Package 'JointAI'

Description

This function continues the sampling from the MCMC chains of an existing object of class 'JointAI'.

Usage

add_samples(object, n.iter, add = TRUE, thin = NULL,
  monitor_params = NULL, progress.bar = "text", mess = TRUE)

Arguments

See Also

*_imp

The vignette Parameter Selection contains some examples on how to specify the argument monitor_params.

Examples

# Example 1:
# Run an initial JointAI model:
mod <- lm_imp(y ~ C1 + C2, data = wideDF, n.iter = 100)

# Continue sampling:
mod_add <- add_samples(mod, n.iter = 200, add = TRUE)


# Example 2:
# Continue sampling, but additionally sample imputed values.
# Note: Setting different parameters to monitor than in the original model
# requires add = FALSE.
imps <- add_samples(mod, n.iter = 200, monitor_params = c("imps" = TRUE),
                    add = FALSE)

Description

A helper function that converts the "name of a survival model" (the "Surv(time, status)" specification) into a valid variable name so that it can be used in the JAGS model syntax.

Usage

clean_survname(x)

Arguments

Examples

clean_survname("Surv(eventtime, event != 'censored')")

Description

This function returns a list of default values for the hyper-parameters.

Usage

default_hyperpars()

Details

norm: hyper-parameters for normal and log-normal models

gamma: hyper-parameters for Gamma models

beta: hyper-parameters for beta models

binom: hyper-parameters for binomial models

poisson: hyper-parameters for poisson models

multinomial: hyper-parameters for multinomial models

ordinal: hyper-parameters for ordinal models

ranef: hyper-parameters for the random effects variance-covariance matrices (when there is only one random effect a Gamma distribution is used instead of the Wishart distribution)

surv: parameters for survival models (survreg, coxph and JM)

Note

From the JAGS user manual on the specification of the Wishart distribution:
For KinvD larger than the dimension of the variance-covariance matrix the prior on the correlation between the random effects is concentrated around 0, so that larger values of KinvD indicate stronger prior belief that the elements of the multivariate normal distribution are independent. For KinvD equal to the number of random effects the Wishart prior puts most weight on the extreme values (correlation 1 or -1).

Examples

default_hyperpars()

# To change the hyper-parameters:
hyp <- default_hyperpars()
hyp$norm['rate_tau_norm'] <- 1e-3
mod <- lm_imp(y ~ C1 + C2 + B1, data = wideDF, hyperpars = hyp, mess = FALSE)

Description

The function plots a set of densities (per chain and coefficient) from the MCMC sample of an object of class "JointAI".

Usage

densplot(object, ...)

## S3 method for class 'JointAI'
densplot(object, start = NULL, end = NULL, thin = NULL,
  subset = c(analysis_main = TRUE), outcome = NULL,
  exclude_chains = NULL, vlines = NULL, nrow = NULL, ncol = NULL,
  joined = FALSE, use_ggplot = FALSE, warn = TRUE, mess = TRUE, ...)

Arguments

See Also

The vignette Parameter Selection contains some examples how to specify the argument subset.

Examples

## Not run: 
# fit a JointAI object:
mod <- lm_imp(y ~ C1 + C2 + M1, data = wideDF, n.iter = 100)

# Example 1: basic densityplot
densplot(mod)
densplot(mod, exclude_chains = 2)


# Example 2: use vlines to mark zero
densplot(mod, col = c("darkred", "darkblue", "darkgreen"),
         vlines = list(list(v = rep(0, nrow(summary(mod)$res$y$regcoef)),
                            col = grey(0.8))))


# Example 3: use vlines to visualize posterior mean and 2.5%/97.5% quantiles
res <- rbind(summary(mod)$res$y$regcoef[, c('Mean', '2.5%', '97.5%')],
             summary(mod)$res$y$sigma[, c('Mean', '2.5%', '97.5%'),
             drop = FALSE]
             )
densplot(mod, vlines = list(list(v = res[, "Mean"], lty = 1, lwd = 2),
                            list(v = res[, "2.5%"], lty = 2),
                            list(v = res[, "97.5%"], lty = 2)))


# Example 4: ggplot version
densplot(mod, use_ggplot = TRUE)


# Example 5: change how the ggplot version looks
library(ggplot2)

densplot(mod, use_ggplot = TRUE) +
  xlab("value") +
  theme(legend.position = 'bottom') +
  scale_color_brewer(palette = 'Dark2', name = 'chain')

## End(Not run)

Description

Return the current state of a 'JointAI' model

Usage

extract_state(object, pattern = paste0("^", c("RinvD", "invD", "tau", "b"),
  "_"))

Arguments

Value

A list with one element per chain of the MCMC sampler, containing the Returns the current state of the MCMC sampler (values of the last iteration) for the subset of nodes identified based on the pattern the user has specified.

