that first, this preliminary analysis can take time for large
datatsets and second, that the generated initial values can be very not
likely and even may converge slowly to a local maximum. This is the reason
why several alternatives exist. The vector of initial values can be directly
specified in B the initial values can be generated (automatically or
randomly) from a model with ng=. Finally, function gridsearch
performs an automatic grid search.
D. NUMERICAL INTEGRATION WITH THE THRESHOLD LINK FUNCTION
When dealing only with continuous outcomes, the computation of the likelihood does not require any numerical integration over the random-effects, so that the estimation procedure is relatively fast. When at least one ordinal outcome is modeled, a numerical integration over the random-effects is required in each computation of the individual contribution to the likelihood. This achieved using a Monte-Carlo procedure. We allow three options: the standard Monte-Carlo simulations, as well as antithetic Monte-Carlo and quasi Monte-Carlo methods as proposed in Philipson et al (2020).
The list returned is:
ns |
number of grouping units in the dataset |
ng |
number of latent classes |
loglik |
log-likelihood of the model |
best |
vector of parameter estimates in the same order as
specified in |
V |
if the model converged (conv=1 or 3), vector containing the upper triangle
matrix of variance-covariance estimates of |
gconv |
vector of convergence criteria: 1. on the parameters, 2. on the likelihood, 3. on the derivatives |
conv |
status of convergence: =1 if the convergence criteria were satisfied, =2 if the maximum number of iterations was reached, =4 or 5 if a problem occured during optimisation |
call |
the matched call |
niter |
number of Marquardt iterations |
N |
internal information used in related functions |
idiag |
internal information used in related functions |
pred |
table of individual predictions and residuals in the underlying
latent process scale; it includes marginal predictions (pred_m), marginal
residuals (resid_m), subject-specific predictions (pred_ss) and
subject-specific residuals (resid_ss) averaged over classes, the transformed
observations in the latent process scale (obs) and finally the
class-specific marginal and subject-specific predictions (with the number of
the latent class: pred_m_1,pred_m_2,...,pred_ss_1,pred_ss_2,...). If |
pprob |
table of posterior classification and posterior individual class-membership probabilities |
Xnames |
list of covariates included in the model |
predRE |
table containing individual predictions of the random-effects : a column per random-effect, a line per subject. |
cholesky |
vector containing the estimates of the Cholesky transformed parameters of the variance-covariance matrix of the random-effects |
estimlink |
table containing the simulated values of each outcome and the corresponding estimated link function |
epsY |
definite positive reals used to rescale the markers in (0,1) when the beta link function is used. By default, epsY=0.5. |
linktype |
indicators of link function types: 0 for linear, 1 for beta, 2 for splines and 3 for thresholds |
linknodes |
vector of nodes useful only for the 'splines' link functions |
data |
the original data set (if returndata is TRUE) |
Cecile Proust-Lima and Viviane Philipps
Proust-Lima C, Philipps V, Liquet B (2017). Estimation of Extended Mixed Models Using Latent Classes and Latent Processes: The R Package lcmm. Journal of Statistical Software, 78(2), 1-56. doi:10.18637/jss.v078.i02
Proust and Jacqmin-Gadda (2005). Estimation of linear mixed models with a mixture of distribution for the random-effects. Comput Methods Programs Biomed 78: 165-73.
Proust, Jacqmin-Gadda, Taylor, Ganiayre, and Commenges (2006). A nonlinear model with latent process for cognitive evolution using multivariate longitudinal data. Biometrics 62, 1014-24.
Proust-Lima, Dartigues and Jacqmin-Gadda (2011). Misuse of the linear mixed model when evaluating risk factors of cognitive decline. Amer J Epidemiol 174(9): 1077-88.
Proust-Lima, Amieva, Jacqmin-Gadda (2013). Analysis of multivariate mixed longitudinal data: A flexible latent process approach. Br J Math Stat Psychol 66(3): 470-87.
Commenges, Proust-Lima, Samieri, Liquet (2012). A universal approximate cross-validation criterion and its asymptotic distribution, Arxiv.
Philipson, Hickey, Crowther, Kolamunnage-Dona (2020). Faster Monte Carlo estimation of semiparametric joint models of time-to-event and multivariate longitudinal data. Computational Statistics & Data Analysis 151.
Proust-Lima, Philipps, Perrot, Blanchin, Sebille (2021). Modeling repeated self-reported outcome data: a continuous-time longitudinal Item Response Theory model. https://arxiv.org/abs/2109.13064
postprob, plot.multlcmm, predictL,
predictY lcmm
## Not run: # Latent process mixed model for two curvilinear outcomes. Link functions are # aproximated by I-splines, the first one has 3 nodes (i.e. 1 internal node 8), # the second one has 4 nodes (i.e. 2 internal nodes 12,25) m1 <- multlcmm(Ydep1+Ydep2~1+Time*X2+contrast(X2),random=~1+Time, subject="ID",randomY=TRUE,link=c("4-manual-splines","3-manual-splines"), intnodes=c(8,12,25),data=data_lcmm) # to reduce the computation time, the same model is estimated using # a vector of initial values m1 <- multlcmm(Ydep1+Ydep2~1+Time*X2+contrast(X2),random=~1+Time, subject="ID",randomY=TRUE,link=c("4-manual-splines","3-manual-splines"), intnodes=c(8,12,25),data=data_lcmm, B=c(-1.071, -0.192, 0.106, -0.005, -0.193, 1.012, 0.870, 0.881, 0.000, 0.000, -7.520, 1.401, 1.607 , 1.908, 1.431, 1.082, -7.528, 1.135 , 1.454 , 2.328, 1.052)) # output of the model summary(m1) # estimated link functions plot(m1,which="linkfunction") # variation percentages explained by linear mixed regression VarExpl(m1,data.frame(Time=0)) #### Heterogeneous latent process mixed model with linear link functions #### and 2 latent classes of trajectory m2 <- multlcmm(Ydep1+Ydep2~1+Time*X2,random=~1+Time,subject="ID", link="linear",ng=2,mixture=~1+Time,classmb=~1+X1,data=data_lcmm, B=c( 18,-20.77,1.16,-1.41,-1.39,-0.32,0.16,-0.26,1.69,1.12,1.1,10.8, 1.24,24.88,1.89)) # summary of the estimation summary(m2) # posterior classification postprob(m2) # longitudinal predictions in the outcomes scales for a given profile of covariates newdata <- data.frame(Time=seq(0,5,length=100),X1=0,X2=0,X3=0) predGH <- predictY(m2,newdata,var.time="Time",methInteg=0,nsim=20) head(predGH) ## End(Not run)## Not run: # Latent process mixed model for two curvilinear outcomes. Link functions are # aproximated by I-splines, the first one has 3 nodes (i.e. 1 internal node 8), # the second one has 4 nodes (i.e. 2 internal nodes 12,25) m1 <- multlcmm(Ydep1+Ydep2~1+Time*X2+contrast(X2),random=~1+Time, subject="ID",randomY=TRUE,link=c("4-manual-splines","3-manual-splines"), intnodes=c(8,12,25),data=data_lcmm) # to reduce the computation time, the same model is estimated using # a vector of initial values m1 <- multlcmm(Ydep1+Ydep2~1+Time*X2+contrast(X2),random=~1+Time, subject="ID",randomY=TRUE,link=c("4-manual-splines","3-manual-splines"), intnodes=c(8,12,25),data=data_lcmm, B=c(-1.071, -0.192, 0.106, -0.005, -0.193, 1.012, 0.870, 0.881, 0.000, 0.000, -7.520, 1.401, 1.607 , 1.908, 1.431, 1.082, -7.528, 1.135 , 1.454 , 2.328, 1.052)) # output of the model summary(m1) # estimated link functions plot(m1,which="linkfunction") # variation percentages explained by linear mixed regression VarExpl(m1,data.frame(Time=0)) #### Heterogeneous latent process mixed model with linear link functions #### and 2 latent classes of trajectory m2 <- multlcmm(Ydep1+Ydep2~1+Time*X2,random=~1+Time,subject="ID", link="linear",ng=2,mixture=~1+Time,classmb=~1+X1,data=data_lcmm, B=c( 18,-20.77,1.16,-1.41,-1.39,-0.32,0.16,-0.26,1.69,1.12,1.1,10.8, 1.24,24.88,1.89)) # summary of the estimation summary(m2) # posterior classification postprob(m2) # longitudinal predictions in the outcomes scales for a given profile of covariates newdata <- data.frame(Time=seq(0,5,length=100),X1=0,X2=0,X3=0) predGH <- predictY(m2,newdata,var.time="Time",methInteg=0,nsim=20) head(predGH) ## End(Not run)
The dataset consists in a subsample of the Paquid prospective cohort study. Repeated measures cognitive measures (MMSE, IST, BVRT psychometric tests), physical dependency (HIER) and depression sympatomatology (CESD) were collected over a maximum period of 20 years along with dementia information (age at dementia diagnosis, dementia diagnosis information). Time-independent socio-demographic information is also provided (CEP, male, age_init).
A data frame with 2250 observations over 500 subjects and 12 variables:
subject identification number
score at the Mini-Mental State Examination (MMSE), a psychometric test of global cognitive functioning (integer in range 0-30)
score at the Benton Visual Retention Test (BVRT), a psychometric test of spatial memory (integer in range 0-15)
score at the Isaacs Set Test (IST) truncated at 15 seconds, a test of verbal memory (integer in range 0-40)
score of physical dependency (0=no dependency, 1=mild dependency, 2=moderate dependency, 3=severe dependency)
score of a short self-report scale CES-D designed to measure depressive symptomatology in the general population (integer in range 0-52)
age at the follow-up visit
indicator of positive diagnosis of dementia
age at dementia diagnosis for dem=1 and at last
contact for dem=0
age at entry in the cohort
binary indicator of educational level
(CEP=1 for subjects who graduated from primary school; CEP=0
otherwise)
binary indicator for gender (male=1
for men; male=0 for women)
Letenneur, L., Commenges, D., Dartigues, J. F., & Barberger-Gateau, P. (1994). Incidence of dementia and Alzheimer's disease in elderly community residents of southwestern France. International Journal of Epidemiology, 23 (6), 1256-61.
summary(paquid)summary(paquid)
This function allows a re-ordering of the latent classes of an estimated model.
permut(m, order, estim = TRUE)permut(m, order, estim = TRUE)
m |
an object inheriting from classes |
order |
a vector (integer between 1 and ng) containing the new order of the latent classes |
estim |
optional boolean specifying if the model should estimated with the reordered parameters as initial values. By default, the model is estimated. If FALSE, only the coefficients in |
An object of the same class as m, with reordered classes, or the initial object with new coefficients if estim is FALSE.