Description

This function returns a dataset containing multiple imputed datasets stacked onto each other (i.e., long format; optionally including the original, incomplete data).
These data can be automatically exported to SPSS (as a .txt file containing the data and a .sps file containing syntax to generate a .sav file). For the export function the foreign package needs to be installed.

Usage

get_MIdat(object, m = 10, include = TRUE, start = NULL, minspace = 50,
  seed = NULL, export_to_SPSS = FALSE, resdir = NULL, filename = NULL)

Arguments

Value

A data.frame in which the original data (if include = TRUE) and the imputed datasets are stacked onto each other.
The variable Imputation_ indexes the imputation, while .rownr links the rows to the rows of the original data. In cross-sectional datasets the variable .id is added as subject identifier.

Note

In order to be able to extract (multiple) imputed datasets the imputed values must have been monitored, i.e., imps = TRUE had to be specified in the argument monitor_params in *_imp.

See Also

plot_imp_distr

Examples

## Not run: 
# fit a model and monitor the imputed values with
# monitor_params = c(imps = TRUE)

mod <- lm_imp(y ~ C1 + C2 + M2, data = wideDF,
              monitor_params = c(imps = TRUE), n.iter = 100)

# Example 1: without export to SPSS
MIs <- get_MIdat(mod, m = 3, seed = 123)



# Example 2: with export for SPSS
# (here: to the temporary directory "temp_dir")

temp_dir <- tempdir()
MIs <- get_MIdat(mod, m = 3, seed = 123, resdir = temp_dir,
                 filename = "example_imputation",
                 export_to_SPSS = TRUE)


## End(Not run)

Description

This function returns a data.frame or a list of data.frames per grouping level. Each of the data.frames has columns variable, #NA (number of missing values) and %NA (proportion of missing values in percent).

Usage

get_missinfo(object)

Arguments

Examples

mod <-  lm_imp(y ~ C1 + B2 + C2, data = wideDF, n.iter = 100)
get_missinfo(mod)

Description

Calculates the Gelman-Rubin criterion for convergence (uses gelman.diag from package coda).

Usage

GR_crit(object, confidence = 0.95, transform = FALSE, autoburnin = TRUE,
  multivariate = TRUE, subset = NULL, exclude_chains = NULL,
  start = NULL, end = NULL, thin = NULL, warn = TRUE, mess = TRUE,
  ...)

Arguments

References

Gelman, A and Rubin, DB (1992) Inference from iterative simulation using multiple sequences, Statistical Science, 7, 457-511.

Brooks, SP. and Gelman, A. (1998) General methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics, 7, 434-455.

See Also

The vignette Parameter Selection contains some examples how to specify the argument subset.

Examples

mod1 <- lm_imp(y ~ C1 + C2 + M2, data = wideDF, n.iter = 100)
GR_crit(mod1)

Description

The JointAI package performs simultaneous imputation and inference for incomplete or complete data under the Bayesian framework. Models for incomplete covariates, conditional on other covariates, are specified automatically and modelled jointly with the analysis model. MCMC sampling is performed in 'JAGS' via the R package rjags.

Main functions

JointAI provides the following main functions that facilitate analysis with different models:

• lm_imp for linear regression

• glm_imp for generalized linear regression

• betareg_imp for regression using a beta distribution

• lognorm_imp for regression using a log-normal distribution

• clm_imp for (ordinal) cumulative logit models

• mlogit_imp for multinomial models

• lme_imp or lmer_imp for linear mixed models

• glme_imp or glmer_imp for generalized linear mixed models

• betamm_imp for mixed models using a beta distribution

• lognormmm_imp for mixed models using a log-normal distribution

• clmm_imp for (ordinal) cumulative logit mixed models

• survreg_imp for parametric (Weibull) survival models

• coxph_imp for (Cox) proportional hazard models

• JM_imp for joint models of longitudinal and survival data

As far as possible, the specification of these functions is analogous to the specification of widely used functions for the analysis of complete data, such as lm, glm, lme (from the package nlme), survreg (from the package survival) and coxph (from the package survival).

Computations can be performed in parallel to reduce computational time, using the package future, the argument shrinkage allows the user to impose a penalty on the regression coefficients of some or all models involved, and hyper-parameters can be changed via the argument hyperpars.

To obtain summaries of the results, the functions summary(), coef() and confint() are available, and results can be visualized with the help of traceplot() or densplot().

The function predict() allows prediction (including credible intervals) from JointAI models.

Evaluation and export

Two criteria for evaluation of convergence and precision of the posterior estimate are available:

• GR_crit implements the Gelman-Rubin criterion ('potential scale reduction factor') for convergence

• MC_error calculates the Monte Carlo error to evaluate the precision of the MCMC sample

Imputed data can be extracted (and exported to SPSS) using get_MIdat(). The function plot_imp_distr() allows visual comparison of the distribution of observed and imputed values.

Other useful functions

• parameters and list_models to gain insight in the specified model

• plot_all and md_pattern to visualize the distribution of the data and the missing data pattern

Vignettes

The following vignettes are available

• Minimal Example:
  A minimal example demonstrating the use of lm_imp, summary.JointAI, traceplot and densplot.

• Visualizing Incomplete Data:
  Demonstrations of the options in plot_all (plotting histograms and bar plots for all variables in the data) and md_pattern (plotting or printing the missing data pattern).

• Model Specification:
  Explanation and demonstration of all parameters that are required or optional to specify the model structure in lm_imp, glm_imp and lme_imp. Among others, the functions parameters, list_models and set_refcat are used.

• Parameter Selection:
  Examples on how to select the parameters/variables/nodes to follow using the argument monitor_params and the parameters/variables/nodes displayed in the summary, traceplot, densplot or when using GR_crit or MC_error.

• MCMC Settings:
  Examples demonstrating how to set the arguments controlling settings of the MCMC sampling, i.e., n.adapt, n.iter, n.chains, thin, inits.

• After Fitting:
  Examples on the use of functions to be applied after the model has been fitted, including traceplot, densplot, summary, GR_crit, MC_error, predict, predDF and get_MIdat.

• Theoretical Background:
  Explanation of the statistical method implemented in JointAI.

References

Erler NS, Rizopoulos D, Lesaffre EMEH (2021). "JointAI: Joint Analysis and Imputation of Incomplete Data in R." Journal of Statistical Software, 100(20), 1-56. doi:10.18637/jss.v100.i20.

Erler, N.S., Rizopoulos, D., Rosmalen, J., Jaddoe, V.W.V., Franco, O. H., & Lesaffre, E.M.E.H. (2016). Dealing with missing covariates in epidemiologic studies: A comparison between multiple imputation and a full Bayesian approach. Statistics in Medicine, 35(17), 2955-2974. doi:10.1002/sim.6944

Erler, N.S., Rizopoulos D., Jaddoe, V.W.V., Franco, O.H. & Lesaffre, E.M.E.H. (2019). Bayesian imputation of time-varying covariates in linear mixed models. Statistical Methods in Medical Research, 28(2), 555–568. doi:10.1177/0962280217730851

Description

An object returned by one of the main functions *_imp.

Value

Description

This function prints information on all models, those explicitly specified by the user and those specified automatically by JointAI for (incomplete) covariates in a JointAI object.

Usage

list_models(object, predvars = TRUE, regcoef = TRUE, otherpars = TRUE,
  priors = TRUE, refcat = TRUE)

Arguments

Note

The models listed by this function are not the actual imputation models, but the conditional models that are part of the specification of the joint distribution. Briefly, the joint distribution is specified as a sequence of conditional models

The actual imputation models are the full conditional distributions \(p(x_1 | \cdot)\) derived from this joint distribution. Even though the conditional distributions do not contain the outcome and all other covariates in their linear predictor, outcome and other covariates are taken into account implicitly, since imputations are sampled from the full conditional distributions. For more details, see Erler et al. (2016) and Erler et al. (2019).

The function list_models prints information on the conditional distributions of the covariates (since they are what is specified; the full-conditionals are automatically derived within JAGS). The outcome is, thus, not part of the printed linear predictor, but is still included during imputation.

References

Erler, N.S., Rizopoulos, D., Rosmalen, J.V., Jaddoe, V.W., Franco, O.H., & Lesaffre, E.M.E.H. (2016). Dealing with missing covariates in epidemiologic studies: A comparison between multiple imputation and a full Bayesian approach. Statistics in Medicine, 35(17), 2955-2974.