Viviane Philipps and Cecile Proust-Lima
## Estimation of a hlme model with 2 classes m2 <- hlme(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3,subject='ID', ng=2,data=data_hlme,B=c(0.11,-0.74,-0.07,20.71, 29.39,-1,0.13,2.45,-0.29,4.5,0.36,0.79,0.97)) ## Exchange class 2 and class 1 m2b <- permut(m2,order=c(2,1))## Estimation of a hlme model with 2 classes m2 <- hlme(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3,subject='ID', ng=2,data=data_hlme,B=c(0.11,-0.74,-0.07,20.71, 29.39,-1,0.13,2.45,-0.29,4.5,0.36,0.79,0.97)) ## Exchange class 2 and class 1 m2b <- permut(m2,order=c(2,1))
This function produces different plots (residuals, goodness-of-fit, estimated link functions, estimated baseline risk/survival and posterior probabilities distributions) of a fitted object of class hlme, lcmm, multlcmm or Jointlcmm.
## S3 method for class 'hlme' plot(x, which = "residuals", var.time, break.times, marg, subset, shades, ...) ## S3 method for class 'lcmm' plot(x, which = "residuals", var.time, break.times, marg, subset, shades, ...) ## S3 method for class 'multlcmm' plot( x, which = "residuals", var.time, break.times, marg, outcome, subset, shades, ... ) ## S3 method for class 'Jointlcmm' plot( x, which = "residuals", var.time, break.times, marg, event, subset, shades, ... ) ## S3 method for class 'mpjlcmm' plot(x, which, event, ...) ## S3 method for class 'externSurv' plot(x, which = "hazard", event, ...) ## S3 method for class 'externX' plot(x, which = "postprob", event, ...)## S3 method for class 'hlme' plot(x, which = "residuals", var.time, break.times, marg, subset, shades, ...) ## S3 method for class 'lcmm' plot(x, which = "residuals", var.time, break.times, marg, subset, shades, ...) ## S3 method for class 'multlcmm' plot( x, which = "residuals", var.time, break.times, marg, outcome, subset, shades, ... ) ## S3 method for class 'Jointlcmm' plot( x, which = "residuals", var.time, break.times, marg, event, subset, shades, ... ) ## S3 method for class 'mpjlcmm' plot(x, which, event, ...) ## S3 method for class 'externSurv' plot(x, which = "hazard", event, ...) ## S3 method for class 'externX' plot(x, which = "postprob", event, ...)
x |
an object inheriting from classes |
which |
a character string indicating the type of plot to produce. For
|
var.time |
for |
break.times |
for |
marg |
for |
subset |
for |
shades |
logical indicating if confidence intervals should be represented with shades. Default to FALSE, confidence intervals are represented as dotted lines. |
... |
other parameters to be passed through to plotting functions.
This includes graphical parameters described in par function and further arguments
legend (character or expression
to appear in the legend. If no legend should be added, |
outcome |
for |
event |
for |
With which="residuals", this function provides the marginal residuals
against the marginal predictions, the subject-specific residuals against the
subject-specific predictions, a normal QQ-plot with confidence bands for the
marginal residuals and a normal QQ-plot with confidence bands for the
subject-specific residuals.
With which="postprob", the function provides the histograms of the
posterior class-membership probabilities stemmed from a Jointlcmm,
lcmm, hlme or multlcmm object.
With which="link" or which="linkfunction", the function
displays the estimated transformation(s) specified in the option link
of lcmm and multlcmm functions. It corresponds to the
(non)linear parameterized link estimated between the oberved longitudinal
outcome and the underlying latent process.
With which="fit", the function provides the class-specific weighted
marginal and subject-specific mean predicted trajectories with time and the
class-specific weighted mean observed trajectories and their 95% confidence
bounds. The predicted and observed class-specific values are weighted means
within each time interval; For each observation or prediction (in the
transformed scale if appropriate), the weights are the class-specific
(posterior with subject-specific or marginal otherwise) probabilities to
belong to the latent class.
With which="baselinerisk" or which="hazard", the function
displays the estimated baseline risk functions for the time-to-event of
interest in each latent class.
With which="survival", the function displays the estimated event-free
probabilities (survival functions) for the time-to-event of interest in each
latent class.
Cecile Proust-Lima, Viviane Philipps and Benoit Liquet
hlme, lcmm, multlcmm,
Jointlcmm
###################### fit, residuals and postprob # estimation of the model m<-lcmm(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3, subject='ID',ng=2,data=data_hlme,B=c(0.41,0.55,-0.18,-0.41, -14.26,-0.34,1.33,13.51,24.65,2.98,1.18,26.26,0.97)) # fit plot(m,which="fit",marg=FALSE,var.time="Time",bty="n") # residuals plot plot(m) # postprob plot plot(m,which="postprob") ###################### fit, linkfunctions #### Estimation of homogeneous mixed models with different assumed link #### functions, a quadratic mean trajectory for the latent process with #### independent random intercept, slope and quadratic slope #### (comparison of linear, Beta and 3 and 5 splines link functions) ## Not run: # linear link function m10<-lcmm(Ydep2~Time+I(Time^2),random=~Time+I(Time^2),subject='ID',ng=1, data=data_lcmm,link="linear", B=c(-0.7454, -0.2031, 0.2715, 0.2916 , 0.6114, -0.0064, 0.0545, 0.0128, 25.3795, 2.2371)) # Beta link function m11<-lcmm(Ydep2~Time+I(Time^2),random=~Time+I(Time^2),subject='ID',ng=1, data=data_lcmm,link="beta",B=c(-0.9109, -0.0831, 0.5194, 0.1910 , 0.8984, -0.0179, -0.0636, 0.0045, 0.5514, -0.7692, 0.7037, 0.0899)) # fit par(mfrow=c(2,1),mar=c(4,4,1,1)) plot(m11,which="fit",var.time="Time",bty="l",ylim=c(-3,0)) plot(m11,which="fit",var.time="Time",marg=FALSE,bty="l",ylim=c(-3,0)) # I-splines with 3 equidistant nodes m12<-lcmm(Ydep2~Time+I(Time^2),random=~Time+I(Time^2),subject='ID',ng=1, data=data_lcmm,link="3-equi-splines",B=c(-0.9272, -0.0753 , 0.5304, 0.1950, 0.9260, -0.0204, -0.0739 , 0.0059, -7.8369, 0.9228 ,-1.4689, 2.0396, 1.8102)) # I-splines with 5 nodes, and interior nodes entered manually m13<-lcmm(Ydep2~Time+I(Time^2),random=~Time+I(Time^2),subject='ID',ng=1, data=data_lcmm,link="5-manual-splines",intnodes=c(10,20,25), B=c(-0.9315, -0.0739 , 0.5254 , 0.1933, 0.9418, -0.0206, -0.0776, 0.0064, -7.8645, 0.7470, 1.2080, 1.5537 , 1.7558 , 1.3386 , 1.0982)) # Plot of estimated different link functions: # (applicable for models that only differ in the "link function" used. # Otherwise, the latent process scale is different and a rescaling # is necessary) plot(m10,which="linkfunction",bty="l") plot(m11,which="linkfunction",bty="l",add=TRUE,col=2) plot(m12,which="linkfunction",bty="l",add=TRUE,col=3) plot(m13,which="linkfunction",bty="l",add=TRUE,col=4) legend("topleft",legend=c("linear","beta","3-Isplines","5-Isplines"), col=1:4,lty=1,bty='n') ## End(Not run) ###################### fit, baselinerisk and survival ## Not run: #### estimation with 3 latent classes (ng=3) - see Jointlcmm #### help for details on the model m3 <- Jointlcmm(fixed= Ydep1~Time*X1,mixture=~Time,random=~Time, classmb=~X3,subject='ID',survival = Surv(Tevent,Event)~ X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",ng=3,data=data_lcmm, B=c(0.7576, 0.4095, -0.8232, -0.2737, 0, 0, 0, 0.2838, -0.6338, 2.6324, 5.3963, -0.0273, 1.3979, 0.8168, -15.041, 10.164, 10.2394, 11.5109, -2.6219, -0.4553, -0.6055, 1.473, -0.0383, 0.8512, 0.0389, 0.2624, 1.4982)) # fit plot(m3,which="fit",var.time="Time",bty="l") plot(m3,which="fit",var.time="Time",marg=FALSE,bty="l",ylim=c(0,15)) # Class-specific predicted baseline risk & survival functions in the # 3-class model retained (for the reference value of the covariates) plot(m3,which="baselinerisk",bty="l") plot(m3,which="baselinerisk",ylim=c(0,5),bty="l") plot(m3,which="survival",bty="l") ## End(Not run)###################### fit, residuals and postprob # estimation of the model m<-lcmm(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3, subject='ID',ng=2,data=data_hlme,B=c(0.41,0.55,-0.18,-0.41, -14.26,-0.34,1.33,13.51,24.65,2.98,1.18,26.26,0.97)) # fit plot(m,which="fit",marg=FALSE,var.time="Time",bty="n") # residuals plot plot(m) # postprob plot plot(m,which="postprob") ###################### fit, linkfunctions #### Estimation of homogeneous mixed models with different assumed link #### functions, a quadratic mean trajectory for the latent process with #### independent random intercept, slope and quadratic slope #### (comparison of linear, Beta and 3 and 5 splines link functions) ## Not run: # linear link function m10<-lcmm(Ydep2~Time+I(Time^2),random=~Time+I(Time^2),subject='ID',ng=1, data=data_lcmm,link="linear", B=c(-0.7454, -0.2031, 0.2715, 0.2916 , 0.6114, -0.0064, 0.0545, 0.0128, 25.3795, 2.2371)) # Beta link function m11<-lcmm(Ydep2~Time+I(Time^2),random=~Time+I(Time^2),subject='ID',ng=1, data=data_lcmm,link="beta",B=c(-0.9109, -0.0831, 0.5194, 0.1910 , 0.8984, -0.0179, -0.0636, 0.0045, 0.5514, -0.7692, 