Erler NS, Rizopoulos D, Lesaffre EMEH (2021). "JointAI: Joint Analysis and Imputation of Incomplete Data in R." Journal of Statistical Software, 100(20), 1-56. doi:10.18637/jss.v100.i20.

Examples

# (set n.adapt = 0 and n.iter = 0 to prevent MCMC sampling to save time)
mod1 <- lm_imp(y ~ C1 + C2 + M2 + O2 + B2, data = wideDF, n.adapt = 0,
               n.iter = 0, mess = FALSE)

list_models(mod1)

Description

A simulated longitudinal dataset.

Usage

data(longDF)

Format

A simulated data frame with 329 rows and 21 variables with data from 100 subjects:

C1

continuous, complete baseline variable

C2

continuous, incomplete baseline variable

B1

binary, complete baseline variable

B2

binary, incomplete baseline variable

M1

unordered factor; complete baseline variable

M2

unordered factor; incomplete baseline variable

O1

ordered factor; complete baseline variable

O2

ordered factor; incomplete baseline variable

P1

count variable; complete baseline variable

P2

count variable; incomplete baseline variable

c1

continuous, complete longitudinal variable

c2

continuous incomplete longitudinal variable

b1

binary, complete longitudinal variable

b2

binary incomplete longitudinal variable

o1

ordered factor; complete longitudinal variable

o2

ordered factor; incomplete longitudinal variable

p1

count variable; complete longitudinal variable

p2

count variable; incomplete longitudinal variable

id

id (grouping) variable

time

continuous complete longitudinal variable

y

continuous, longitudinal (outcome) variable

Description

Calculate, print and plot the Monte Carlo error of the samples from a 'JointAI' model, combining the samples from all MCMC chains.

Usage

MC_error(x, subset = NULL, exclude_chains = NULL, start = NULL,
  end = NULL, thin = NULL, digits = 2, warn = TRUE, mess = TRUE, ...)

## S3 method for class 'MCElist'
plot(x, data_scale = TRUE, plotpars = NULL,
  ablinepars = list(v = 0.05), minlength = 20, ...)

Arguments

Value

An object of class MCElist with elements unscaled, scaled and digits. The first two are matrices with columns est (posterior mean), MCSE (Monte Carlo error), SD (posterior standard deviation) and MCSE/SD (Monte Carlo error divided by post. standard deviation.)

Functions

• plot(MCElist): plot Monte Carlo error

Note

Lesaffre & Lawson (2012; p. 195) suggest the Monte Carlo error of a parameter should not be more than 5% of the posterior standard deviation of this parameter (i.e., $MCSE/SD \le 0.05$).

Long variable names:
The default plot margins may not be wide enough when variable names are longer than a few characters. The plot margin can be adjusted (globally) using the argument "mar" in par.

References

Lesaffre, E., & Lawson, A. B. (2012). Bayesian Biostatistics. John Wiley & Sons.

See Also

The vignette Parameter Selection provides some examples how to specify the argument subset.

Examples

## Not run: 

mod <- lm_imp(y ~ C1 + C2 + M2, data = wideDF, n.iter = 100)

MC_error(mod)

plot(MC_error(mod), ablinepars = list(lty = 2),
     plotpars = list(pch = 19, col = 'blue'))

## End(Not run)

Description

Obtain a plot of the pattern of missing data and/or return the pattern as a matrix.

Usage

md_pattern(data, color = c(grDevices::grey(0.1), grDevices::grey(0.7)),
  border = grDevices::grey(0.5), plot = TRUE, pattern = FALSE,
  print_xaxis = TRUE, ylab = "Number of observations per pattern",
  print_yaxis = TRUE, legend.position = "bottom", sort_columns = TRUE,
  ...)

Arguments

Note

This function requires the ggplot2 package to be installed.

See Also

See the vignette Visualizing Incomplete Data for more examples.

Examples

op <- par(mar = c(3, 1, 1.5, 1.5), mgp = c(2, 0.6, 0))
md_pattern(wideDF)
par(op)

Description

Main analysis functions to estimate different types of models using MCMC sampling, while imputing missing values.