0.7037, 0.0899)) # fit par(mfrow=c(2,1),mar=c(4,4,1,1)) plot(m11,which="fit",var.time="Time",bty="l",ylim=c(-3,0)) plot(m11,which="fit",var.time="Time",marg=FALSE,bty="l",ylim=c(-3,0)) # I-splines with 3 equidistant nodes m12<-lcmm(Ydep2~Time+I(Time^2),random=~Time+I(Time^2),subject='ID',ng=1, data=data_lcmm,link="3-equi-splines",B=c(-0.9272, -0.0753 , 0.5304, 0.1950, 0.9260, -0.0204, -0.0739 , 0.0059, -7.8369, 0.9228 ,-1.4689, 2.0396, 1.8102)) # I-splines with 5 nodes, and interior nodes entered manually m13<-lcmm(Ydep2~Time+I(Time^2),random=~Time+I(Time^2),subject='ID',ng=1, data=data_lcmm,link="5-manual-splines",intnodes=c(10,20,25), B=c(-0.9315, -0.0739 , 0.5254 , 0.1933, 0.9418, -0.0206, -0.0776, 0.0064, -7.8645, 0.7470, 1.2080, 1.5537 , 1.7558 , 1.3386 , 1.0982)) # Plot of estimated different link functions: # (applicable for models that only differ in the "link function" used. # Otherwise, the latent process scale is different and a rescaling # is necessary) plot(m10,which="linkfunction",bty="l") plot(m11,which="linkfunction",bty="l",add=TRUE,col=2) plot(m12,which="linkfunction",bty="l",add=TRUE,col=3) plot(m13,which="linkfunction",bty="l",add=TRUE,col=4) legend("topleft",legend=c("linear","beta","3-Isplines","5-Isplines"), col=1:4,lty=1,bty='n') ## End(Not run) ###################### fit, baselinerisk and survival ## Not run: #### estimation with 3 latent classes (ng=3) - see Jointlcmm #### help for details on the model m3 <- Jointlcmm(fixed= Ydep1~Time*X1,mixture=~Time,random=~Time, classmb=~X3,subject='ID',survival = Surv(Tevent,Event)~ X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",ng=3,data=data_lcmm, B=c(0.7576, 0.4095, -0.8232, -0.2737, 0, 0, 0, 0.2838, -0.6338, 2.6324, 5.3963, -0.0273, 1.3979, 0.8168, -15.041, 10.164, 10.2394, 11.5109, -2.6219, -0.4553, -0.6055, 1.473, -0.0383, 0.8512, 0.0389, 0.2624, 1.4982)) # fit plot(m3,which="fit",var.time="Time",bty="l") plot(m3,which="fit",var.time="Time",marg=FALSE,bty="l",ylim=c(0,15)) # Class-specific predicted baseline risk & survival functions in the # 3-class model retained (for the reference value of the covariates) plot(m3,which="baselinerisk",bty="l") plot(m3,which="baselinerisk",ylim=c(0,5),bty="l") plot(m3,which="survival",bty="l") ## End(Not run)
This function displays the predicted cause-specific cumulative incidences derived from a joint latent class model according to a profile of covariates. does. ~~
## S3 method for class 'cuminc' plot( x, profil = 1, event = 1, add = FALSE, legend, legend.loc = "topleft", ... )## S3 method for class 'cuminc' plot( x, profil = 1, event = 1, add = FALSE, legend, legend.loc = "topleft", ... )
x |
an object of class |
profil |
an integer giving the profile number for which the cumulative incidences are to be plotted. |
event |
an integer giving the event indicator for which the cumulative incidence are to be plotted. |
add |
logical indicating if the curves should be added to an existing plot. Default to FALSE. |
legend |
character or expression to appear in the legend. If no legend
should be added, |
legend.loc |
keyword for the position of the legend from the list
|
... |
other parameters to be passed through to plotting functions |
returns NULL
Viviane Philipps and Cecile Proust-Lima
Jointlcmm, plot.Jointlcmm, cuminc
This function displays plots related to predictive accuracy functions:
epoce and Diffepoce.
## S3 method for class 'Diffepoce' plot(x, ...) ## S3 method for class 'epoce' plot(x, ...)## S3 method for class 'Diffepoce' plot(x, ...) ## S3 method for class 'epoce' plot(x, ...)
x |
an object inheriting from classes |
... |
other parameters to be passed through to plotting functions |
These functions do not apply for the moment with multiple causes of event (competing risks).
For epoce objects, the function displays the EPOCE estimate (either
MPOL or CVPOL) according to the time of prediction. For Diffepoce
objects, plot displays the difference in EPOCE estimates (either MPOL
or CVPOL) and its 95% tracking interval between two joint latent class
models
Returns plots related to epoce and Diffepoce
Cecile Proust-Lima and Viviane Philipps
## Not run: # estimation of the joint latent class model m3 <- Jointlcmm(fixed= Ydep1~Time*X1,mixture=~Time,random=~Time, classmb=~X3,subject='ID',survival = Surv(Tevent,Event)~X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",ng=3,data=data_lcmm, B=c(0.7667, 0.4020, -0.8243, -0.2726, 0.0000, 0.0000, 0.0000, 0.3020, -0.6212, 2.6247, 5.3139, -0.0255, 1.3595, 0.8172, -11.6867, 10.1668, 10.2355, 11.5137, -2.6209, -0.4328, -0.6062, 1.4718, -0.0378, 0.8505, 0.0366, 0.2634, 1.4981)) # predictive accuracy of the model evaluated with EPOCE VecTime <- c(1,3,5,7,9,11,13,15) cvpl <- epoce(m3,var.time="Time",pred.times=VecTime) summary(cvpl) plot(cvpl,bty="l",ylim=c(0,2)) ## End(Not run)## Not run: # estimation of the joint latent class model m3 <- Jointlcmm(fixed= Ydep1~Time*X1,mixture=~Time,random=~Time, classmb=~X3,subject='ID',survival = Surv(Tevent,Event)~X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",ng=3,data=data_lcmm, B=c(0.7667, 0.4020, -0.8243, -0.2726, 0.0000, 0.0000, 0.0000, 0.3020, -0.6212, 2.6247, 5.3139, -0.0255, 1.3595, 0.8172, -11.6867, 10.1668, 10.2355, 11.5137, -2.6209, -0.4328, -0.6062, 1.4718, -0.0378, 0.8505, 0.0366, 0.2634, 1.4981)) # predictive accuracy of the model evaluated with EPOCE VecTime <- c(1,3,5,7,9,11,13,15) cvpl <- epoce(m3,var.time="Time",pred.times=VecTime) summary(cvpl) plot(cvpl,bty="l",ylim=c(0,2)) ## End(Not run)
This function provides a graphical representation of individual dynamic predictions obtained from a joint latent class model and plots simultaneously the observed outcome.
## S3 method for class 'dynpred' plot(x, subject = NULL, landmark = NULL, horizon = NULL, add = FALSE, ...)## S3 method for class 'dynpred' plot(x, subject = NULL, landmark = NULL, horizon = NULL, add = FALSE, ...)
x |
a dynpred object, containing the predicted probabilities of event in a time window, obtained from a joint latent class model. |
subject |
a vector containing the identifiers of the subjects the user wants to display. If NULL (the default), all subjects are plotted. |
landmark |
a vector containing the landmark times from which the probabilities are to be plotted. If NULL (the default), all landmarks are used. If several horizon are specified, only one landmark should be selected. |
horizon |
a vector containing the horizon times from which the probabilities are to be plotted. If NULL (the default), all horizons are used. If several landmarks are specified, only one horizon should be selected. |
add |
logical indicating if the plot should be added to an existing plot. By default (add=FALSE), a new plot is created. |
... |
optional graphical parameters. |
Two types of plot are provided for the moment :
- if one horizon is selected (and one or several landmarks), each prediction is represented by a point at the landmark time. If available, the predictions are surrounded by confidence intervals.
- if several horizons (t1, t2, etc) and only one landmark (s) is selected, a line linking the predictions (placed at abscissa s+t1, s+t2, etc) is drawn. Confidence bands (if available) are represented as dotted lines.
returns NULL
Cecile Proust-Lima, Viviane Philipps
## Not run: ## Joint latent class model with 2 classes : m32 <- Jointlcmm(Ydep1~Time*X1,mixture=~Time,random=~Time,subject="ID", classmb=~X3,ng=2,survival=Surv(Tevent,Event)~X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",data=data_lcmm,B = c(0.64, -0.62, 0, 0, 0.52, 0.81, 0.41, 0.78, 0.1, 0.77, -0.05, 10.43, 11.3, -2.6, -0.52, 1.41, -0.05, 0.91, 0.05, 0.21, 1.5)) ## Predictions at landmark 10 and 12 for horizon 3, 5 and 10 for two subjects : dynpred.m32 <- dynpred(m32,landmark=c(10,12),horizon=c(3,5,10),var.time="Time", fun.time=function(x){10*x},newdata=data_lcmm[4:8,],draws=TRUE,ndraws=2000) ## Plot of the predictions at landmark 10 for horizon 3,5,10 : plot(dynpred.m32,landmark=10) ## Plot of the predictions at landmark 10 and 12 for horizon 3 : plot(dynpred.m32,horizon=3) ## End(Not run)## Not run: ## Joint latent class model with 2 classes : m32 <- Jointlcmm(Ydep1~Time*X1,mixture=~Time,random=~Time,subject="ID", classmb=~X3,ng=2,survival=Surv(Tevent,Event)~X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",data=data_lcmm,B = c(0.64, -0.62, 0, 0, 0.52, 0.81, 0.41, 0.78, 0.1, 0.77, -0.05, 10.43, 11.3, -2.6, -0.52, 1.41, -0.05, 0.91, 0.05, 0.21, 1.5)) ## Predictions at landmark 10 and 12 for horizon 3, 5 and 10 for two subjects : dynpred.m32 <- dynpred(m32,landmark=c(10,12),horizon=c(3,5,10),var.time="Time", fun.time=function(x){10*x},newdata=data_lcmm[4:8,],draws=TRUE,ndraws=2000) ## Plot of the predictions at landmark 10 for horizon 3,5,10 : plot(dynpred.m32,landmark=10) ## Plot of the predictions at landmark 10 and 12 for horizon 3 : plot(dynpred.m32,horizon=3) ## End(Not run)
This function plots the information functions stemmed
from a lcmm or multlcmm object with ordinal outcomes modeled via threshold links.