Usage

lm_imp(formula, data, n.chains = 3, n.adapt = 100, n.iter = 0,
  thin = 1, monitor_params = c(analysis_main = TRUE), auxvars = NULL,
  refcats = NULL, models = NULL, no_model = NULL, shrinkage = FALSE,
  ppc = TRUE, seed = NULL, inits = NULL, warn = TRUE, mess = TRUE,
  ...)

glm_imp(formula, family, data, n.chains = 3, n.adapt = 100, n.iter = 0,
  thin = 1, monitor_params = c(analysis_main = TRUE), auxvars = NULL,
  refcats = NULL, models = NULL, no_model = NULL, shrinkage = FALSE,
  ppc = TRUE, seed = NULL, inits = NULL, warn = TRUE, mess = TRUE,
  ...)

clm_imp(formula, data, n.chains = 3, n.adapt = 100, n.iter = 0,
  thin = 1, monitor_params = c(analysis_main = TRUE), auxvars = NULL,
  refcats = NULL, nonprop = NULL, rev = NULL, models = NULL,
  no_model = NULL, shrinkage = FALSE, ppc = TRUE, seed = NULL,
  inits = NULL, warn = TRUE, mess = TRUE, ...)

lognorm_imp(formula, data, n.chains = 3, n.adapt = 100, n.iter = 0,
  thin = 1, monitor_params = c(analysis_main = TRUE), auxvars = NULL,
  refcats = NULL, models = NULL, no_model = NULL, shrinkage = FALSE,
  ppc = TRUE, seed = NULL, inits = NULL, warn = TRUE, mess = TRUE,
  ...)

betareg_imp(formula, data, n.chains = 3, n.adapt = 100, n.iter = 0,
  thin = 1, monitor_params = c(analysis_main = TRUE), auxvars = NULL,
  refcats = NULL, models = NULL, no_model = NULL, shrinkage = FALSE,
  ppc = TRUE, seed = NULL, inits = NULL, warn = TRUE, mess = TRUE,
  ...)

mlogit_imp(formula, data, n.chains = 3, n.adapt = 100, n.iter = 0,
  thin = 1, monitor_params = c(analysis_main = TRUE), auxvars = NULL,
  refcats = NULL, models = NULL, no_model = NULL, shrinkage = FALSE,
  ppc = TRUE, seed = NULL, inits = NULL, warn = TRUE, mess = TRUE,
  ...)

lme_imp(fixed, data, random, n.chains = 3, n.adapt = 100, n.iter = 0,
  thin = 1, monitor_params = c(analysis_main = TRUE), auxvars = NULL,
  refcats = NULL, rd_vcov = "blockdiag", models = NULL,
  no_model = NULL, shrinkage = FALSE, ppc = TRUE, seed = NULL,
  inits = NULL, warn = TRUE, mess = TRUE, ...)

lmer_imp(fixed, data, random, n.chains = 3, n.adapt = 100, n.iter = 0,
  thin = 1, monitor_params = c(analysis_main = TRUE), auxvars = NULL,
  refcats = NULL, rd_vcov = "blockdiag", models = NULL,
  no_model = NULL, shrinkage = FALSE, ppc = TRUE, seed = NULL,
  inits = NULL, warn = TRUE, mess = TRUE, ...)

glme_imp(fixed, data, random, family, n.chains = 3, n.adapt = 100,
  n.iter = 0, thin = 1, monitor_params = c(analysis_main = TRUE),
  auxvars = NULL, refcats = NULL, rd_vcov = "blockdiag", models = NULL,
  no_model = NULL, shrinkage = FALSE, ppc = TRUE, seed = NULL,
  inits = NULL, warn = TRUE, mess = TRUE, ...)

glmer_imp(fixed, data, random, family, n.chains = 3, n.adapt = 100,
  n.iter = 0, thin = 1, monitor_params = c(analysis_main = TRUE),
  auxvars = NULL, refcats = NULL, rd_vcov = "blockdiag", models = NULL,
  no_model = NULL, shrinkage = FALSE, ppc = TRUE, seed = NULL,
  inits = NULL, warn = TRUE, mess = TRUE, ...)

betamm_imp(fixed, random, data, n.chains = 3, n.adapt = 100, n.iter = 0,
  thin = 1, monitor_params = c(analysis_main = TRUE), auxvars = NULL,
  refcats = NULL, rd_vcov = "blockdiag", models = NULL,
  no_model = NULL, shrinkage = FALSE, ppc = TRUE, seed = NULL,
  inits = NULL, warn = TRUE, mess = TRUE, ...)