## S3 method for class 'ItemInfo' plot( x, which = "ItemInfo", outcome = "all", legend.loc = "topright", legend = NULL, add = FALSE, shades = TRUE, ... )## S3 method for class 'ItemInfo' plot( x, which = "ItemInfo", outcome = "all", legend.loc = "topright", legend = NULL, add = FALSE, shades = TRUE, ... )
x |
an object inheriting from classes |
which |
character specifying the values to plot. Should be one of 'ItemInfo' for the Fisher information function of the ordinal outcomes, 'LevelInfo' for the information of each item's level or 'LevelProb' for the probability of the item's levels. Default to 'ItemInfo'. |
outcome |
character specifying the outcome to consider. Default to "all". |
legend.loc |
keyword for the position of the legend from the list
|
legend |
character or expression to appear in the legend. If no legend
should be added, |
add |
logical indicating if the curves should be added to an existing plot. Default to FALSE. |
shades |
logical indicating if confidence intervals should be represented with shades. Default to FALSE, the confidence intervals are represented with dotted lines. |
... |
other parameters to be passed through to plotting functions or to legend |
Viviane Philipps and Cecile Proust-Lima
This function provides the class-specific predicted trajectories stemmed
from a hlme, lcmm, multlcmm or Jointlcmm object.
## S3 method for class 'predictL' plot(x, legend.loc = "topright", legend, add = FALSE, shades = FALSE, ...) ## S3 method for class 'predictY' plot( x, outcome = 1, legend.loc = "topright", legend, add = FALSE, shades = FALSE, ... ) ## S3 method for class 'predictYcond' plot(x, legend.loc = "topleft", legend, add = FALSE, shades = TRUE, ...)## S3 method for class 'predictL' plot(x, legend.loc = "topright", legend, add = FALSE, shades = FALSE, ...) ## S3 method for class 'predictY' plot( x, outcome = 1, legend.loc = "topright", legend, add = FALSE, shades = FALSE, ... ) ## S3 method for class 'predictYcond' plot(x, legend.loc = "topleft", legend, add = FALSE, shades = TRUE, ...)
x |
an object inheriting from classes |
legend.loc |
keyword for the position of the legend from the list
|
legend |
character or expression to appear in the legend. If no legend
should be added, |
add |
logical indicating if the curves should be added to an existing plot. Default to FALSE. |
shades |
logical indicating if confidence intervals should be represented with shades. Default to FALSE, the confidence intervals are represented with dotted lines. |
... |
other parameters to be passed through to plotting functions or to legend |
outcome |
for |
Cecile Proust-Lima, Benoit Liquet and Viviane Philipps
hlme, lcmm, Jointlcmm,
multlcmm
################# Prediction from linear latent class model ## fitted model m<-lcmm(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3, subject='ID',ng=2,data=data_hlme,B=c(0.41,0.55,-0.18,-0.41, -14.26,-0.34,1.33,13.51,24.65,2.98,1.18,26.26,0.97)) ## newdata for predictions plot newdata<-data.frame(Time=seq(0,5,length=100), X1=rep(0,100),X2=rep(0,100),X3=rep(0,100)) plot(predictL(m,newdata,var.time="Time"),legend.loc="right",bty="l") ## data from the first subject for predictions plot firstdata<-data_hlme[1:3,] plot(predictL(m,firstdata,var.time="Time"),legend.loc="right",bty="l") ## Not run: ################# Prediction from a joint latent class model ## fitted model - see help of Jointlcmm function for details on the model m3 <- Jointlcmm(fixed= Ydep1~Time*X1,mixture=~Time,random=~Time, classmb=~X3,subject='ID',survival = Surv(Tevent,Event)~X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",ng=3,data=data_lcmm, B=c(0.7576, 0.4095, -0.8232, -0.2737, 0, 0, 0, 0.2838, -0.6338, 2.6324, 5.3963, -0.0273, 1.398, 0.8168, -15.041, 10.164, 10.2394, 11.5109, -2.6219, -0.4553, -0.6055, 1.473, -0.0383, 0.8512, 0.0389, 0.2624, 1.4982)) # class-specific predicted trajectories #(with characteristics of subject ID=193) data <- data_lcmm[data_lcmm$ID==193,] plot(predictY(m3,newdata=data,var.time="Time"),bty="l") ## End(Not run)################# Prediction from linear latent class model ## fitted model m<-lcmm(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3, subject='ID',ng=2,data=data_hlme,B=c(0.41,0.55,-0.18,-0.41, -14.26,-0.34,1.33,13.51,24.65,2.98,1.18,26.26,0.97)) ## newdata for predictions plot newdata<-data.frame(Time=seq(0,5,length=100), X1=rep(0,100),X2=rep(0,100),X3=rep(0,100)) plot(predictL(m,newdata,var.time="Time"),legend.loc="right",bty="l") ## data from the first subject for predictions plot firstdata<-data_hlme[1:3,] plot(predictL(m,firstdata,var.time="Time"),legend.loc="right",bty="l") ## Not run: ################# Prediction from a joint latent class model ## fitted model - see help of Jointlcmm function for details on the model m3 <- Jointlcmm(fixed= Ydep1~Time*X1,mixture=~Time,random=~Time, classmb=~X3,subject='ID',survival = Surv(Tevent,Event)~X1+mixture(X2), hazard="3-quant-splines",hazardtype="PH",ng=3,data=data_lcmm, B=c(0.7576, 0.4095, -0.8232, -0.2737, 0, 0, 0, 0.2838, -0.6338, 2.6324, 5.3963, -0.0273, 1.398, 0.8168, -15.041, 10.164, 10.2394, 11.5109, -2.6219, -0.4553, -0.6055, 1.473, -0.0383, 0.8512, 0.0389, 0.2624, 1.4982)) # class-specific predicted trajectories #(with characteristics of subject ID=193) data <- data_lcmm[data_lcmm$ID==193,] plot(predictY(m3,newdata=data,var.time="Time"),bty="l") ## End(Not run)
hlme, lcmm,
multlcmm or Jointlcmm estimationThis function provides informations about the posterior classification
stemmed from a hlme, lcmm, multlcmm, Jointlcmm,
mpjlcmm, externSurv or externX object.
postprob(x, threshold = c(0.7, 0.8, 0.9), ...)postprob(x, threshold = c(0.7, 0.8, 0.9), ...)
x |
an object inheriting from classes |
threshold |
optional vector of thresholds for the posterior probabilities |
... |
further arguments to be passed to or from other methods. They are ignored in this function. |
This function provides the number of subjects classified a posteriori in
each latent class, the percentage of subjects classified with a posterior
probability above a certain threshold, and the classification table that
contains the mean of the posterior probability of belonging to each latent
class over the subjects classified in each of the latent classes. This table
aims at evaluating the quality of the posterior classification. For
hlme, lcmm objects, the posterior classification and the
classification table are derived from the posterior class-membership
probabilities given the vector of repeated measures that are contained in
pprob output matrix. For a Jointlcmm object, the first posterior
classification and the classification table are derived from the posterior
class-membership probabilities given the vector of repeated measures and the
time-to-event information (that are contained in columns probYT1, probYT2,
etc in pprob output matrix). The second posterior classification is derived
from the posterior class-membership probabilities given only the vector of
repeated measures (that are contained in columns probY1, probY2, etc in
pprob output matrix).
A list containing the posterior classification, the posterior classification table and the percentage of subjects classified with a posterior probability above the given thresholds.
This function can only be used with latent class mixed models and joint latent class mixed models that include at least 2 latent classes
Cecile Proust-Lima, Benoit Liquet and Viviane Philipps
Jointlcmm, lcmm,
hlme, plot.lcmm
m<-lcmm(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3, subject='ID',ng=2,data=data_hlme,B=c(0.41,0.55,-0.18,-0.41, -14.26,-0.34,1.33,13.51,24.65,2.98,1.18,26.26,0.97)) postprob(m)m<-lcmm(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3, subject='ID',ng=2,data=data_hlme,B=c(0.41,0.55,-0.18,-0.41, -14.26,-0.34,1.33,13.51,24.65,2.98,1.18,26.26,0.97)) postprob(m)
This function provides the posterior classification and posterior individual class-membership probabilities for external data.
predictClass(model, newdata, subject = NULL)predictClass(model, newdata, subject = NULL)
model |
an object inheriting from class |
newdata |
data frame containing the data from which predictions are to be computed. The data frame should include at least all the covariates listed in model$Xnames2, the outcome(s) and the grouping structure. Names should match exactly. |
subject |
character specifying the name of the grouping structure. If NULL (the default), the same as in the model will be used. |
a matrix with 2+ng columns: the grouping structure, the predicted class and the ng posterior class-membership probabilities.
Sasha Cuau, Viviane Philipps, Cecile Proust-Lima
## Not run: library(NormPsy) paquid$normMMSE <- normMMSE(paquid$MMSE) paquid$age65 <- (paquid$age - 65)/10 m2b <- hlme(normMMSE ~ age65+I(age65^2)+CEP, random =~ age65+I(age65^2), subject = 'ID', data = paquid, ng = 2, mixture =~ age65+I(age65^2), B = c(0, 60, 40, 0, -4, 0, -10, 10, 212.869397, -216.421323,456.229910, 55.713775, -145.715516, 59.351000, 10.072221)) predictClass(m2b, newdata=paquid[1:6,]) ## End(Not run)## Not run: library(NormPsy) paquid$normMMSE <- normMMSE(paquid$MMSE) paquid$age65 <- (paquid$age - 65)/10 m2b <- hlme(normMMSE ~ age65+I(age65^2)+CEP, random =~ age65+I(age65^2), subject = 'ID', data = paquid, ng = 2, mixture =~ age65+I(age65^2), B = c(0, 60, 40, 0, -4, 0, -10, 10, 212.869397, -216.421323,456.229910, 55.713775, -145.715516, 59.351000, 10.072221)) predictClass(m2b, newdata=paquid[1:6,]) ## End(Not run)
lcmm, Jointlcmm and multlcmm objectsThis function provides a matrix containing the class-specific predicted
trajectories computed in the latent process scale, that is the latent
process underlying the curvilinear outcome(s), for a profile of covariates
specified by the user. This function applies only to lcmm and
multlcmm objects. The function plot.predict provides directly
the plot of these class-specific predicted trajectories. The function
predictY provides the class-specific predicted trajectories computed
in the natural scale of the outcome(s).
predictL(x, newdata, var.time, na.action = 1, confint = FALSE, ...)predictL(x, newdata, var.time, na.action = 1, confint = FALSE, ...)
x |
an object inheriting from class |
newdata |
data frame containing the data from which predictions are
computed. The data frame should include at least all the covariates listed
in x$Xnames2. Names in the data frame should be exactly x$Xnames2 that are
the names of covariates specified in |
var.time |
A character string containing the name of the variable that corresponds to time in the data frame (x axis in the plot). |
na.action |
Integer indicating how NAs are managed. The default is 1 for 'na.omit'. The alternative is 2 for 'na.fail'. Other options such as 'na.pass' or 'na.exclude' are not implemented in the current version. |
confint |
logical indicating if confidence should be provided. Default to FALSE. |
... |
further arguments to be passed to or from other methods. They are ignored in this function. |
An object of class predictL with values :
- pred : a matrix containing the class-specific predicted values in
the latent process scale, the lower and the upper limits of the confidence
intervals (if calculated).
- times : the var.time variable from newdata
Cecile Proust-Lima, Viviane Philipps
#### Prediction from a 2-class model with a Splines link function ## Not run: ## fitted model m<-lcmm(Ydep2~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3, subject='ID',ng=2,data=data_lcmm,link="splines",B=c( -0.175, -0.191, 0.654, -0.443, -0.345, -1.780, 0.913, 0.016, 0.389, 0.028, 0.083, -7.349, 0.722, 0.770, 1.376, 1.653, 1.640, 1.285)) summary(m) ## predictions for times from 0 to 5 for X1=0 newdata<-data.frame(Time=seq(0,5,length=100), X1=rep(0,100),X2=rep(0,100),X3=rep(0,100)) predictL(m,newdata,var.time="Time") ## predictions for times from 0 to 5 for X1=1 newdata$X1 <- 1 predictY(m,newdata,var.time="Time") ## End(Not run)#### Prediction from a 2-class model with a Splines link function ## Not run: ## fitted model m<-lcmm(Ydep2~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3, subject='ID',ng=2,data=data_lcmm,link="splines",B=c( -0.175, -0.191, 0.654, -0.443, -0.345, -1.780, 0.913, 0.016, 0.389, 0.028, 0.083, -7.349, 0.722, 0.770, 1.376, 1.653, 1.640, 1.285)) summary(m) ## predictions for times from 0 to 5 for X1=0 newdata<-data.frame(Time=seq(0,5,length=100), X1=rep(0,100),X2=rep(0,100),X3=rep(0,100)) predictL(m,newdata,var.time="Time") ## predictions for times from 0 to 5 for X1=1 newdata$X1 <- 1 predictY(m,newdata,var.time="Time") ## End(Not run)
lcmm,
Jointlcmm and multlcmm
This function provides 95% confidence intervals around the estimated
transformation given in estimlink attribute of lcmm, Jointlcmm
and multlcmm objects. It can also be used to evaluate the link
functions at other values than those given in attribute estimlink of
lcmm, Jointlcmm or multlcmm object.
predictlink(x, ndraws, Yvalues, ...)predictlink(x, ndraws, Yvalues, ...)
x |
an object inheriting from classes |
ndraws |
the number of draws that should be generated to approximate the posterior distribution of the transformed values. By default, ndraws=2000. |
Yvalues |
a vector (for a |
... |
other parameters (ignored) |
An object of class predictlink with values :
- pred :
For a lcmm or Jointlcmm object, a data frame containing the
values at which the transformation is evaluated, the transformed values and
the lower and the upper limits of the confidence intervals (if ndraws>0).
For a multlcmm object, a data frame containing the indicator of the
outcome, the values at which the transformations are evaluated,the
transformed values and the lower and the upper limits of the confidence
intervals (if ndraws>0).
- object : the object from which the link function is predicted
Cecile Proust-Lima and Viviane Philipps
lcmm, multlcmm,
plot.lcmm, plot.predictlink
## Not run: ## Univariate mixed model with splines link funciton m14<-lcmm(Ydep2~Time+I(Time^2),random=~Time,subject='ID',ng=1, data=data_lcmm,link="5-manual-splines",intnodes=c(10,20,25), B=c(-0.89255, -0.09715, 0.56335, 0.21967, 0.61937, -7.90261, 0.75149, -1.22357, 1.55832, 1.75324, 1.33834, 1.0968)) ##Transformed values of several scores and their confidence intervals transf.m14 <- predictlink(m14,ndraws=2000,Yvalues=c(0,1,7:30)) plot(transf.m14) ## Multivariate mixed model with splines link functions m1 <- multlcmm(Ydep1+Ydep2~1+Time*X2+contrast(X2),random=~1+Time, subject="ID",randomY=TRUE,link=c("4-manual-splines","3-manual-splines"), intnodes=c(8,12,25),data=data_lcmm, B=c(-1.071, -0.192, 0.106, -0.005, -0.193, 1.012, 0.870, 0.881, 0.000, 0.000, -7.520, 1.401, 1.607 , 1.908, 1.431, 1.082, -7.528, 1.135 , 1.454 , 2.328, 1.052)) ##Confidence intervals for the transformed values (given in m1$estimlink) transf.m1 <- predictlink(m1,ndraws=200) plot(transf.m1) ## End(Not run)## Not run: ## Univariate mixed model with splines link funciton m14<-lcmm(Ydep2~Time+I(Time^2),random=~Time,subject='ID',ng=1, data=data_lcmm,link="5-manual-splines",intnodes=c(10,20,25), B=c(-0.89255, -0.09715, 0.56335, 0.21967, 0.61937, -7.90261, 0.75149, -1.22357, 1.55832, 1.75324, 1.33834, 1.0968)) ##Transformed values of several scores and their confidence intervals transf.m14 <- predictlink(m14,ndraws=2000,Yvalues=c(0,1,7:30)) plot(transf.m14) ## Multivariate mixed model with splines link functions m1 <- multlcmm(Ydep1+Ydep2~1+Time*X2+contrast(X2),random=~1+Time, subject="ID",randomY=TRUE,link=c("4-manual-splines","3-manual-splines"), intnodes=c(8,12,25),data=data_lcmm, B=c(-1.071, -0.192, 0.106, -0.005, -0.193, 1.012, 0.870, 0.881, 0.000, 0.000, -7.520, 1.401, 1.607 , 1.908, 1.431, 1.082, -7.528, 1.135 , 1.454 , 2.328, 1.052)) ##Confidence intervals for the transformed values (given in m1$estimlink) transf.m1 <- predictlink(m1,ndraws=200) plot(transf.m1) ## End(Not run)
The function computes the predicted values of the random effects given observed data provided in input. With multiple latent classes, these predictions are averaged over classes using the posterior class-membership probabilities.
predictRE(model, newdata, subject = NULL)predictRE(model, newdata, subject = NULL)
model |
an object inheriting from class |
newdata |
data frame containing the data from which predictions are to be computed. The data frame should include at least all the covariates listed in model$Xnames2, the marker(s) values and the grouping structure. Names should match exactly the names of the variables in the model. |
subject |
character specifying the name of the grouping structure. If NULL (the default), the same as in the model will be used. |
a matrix containing the grouping structure and the predicted random-effects.
Sasha Cuau, Viviane Philipps, Cecile Proust-Lima
## Not run: library(NormPsy) paquid$normMMSE <- normMMSE(paquid$MMSE) paquid$age65 <- (paquid$age - 65)/10 m2b <- hlme(normMMSE ~ age65+I(age65^2)+CEP, random =~ age65+I(age65^2), subject = 'ID', data = paquid, ng = 2, mixture =~ age65+I(age65^2), B = c(0, 60, 40, 0, -4, 0, -10, 10, 212.869397, -216.421323,456.229910, 55.713775, -145.715516, 59.351000, 10.072221)) predictRE(m2b,newdata=paquid[1:6,]) ## End(Not run)## Not run: library(NormPsy) paquid$normMMSE <- normMMSE(paquid$MMSE) paquid$age65 <- (paquid$age - 65)/10 m2b <- hlme(normMMSE ~ age65+I(age65^2)+CEP, random =~ age65+I(age65^2), subject = 'ID', data = paquid, ng = 2, mixture =~ age65+I(age65^2), B = c(0, 60, 40, 0, -4, 0, -10, 10, 212.869397, -216.421323,456.229910, 55.713775, -145.715516, 59.351000, 10.072221)) predictRE(m2b,newdata=paquid[1:6,]) ## End(Not run)
hlme,
lcmm, multlcmm or Jointlcmm object in the natural scale
of the longitudinal outcome(s) computed from a profile of covariates (marginal) or
individual data (subject specific in case of hlme).For hlme and Jointlcmm objects, the function computes the
predicted values of the longitudinal marker (in each latent class of ng>1) for a
specified profile of covariates. For lcmm and multlcmm
objects, the function computes predicted values in the natural scale of the
outcomes for a specified profile of covariates. For linear and threshold
links, the predicted values are computed analytically. For splines and Beta
links, a Gauss-Hermite or Monte-Carlo integration are used to numerically
compute the predictions. In addition, for any type of link function,
confidence bands (and median) can be computed by a Monte Carlo approximation
of the posterior distribution of the predicted values.