lognormmm_imp(fixed, random, data, n.chains = 3, n.adapt = 100,
  n.iter = 0, thin = 1, monitor_params = c(analysis_main = TRUE),
  auxvars = NULL, refcats = NULL, rd_vcov = "blockdiag", models = NULL,
  no_model = NULL, shrinkage = FALSE, ppc = TRUE, seed = NULL,
  inits = NULL, warn = TRUE, mess = TRUE, ...)

clmm_imp(fixed, data, random, n.chains = 3, n.adapt = 100, n.iter = 0,
  thin = 1, monitor_params = c(analysis_main = TRUE), auxvars = NULL,
  refcats = NULL, nonprop = NULL, rev = NULL, rd_vcov = "blockdiag",
  models = NULL, no_model = NULL, shrinkage = FALSE, ppc = TRUE,
  seed = NULL, inits = NULL, warn = TRUE, mess = TRUE, ...)

mlogitmm_imp(fixed, data, random, n.chains = 3, n.adapt = 100,
  n.iter = 0, thin = 1, monitor_params = c(analysis_main = TRUE),
  auxvars = NULL, refcats = NULL, rd_vcov = "blockdiag", models = NULL,
  no_model = NULL, shrinkage = FALSE, ppc = TRUE, seed = NULL,
  inits = NULL, warn = TRUE, mess = TRUE, ...)

survreg_imp(formula, data, n.chains = 3, n.adapt = 100, n.iter = 0,
  thin = 1, monitor_params = c(analysis_main = TRUE), auxvars = NULL,
  refcats = NULL, models = NULL, no_model = NULL, shrinkage = FALSE,
  ppc = TRUE, seed = NULL, inits = NULL, warn = TRUE, mess = TRUE,
  ...)

coxph_imp(formula, data, df_basehaz = 6, n.chains = 3, n.adapt = 100,
  n.iter = 0, thin = 1, monitor_params = c(analysis_main = TRUE),
  auxvars = NULL, refcats = NULL, models = NULL, no_model = NULL,
  shrinkage = FALSE, ppc = TRUE, seed = NULL, inits = NULL,
  warn = TRUE, mess = TRUE, ...)

JM_imp(formula, data, df_basehaz = 6, n.chains = 3, n.adapt = 100,
  n.iter = 0, thin = 1, monitor_params = c(analysis_main = TRUE),
  auxvars = NULL, timevar = NULL, refcats = NULL,
  rd_vcov = "blockdiag", models = NULL, no_model = NULL,
  assoc_type = NULL, shrinkage = FALSE, ppc = TRUE, seed = NULL,
  inits = NULL, warn = TRUE, mess = TRUE, ...)

Arguments

Value

An object of class JointAI.

Model formulas

Random effects

It is possible to specify multi-level models as it is done in the package nlme, using fixed and random, or as it is done in the package lme4, using formula and specifying the random effects in brackets:

formula = y ~ x1 + x2 + x3 + (1 | id)

is equivalent to

fixed = y ~ x1 + x2 + x3, random = ~ 1|id

Multiple levels of grouping

For multiple levels of grouping the specification using formula should be used. There is no distinction between nested and crossed random effects, i.e., ... + (1 | id) + (1 | center) is treated the same as ... + (1 | center/id).

Nested vs crossed random effects

The distinction between nested and crossed random effects should come from the levels of the grouping variables, i.e., if id is nested in center, then there cannot be observations with the same id but different values for center.

Modelling multiple models simultaneously & joint models

To fit multiple main models at the same time, a list of formula objects can be passed to the argument formula. Outcomes of one model may be contained as covariates in another model and it is possible to combine models for variables on different levels, for example:

formula = list(y ~ x1 + x2 + x3 + x4 + time + (time | id),
                     x2 ~ x3 + x4 + x5)

This principle is also used for the specification of a joint model for longitudinal and survival data.

Note that it is not possible to specify multiple models for the same outcome variable.

Random effects variance-covariance structure

(Note: This feature is new and has not been fully tested yet.)

By default, a block-diagonal structure is assumed for the variance-covariance matrices of the random effects in models with random effects. This means that per outcome and level random effects are assumed to be correlated, but random effects of different outcomes are modelled as independent. The argument rd_vcov allows the user specify different assumptions about these variance-covariance matrices. Implemented structures are full, blockdiag and indep (all off-diagonal elements are zero).