## S3 method for class 'Jointlcmm' predictY( x, newdata, var.time, methInteg = 0, nsim = 20, draws = FALSE, ndraws = 2000, na.action = 1, ... ) ## S3 method for class 'hlme' predictY( x, newdata, var.time, draws = FALSE, na.action = 1, marg = TRUE, subject = NULL, ... ) ## S3 method for class 'lcmm' predictY( x, newdata, var.time, methInteg = 0, nsim = 20, draws = FALSE, ndraws = 2000, na.action = 1, ... ) predictY(x, newdata, var.time, ...) ## S3 method for class 'multlcmm' predictY( x, newdata, var.time, methInteg = 0, nsim = 20, draws = FALSE, ndraws = 2000, na.action = 1, ... )## S3 method for class 'Jointlcmm' predictY( x, newdata, var.time, methInteg = 0, nsim = 20, draws = FALSE, ndraws = 2000, na.action = 1, ... ) ## S3 method for class 'hlme' predictY( x, newdata, var.time, draws = FALSE, na.action = 1, marg = TRUE, subject = NULL, ... ) ## S3 method for class 'lcmm' predictY( x, newdata, var.time, methInteg = 0, nsim = 20, draws = FALSE, ndraws = 2000, na.action = 1, ... ) predictY(x, newdata, var.time, ...) ## S3 method for class 'multlcmm' predictY( x, newdata, var.time, methInteg = 0, nsim = 20, draws = FALSE, ndraws = 2000, na.action = 1, ... )
x |
an object inheriting from class |
newdata |
data frame containing the data from which predictions are to be
computed. The data frame should include at least all the covariates listed
in x$Xnames2. Names in the data frame should be exactly x$Xnames2 that are
the names of covariates specified in |
var.time |
A character string containing the name of the variable that corresponds to time in the data frame (x axis in the plot). |
methInteg |
optional integer specifying the type of numerical integration required only for predictions with splines or Beta link functions. Value 0 (by default) specifies a Gauss-Hermite integration which is very rapid but neglects the correlation between the predicted values (in presence of random-effects). Value 1 refers to a Monte-Carlo integration which is slower but correctly account for the correlation between the predicted values. |
nsim |
For a |
draws |
optional boolean specifying whether median and confidence bands
of the predicted values should be computed (TRUE) - whatever the type of
link function. For a |
ndraws |
For a |
na.action |
Integer indicating how NAs are managed. The default is 1 for 'na.omit'. The alternative is 2 for 'na.fail'. Other options such as 'na.pass' or 'na.exclude' are not implemented in the current version. |
... |
further arguments to be passed to or from other methods. Only the argument 'median' will be used, other are ignored. 'median' should be a logical indicating whether the median should be computed. By default, the mean value is computed. |
marg |
Optional boolean specifying whether the
predictions are marginal (the default) or subject-specific (marg=FALSE). marge=FALSE
only works with |
subject |
For a |
An object of class predictY with values :
- pred : a matrix with the same rows (number and order) as in
newdata.
For hlme objects and lcmm or Jointlcmm with
draws=FALSE, returns a matrix with ng columns corresponding to the ng
class-specific vectors of predicted values computed at the point estimate
For objects of class lcmm or Jointlcmm with draws=TRUE,
returns a matrix with ng*3 columns representing the ng class-specific 50%,
2.5% and 97.5% percentiles of the approximated posterior distribution of
the class-specific predicted values.
For objects of class multlcmm with draws=FALSE, returns a
matrix with ng+1 columns: the first column indicates the name of the outcome
which is predicted and the ng subsequent columns correspond to the ng
class-specific vectors of predicted values computed at the point estimate
For objects of class multlcmm with draws=TRUE, returns a
matrix with ng*3+1 columns: the first column indicates the name of the
outcome which is predicted and the ng*3 subsequent columns correspond to the
ng class-specific 50%, 2.5% and 97.5% percentiles of the approximated
posterior distribution of the class-specific predicted values.
For objects of class hlme with marg=FALSE, returns a matrix
with 2+ng columns : the grouping structure, subject-specific predictions (pred_ss) averaged
over classes and the class-specific subject-specific predictions (with the
number of the latent class: pred_ss_1,pred_ss_2,...)
- times : the var.time variable from newdata
Cecile Proust-Lima, Viviane Philipps, Sasha Cuau
lcmm, multlcmm, hlme,
Jointlcmm
#### Prediction from a 2-class model with a Splines link function ## Not run: ## fitted model m<-lcmm(Ydep2~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3, subject='ID',ng=2,data=data_lcmm,link="splines",B=c( -0.175, -0.191, 0.654, -0.443, -0.345, -1.780, 0.913, 0.016, 0.389, 0.028, 0.083, -7.349, 0.722, 0.770, 1.376, 1.653, 1.640, 1.285)) summary(m) ## predictions for times from 0 to 5 for X1=0 newdata<-data.frame(Time=seq(0,5,length=100), X1=rep(0,100),X2=rep(0,100),X3=rep(0,100)) pred0 <- predictY(m,newdata,var.time="Time") head(pred0) ## Option draws=TRUE to compute a MonteCarlo # approximation of the predicted value distribution # (quite long with ndraws=2000 by default) \dontrun{ pred0MC <- predictY(m,newdata,draws=TRUE,var.time="Time") } ## predictions for times from 0 to 5 for X1=1 newdata$X1 <- 1 pred1 <- predictY(m,newdata,var.time="Time") ## Option draws=TRUE to compute a MonteCarlo # approximation of the predicted value distribution # (quite long with ndraws=2000 by default) \dontrun{ pred1MC <- predictY(m,newdata,draws=TRUE,var.time="Time") } ## End(Not run)#### Prediction from a 2-class model with a Splines link function ## Not run: ## fitted model m<-lcmm(Ydep2~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3, subject='ID',ng=2,data=data_lcmm,link="splines",B=c( -0.175, -0.191, 0.654, -0.443, -0.345, -1.780, 0.913, 0.016, 0.389, 0.028, 0.083, -7.349, 0.722, 0.770, 1.376, 1.653, 1.640, 1.285)) summary(m) ## predictions for times from 0 to 5 for X1=0 newdata<-data.frame(Time=seq(0,5,length=100), X1=rep(0,100),X2=rep(0,100),X3=rep(0,100)) pred0 <- predictY(m,newdata,var.time="Time") head(pred0) ## Option draws=TRUE to compute a MonteCarlo # approximation of the predicted value distribution # (quite long with ndraws=2000 by default) \dontrun{ pred0MC <- predictY(m,newdata,draws=TRUE,var.time="Time") } ## predictions for times from 0 to 5 for X1=1 newdata$X1 <- 1 pred1 <- predictY(m,newdata,var.time="Time") ## Option draws=TRUE to compute a MonteCarlo # approximation of the predicted value distribution # (quite long with ndraws=2000 by default) \dontrun{ pred1MC <- predictY(m,newdata,draws=TRUE,var.time="Time") } ## End(Not run)
lcmm, multlcmm or Jointlcmm
object in the natural scale of the longitudinal outcome(s) for specified
latent process values.The function computes the predicted values of the longitudinal markers in their natural scale for specified values of the latent process. For splines and Beta links, a Gauss-Hermite integration is used to numerically compute the predictions. In addition, for any type of link function, confidence bands (and median) can be computed by a Monte Carlo approximation of the posterior distribution of the predicted values.
predictYcond( x, lprocess, condRE_Y = FALSE, nsim = 200, draws = FALSE, ndraws = 2000, ... )predictYcond( x, lprocess, condRE_Y = FALSE, nsim = 200, draws = FALSE, ndraws = 2000, ... )
x |
an object inheriting from class |
lprocess |
numeric vector containing the latent process values at which the predictions should be computed. |
condRE_Y |
for multlcmm objects only, logical indicating if the predictions are conditional to the outcome specific random effects or not. Default to FALSE, the predictions are marginal to these random effects. |
nsim |
number of points used in the numerical integration (Monte-Carlo) with splines or Beta link functions. nsim should be relatively important (nsim=200 by default). |
draws |
optional boolean specifying whether median and confidence bands of the predicted values should be computed (TRUE) - whatever the type of link function. A Monte Carlo approximation of the posterior distribution of the predicted values is computed and the median, 2.5% and 97.5% percentiles are given. Otherwise, the predicted values are computed at the point estimate. By default, draws=FALSE. |
ndraws |
if draws=TRUE, ndraws specifies the number of draws that should be generated to approximate the posterior distribution of the predicted values. By default, ndraws=2000. |
... |
further arguments to be passed to or from other methods. They are ignored in this function. |
An object of class predictYcond with values :
- pred :
If draws=FALSE, returns a matrix with 3 columns : the first column indicates the
name of the outcome, the second indicates the latent process value and the last
is the computed prediction.
If draws=TRUE, returns a matrix with 5 columns : the name of the outcome, the
latent process value and the 50%, 2.5% and 97.5% percentiles of the approximated
posterior distribution of predicted values.
- object : the model from which the predictions are computed.
Cecile Proust-Lima, Viviane Philipps
## Not run: m12 <- lcmm(Ydep2~Time+I(Time^2),random=~Time,subject='ID',ng=1, data=data_lcmm,link="3-equi-splines") predm12 <- predictYcond(m12,lprocess=seq(-8,2,length.out=100),draws=TRUE) plot(predm12) ## End(Not run)## Not run: m12 <- lcmm(Ydep2~Time+I(Time^2),random=~Time,subject='ID',ng=1, data=data_lcmm,link="3-equi-splines") predm12 <- predictYcond(m12,lprocess=seq(-8,2,length.out=100),draws=TRUE) plot(predm12) ## End(Not run)
hlme, lcmm,
Jointlcmm,multlcmm, epoce or Diffepoce objectsThe function provides a brief summary of hlme,
lcmm,multlcmm or Jointlcmm estimations, and
epoce or Diffepoce computations.
## S3 method for class 'lcmm' print(x, ...)## S3 method for class 'lcmm' print(x, ...)
x |
an object inheriting from classes |
... |
further arguments to be passed to or from other methods. They are ignored in this function. |
Cecile Proust-Lima, Viviane Philipps, Amadou Diakite and Benoit Liquet
hlme, lcmm, Jointlcmm,
epoce, Diffepoce
The data mimic the PREDIALA study described and analyzed in Proust-Lima et al (2021 - https://arxiv.org/abs/2109.13064). The study aims to describe the trajectories of depressive symptomatology of patients suffering end-stage renal disease and registered on the renal transplant waiting list. Repeated measures of anxiety and depression (HADS) were simulated at different times of measurement for 561 subjects. Four time-independent covariates were also generated: group (dialyzed or pre-emptive), sex and age at entry in the cohort and time on the waiting list at entry in the cohort.
A data frame with 1140 observations on the following 13 variables.
group with 0=dialyzed and 1=preemptive
sex with 0=woman and 1=man
age at entry in the cohort
item 2 of HADS measuring depression
item 4 of HADS measuring depression
item 6 of HADS measuring depression
item 8 of HADS measuring depression
item 10 of HADS measuring depression
item 12 of HADS measuring depression
item 14 of HADS measuring depression
subject identification number
time of measurement
time on the waiting list at entry in the cohort
This function simulates a sample according to a model estimated with hlme,
lcmm, multlcmm or Jointlcmm functions.
## S3 method for class 'lcmm' simulate( object, nsim, seed, times, tname = NULL, n, Xbin = NULL, Xcont = NULL, entry = 0, dropout = NULL, pMCAR = 0, ... )## S3 method for class 'lcmm' simulate( object, nsim, seed, times, tname = NULL, n, Xbin = NULL, Xcont = NULL, entry = 0, dropout = NULL, pMCAR = 0, ... )
object |
an object of class |
nsim |
not used (for compatibility with stats::simulate). The function simulates only one sample |
seed |
the random seed |
times |
either a data frame with 2 columns containing IDs and measurement times, or a vector of length 4 specifying the minimal and maximum measurement times, the spacing between 2 consecutive visits and the margin around this spacing |
tname |
the name of the variable representing the measurement times in |
n |
number of subjects to simulate. Required only if times is not a data frame. |
Xbin |
an optional named list giving the probabilities of the binary
covariates to simulate. The list's names should match the binary covariate's names
used in |
Xcont |
an optional named list giving the mean and standard deviation
of the Gaussian covariates to simulate. The list's names should match the
continuous covariate's names used in |
entry |
expression to simulate a subject's entry time. Default to 0. |
dropout |
expression to simulate a subject's time to dropout. Default to NULL, no dropout is considered. |
pMCAR |
optional numeric giving an observation's probability to be missing. Default to 0, no missing data are introduced. |
... |
additionnal options. None is used yet. |
a data frame with one line per observation and one column per variable. Variables appears in the following order : subject id, measurement time, entry time, binary covariates, continuous covariates, longitudinal outcomes, latent class, entry time, survival time, event indicator.
Viviane Philipps and Cecile Proust-Lima
## estimation of a 2 classes mixed model m2 <- hlme(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3,subject='ID', ng=2,data=data_hlme,B=c(0.11,-0.74,-0.07,20.71, 29.39,-1,0.13,2.45,-0.29,4.5,0.36,0.79,0.97)) ## simulate according to model m2 with same number of subjects and ## same measurement times as in data_lcmm. Binary covariates X1 and X2 are simulated ## according to a Bernoulli distribution with probability p=0.5, continuous covariate ## X3 is simulated according to a Gaussian distribution with mean=1 and sd=1 : dsim1 <- simulate(m2, times=data_hlme[,c("ID","Time")], Xbin=list(X1=0.5, X2=0.5), Xcont=list(X3=c(1,1))) ## simulate a dataset of 300 subjects according to the same model ## with new observation times, equally spaced and ranging from 0 to 3 : dsim2 <- simulate(m2, times=c(0,3,0.5,0), n=300, tname="Time", Xbin=list(X1=0.5, X2=0.5), Xcont=list(X3=c(1,1)))## estimation of a 2 classes mixed model m2 <- hlme(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3,subject='ID', ng=2,data=data_hlme,B=c(0.11,-0.74,-0.07,20.71, 29.39,-1,0.13,2.45,-0.29,4.5,0.36,0.79,0.97)) ## simulate according to model m2 with same number of subjects and ## same measurement times as in data_lcmm. Binary covariates X1 and X2 are simulated ## according to a Bernoulli distribution with probability p=0.5, continuous covariate ## X3 is simulated according to a Gaussian distribution with mean=1 and sd=1 : dsim1 <- simulate(m2, times=data_hlme[,c("ID","Time")], Xbin=list(X1=0.5, X2=0.5), Xcont=list(X3=c(1,1))) ## simulate a dataset of 300 subjects according to the same model ## with new observation times, equally spaced and ranging from 0 to 3 : dsim2 <- simulate(m2, times=c(0,3,0.5,0), n=300, tname="Time", Xbin=list(X1=0.5, X2=0.5), Xcont=list(X3=c(1,1)))
coef and vcov for hlme, lcmm, mutlcmm, Jointlcmm, mpjlcmm, externSurv, and externX models, fixef, ranef, fitted and residuals methods for estimated hlme, lcmm, mutlcmm and Jointlcmm models.
## S3 method for class 'hlme' coef(object, ...)## S3 method for class 'hlme' coef(object, ...)
object |
an object of class |
... |
other arguments. There are ignored in these functions. |
For coef, the vector of the estimates.
For vcov, the variance-covariance matrix of the estimates.
For fixef : - for hlme, lcmm and multlcmm
objects, a list containing the fixed effects estimates in the
class-membership model and in the longitudinal model. - for
Jointlcmm objects, a list containing the fixed effects estimates in
the class-membership model, the survival model and in the longitudinal
model.
For ranef, a matrix (nrow=number of subjects, ncol=number of
covariates with random effect) containing the individual random effects.
For fitted, a vector containing the subject-specific predictions
extracted from object.
For residuals, a vector containing the subject-specific residuals
extracted from object.
Cecile Proust-Lima, Viviane Philipps
hlme, lcmm, Jointlcmm, multlcmm,
mpjlcmm, externSurv, externX,
epoce or Diffepoce objectsThe function provides a summary of hlme, lcmm, multlcmm
and Jointlcmm estimations, or epoce and Diffepoce
computations.
## S3 method for class 'lcmm' summary(object, ...)## S3 method for class 'lcmm' summary(object, ...)
object |
an object inheriting from classes |
... |
further arguments to be passed to or from other methods. They are ignored in this function. |
For epoce or Diffepoce objects, returns NULL. For
hlme, lcmm, Jointlcmm or multlcmm returns also a
matrix containing the fixed effect estimates in the longitudinal model,
their standard errors, Wald statistics and p-values
Cecile Proust-Lima, Viviane Philipps, Amadou Diakite and Benoit Liquet
hlme, lcmm, multlcmm,
Jointlcmm, epoce, Diffepoce
This function provides a plot summarizing the results of different models
fitted by hlme, lcmm, multlcmm, Jointlcmm,
mpjlcmm or externVar.
summaryplot( m1, ..., which = c("BIC", "entropy", "ICL"), mfrow = c(1, length(which)), xaxis = "G" )summaryplot( m1, ..., which = c("BIC", "entropy", "ICL"), mfrow = c(1, length(which)), xaxis = "G" )
m1 |
an object of class |
... |
further arguments, in particular other objects of class
|
which |
character vector indicating which results should be plotted. Possible values are "loglik", "conv", "npm", "AIC", "BIC", "SABIC", "entropy", "ICL", "ICL1", "ICL2". |
mfrow |
for multiple plots, number of rows and columns to split the graphical device. Default to one line and length(which) columns. |
xaxis |
the abscissa of the plot. Default to "G", the number of latent classes. |
Can be reported the usual criteria used to assess the fit and the clustering of the data: - maximum log-likelihood L (the higher the better) - number of parameters P, number of classes G, convergence criterion (1 = converged) - AIC (the lower the better) computed as -2L+2P - BIC (the lower the better) computed as -2L+ P log(N) where N is the number of subjects - SABIC (the lower the better) computed as -2L+ P log((N+2)/24) - Entropy (the closer to one the better) computed as 1-sum[pi_ig*log(pi_ig)]/(N*log(G)) where pi_ig is the posterior probability that subject i belongs to class g - ICL (the lower the better) computed in two ways : ICL1 = BIC - sum[pi_ig*log(pi_ig)] or ICL2 = BIC - 2*sum(log(max(pi_ig)), where the max is taken over the classes for each subject. -
Sasha Cuau, Viviane Philipps, Cecile Proust-Lima
## Not run: library(NormPsy) paquid$normMMSE <- normMMSE(paquid$MMSE) paquid$age65 <- (paquid$age - 65)/10 m1 <- hlme(normMMSE~age65+I(age65^2)+CEP, random=~age65+I(age65^2), subject='ID', data=paquid) m2 <- hlme(normMMSE~age65+I(age65^2)+CEP, random=~age65+I(age65^2), subject='ID', data=paquid, ng = 2, mixture=~age65+I(age65^2), B=m1) m3g <- gridsearch(hlme(normMMSE~age65+I(age65^2)+CEP, random=~age65+I(age65^2), subject='ID', data=paquid, ng=3, mixture=~age65+I(age65^2)), rep=100, maxiter=30, minit=m1) summaryplot(m1, m2, m3g, which=c("BIC","entropy","ICL"),bty="l",pch=20,col=2) ## End(Not run)## Not run: library(NormPsy) paquid$normMMSE <- normMMSE(paquid$MMSE) paquid$age65 <- (paquid$age - 65)/10 m1 <- hlme(normMMSE~age65+I(age65^2)+CEP, random=~age65+I(age65^2), subject='ID', data=paquid) m2 <- hlme(normMMSE~age65+I(age65^2)+CEP, random=~age65+I(age65^2), subject='ID', data=paquid, ng = 2, mixture=~age65+I(age65^2), B=m1) m3g <- gridsearch(hlme(normMMSE~age65+I(age65^2)+CEP, random=~age65+I(age65^2), subject='ID', data=paquid, ng=3, mixture=~age65+I(age65^2)), rep=100, maxiter=30, minit=m1) summaryplot(m1, m2, m3g, which=c("BIC","entropy","ICL"),bty="l",pch=20,col=2) ## End(Not run)
This function provides a table summarizing the results of different models
fitted by hlme, lcmm, multlcmm, Jointlcmm,
mpjlcmm or externVar.
summarytable( m1, ..., which = c("G", "loglik", "npm", "BIC", "%class"), display = TRUE )summarytable( m1, ..., which = c("G", "loglik", "npm", "BIC", "%class"), display = TRUE )
m1 |
an object of class |
... |
further arguments, in particular other objects of class
|
which |
character vector indicating which results should be returned. Possible values are "G", "loglik", "conv", "npm", "AIC", "BIC", "SABIC", "entropy", "ICL", "ICL1", "ICL2", "%class". |
display |
logical indicating whether the table should be printed (the default) or not (display=FALSE) |
Can be reported the usual criteria used to assess the fit and the clustering of the data: - maximum log-likelihood L (the higher the better) - number of parameters P, number of classes G, convergence criterion (1 = converged) - AIC (the lower the better) computed as -2L+2P - BIC (the lower the better) computed as -2L+ P log(N) where N is the number of subjects - SABIC (the lower the better) computed as -2L+ P log((N+2)/24) - Entropy (the closer to one the better) computed in two ways : ICL1 = 1-sum[pi_ig*log(pi_ig)]/(N*log(G)) where pi_ig is the posterior probability that subject i belongs to class g - ICL (the lower the better) computed in two ways : ICL1 = BIC - sum[pi_ig*log(pi_ig)] or ICL2 = BIC - 2*sum(log(max(pi_ig)), where the max is taken over the classes for each subject. -
a matrix giving for each model the values of the requested indexes. By default, the number a latent classes, the log-likelihood, the number of parameters, the BIC and the posterior probability of the latent classes.
Cecile Proust-Lima, Viviane Philipps
summary, hlme, lcmm,
multlcmm, Jointlcmm
This function updates the longitudinal submodels of a mpjlcmm object by injecting the estimated parameters and their variances in each hlme/lcmm/multlcmm model used to define the multi-process joint model. The same (uni-process) models as specified in the mpjlcmm call are returned, with updated outputs for best, V, conv, cholesky, pred, predRE, predRE_Y, pprob. All postfit functions (plots, predictions, ...) can then be called on the updated hlme/lcmm/multlcmm models. See mpjlcmm's help page for examples.
## S3 method for class 'mpjlcmm' update(object, ...)## S3 method for class 'mpjlcmm' update(object, ...)
object |
an estimated mpjlcmm model |
... |
not used |
A list of hlme/lcmm/multlcmm models. The models appear in the same order as specified in the call to the mpjlcmm function.
This function provides the variance-covariance matrix of the estimates. vcov is an alias for it.
VarCov(x)VarCov(x)
x |
an object of class |
a matrix containing the variance-covariance of the estimates. For
the parameters of the matrix of variance-covariance of the random effects,
the Cholesky transformed parameters are considered so that VarCov provides
the covariance matrix of function estimates with cholesky=TRUE.
Cecile Proust-Lima, Viviane Philipps
Fromm the Cholesky transformed parameters, this function provides estimates, standard errors and Wald test for the parameters of the variance-covariance matrix of the random effects.
VarCovRE(Mod)VarCovRE(Mod)
Mod |
an object of class |
a matrix containing the estimates of the parameters of the variance-covariance matrix of the random effects, their standard errors, and, for the covariance parameters, the Wald statistic and the associated p-value.
Cecile Proust-Lima, Lionelle Nkam and Viviane Philipps
The function provides the percentage of variance explained by the (latent
class) linear mixed regression in a model estimated with hlme,
lcmm, multlcmm or Jointlcmm.
VarExpl(x, values)VarExpl(x, values)
x |
an object of class |
values |
a data frame with a unique row that contains the values of the variables in random and the time variable in the correlation process from which the percentage of variance should be calculated. |
For hlme, lcmm, and Jointlcmm objects, the
function returns a matrix with 1 row and ng (ie the number of latent
classes) columns containing (the class specific) percentages of variance
explained by the linear mixed regression.
For multlcmm objects, the function returns a matrix containing (the
class specific) percentages of variance explained by the linear mixed
regression for each outcome. The resulting matrix is composed of as many
rows as outcomes and as many columns as latent classes.
Cecile Proust-Lima, Viviane Philipps
hlme, lcmm, multlcmm,
Jointlcmm
## Not run: m1 <- multlcmm(Ydep1+Ydep2~1+Time*X2+contrast(X2),random=~1+Time, subject="ID",randomY=TRUE,link=c("4-manual-splines","3-manual-splines"), intnodes=c(8,12,25),data=data_lcmm, B=c(-1.071, -0.192, 0.106, -0.005, -0.193, 1.012, 0.870, 0.881, 0.000, 0.000, -7.520, 1.401, 1.607 , 1.908, 1.431, 1.082, -7.528, 1.135 , 1.454 , 2.328, 1.052)) # variation percentages explained by linear mixed regression VarExpl(m1,data.frame(Time=0)) ## End(Not run)## Not run: m1 <- multlcmm(Ydep1+Ydep2~1+Time*X2+contrast(X2),random=~1+Time, subject="ID",randomY=TRUE,link=c("4-manual-splines","3-manual-splines"), intnodes=c(8,12,25),data=data_lcmm, B=c(-1.071, -0.192, 0.106, -0.005, -0.193, 1.012, 0.870, 0.881, 0.000, 0.000, -7.520, 1.401, 1.607 , 1.908, 1.431, 1.082, -7.528, 1.135 , 1.454 , 2.328, 1.052)) # variation percentages explained by linear mixed regression VarExpl(m1,data.frame(Time=0)) ## End(Not run)
This function provides multivariate and univariate Wald tests for
combinations of parameters from hlme, lcmm, multlcmm,
Jointlcmm or mpjlcmm models.
WaldMult(Mod, pos = NULL, contrasts = NULL, name = NULL, value = NULL)WaldMult(Mod, pos = NULL, contrasts = NULL, name = NULL, value = NULL)
Mod |
an object of class |
pos |
a vector containing the indices in |
contrasts |
a numeric vector of same length as pos. If NULL (the default), a simultaneous test of the appropriate parameters is realised. If contrasts is specified, the quantity to test is the dot product of pos and contrasts. |
name |
a character containing the name the user wants to give to the test. By default, the name's test is the null hypothesis. |
value |
the value(s) to test against. By default, test against 0. |
If contrasts is NULL, the function returns a matrix with 1 row and 2 columns containing the value of the Wald test's statistic and the associated p-value.
If contrasts is not NULL, the function returns a matrix with 1 row and 4 columns containing the value of the coefficient (dot product of pos and contrasts), his standard deviation, the value of the Wald test's statistic and the associated p-value.
Cecile Proust-Lima, Lionelle Nkam and Viviane Philipps
This function crosses the posterior classifications of two estimated models
xclass(m1, m2)xclass(m1, m2)
m1 |
an object inheriting from classes |
m2 |
an object inheriting from classes |
the contingency table of the two classifications
Viviane Philipps and Cecile Proust-Lima
## Estimation of the models m2 <- hlme(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3,subject='ID',ng=2, data=data_hlme,B=c(0.11,-0.74,-0.07,20.71,29.39,-1,0.13,2.45,-0.29,4.5,0.36,0.79,0.97)) m3 <- hlme(fixed = Y ~ Time * X1, mixture = ~Time, random = ~Time,subject = "ID", classmb = ~X2 + X3, ng = 3, data = data_hlme,B=c(-0.21, 0.31, -2.11, -0.81, -0.24, -0.18, 25.4, 20.09, 30.18, -0.43, -1.1, 0.25, 2.37, -0.29, 2.34, 0.03, 0.74, 0.97)) ## Compare the classifications xclass(m2,m3) # The 39 subjects in class 2 of m3 come from class 1 of m2. # In the same way, all the subjects in class 3 come from class 2 of m2. # Class 1 of m3 mixes subject from class 1 and class 2 of m2.## Estimation of the models m2 <- hlme(Y~Time*X1,mixture=~Time,random=~Time,classmb=~X2+X3,subject='ID',ng=2, data=data_hlme,B=c(0.11,-0.74,-0.07,20.71,29.39,-1,0.13,2.45,-0.29,4.5,0.36,0.79,0.97)) m3 <- hlme(fixed = Y ~ Time * X1, mixture = ~Time, random = ~Time,subject = "ID", classmb = ~X2 + X3, ng = 3, data = data_hlme,B=c(-0.21, 0.31, -2.11, -0.81, -0.24, -0.18, 25.4, 20.09, 30.18, -0.43, -1.1, 0.25, 2.37, -0.29, 2.34, 0.03, 0.74, 0.97)) ## Compare the classifications xclass(m2,m3) # The 39 subjects in class 2 of m3 come from class 1 of m2. # In the same way, all the subjects in class 3 come from class 2 of m2. # Class 1 of m3 mixes subject from class 1 and class 2 of m2.