If rd_vcov is set to one of these options, the structure is assumed for all random effects variance-covariance matrices. Alternatively, it is possible to specify a named list of vectors, where the names are the structures and the vectors contain the names of the response variables which are included in this structure.

For example, for a multivariate mixed model with five outcomes y1, ..., y5, the specification could be:

rd_vcov = list(blockdiag = c("y1", "y2"),
               full = c("y3", "y4"),
               indep = "y5")

This would entail that the random effects for y3 and y4 are assumed to be correlated (within and across outcomes), random effects for y1 and y2 are assumed to be correlated within each outcome, and the random effects for y5 are assumed to be independent.

It is possible to have multiple sets of response variables for which separate full variance-covariance matrices are used, for example:

rd_vcov = list(full = c("y1", "y2", "y5"),
               full = c("y3", "y4"))

In models with multiple levels of nesting, separate structures can be specified per level:

rd_vcov = list(id = list(blockdiag = c("y1", "y2"),
                         full = c("y3", "y4"),
                         indep = "y5"),
              center = "indep")

Survival models with frailties or time-varying covariates

Random effects specified in brackets can also be used to indicate a multi-level structure in survival models, as would, for instance be needed in a multi-centre setting, where patients are from multiple hospitals.

It also allows to model time-dependent covariates in a proportional hazards survival model (using coxph_imp), also in combination with additional grouping levels.

In time-dependent proportional hazards models, last-observation-carried-forward is used to fill in missing values in the time-varying covariates, and to determine the value of the covariate at the event time. Preferably, all time-varying covariates should be measured at baseline (timevar = 0). If a value for a time-varying covariate needs to be filled in and there is no previous observation, the next observation will be carried backward.

Differences to basic regression models

It is not possible to specify transformations of outcome variables, i.e., it is not possible to use a model formula like

log(y) ~ x1 + x2 + ...

In the specific case of a transformation with the natural logarithm, a log-normal model can be used instead of a normal model.

Moreover, it is not possible to use . to indicate that all variables in a data.frame other than the outcome variable should be used as covariates. I.e., a formula y ~ . is not valid in JointAI.

Data structure

For multi-level settings, the data must be in long format, so that repeated measurements are recorded in separate rows.

For survival data with time-varying covariates (coxph_imp and JM_imp) the data should also be in long format. The survival/censoring times and event indicator variables must be stored in separate variables in the same data and should be constant across all rows referring to the same subject.

During the pre-processing of the data the survival/censoring times will automatically be merged with the observation times of the time-varying covariates (which must be supplied via the argument timevar).

It is possible to have multiple time-varying covariates, which do not have to be measured at the same time points, but there can only be one timevar.

Distribution families and link functions

Imputation methods / model types

Implemented model types that can be chosen in the argument models for baseline covariates (not repeatedly measured) are:

For repeatedly measured variables the following model types are available:

When models are specified for only a subset of the variables for which a model is needed, the default model choices (as indicated in the tables) are used for the unspecified variables.

Parameters to follow (monitor_params)

See also the vignette: Parameter Selection

Named vector specifying which parameters should be monitored. This can be done either directly by specifying the name of the parameter or indirectly by one of the key words selecting a set of parameters. Except for other, in which parameter names are specified directly, parameter (groups) are just set as TRUE or FALSE.

Models are divided into two groups, the main models, which are the models for which the user has explicitly specified a formula (via formula or fixed), and all other models, for which models were specified automatically.

If left unspecified, monitor_params = c("analysis_main" = TRUE) will be used.

For example:
monitor_params = c(analysis_main = TRUE, tau_main = TRUE, sigma_main = FALSE) would monitor the regression parameters betas and the residual precision tau_main instead of the residual standard deviation sigma_main.

For a linear model, monitor_params = c(imps = TRUE) would monitor betas, and sigma_main (because analysis_main = TRUE by default) as well as the imputed values.

Cumulative logit (mixed) models

In the default setting for cumulative logit models, i.e, rev = NULL, the odds for a variable \(y\) with \(K\) ordered categories are defined as \[\log\left(\frac{P(y_i > k)}{P(y_i \leq k)}\right) = \gamma_k + \eta_i, \quad k = 1, \ldots, K-1,\] where \(\gamma_k\) is a category specific intercept and \(\eta_i\) the subject specific linear predictor.

To reverse the odds to \[\log\left(\frac{P(y_i \leq k)}{P(y_i > k)}\right) = \gamma_k + \eta_i, \quad k = 1, \ldots, K-1,\] the name of the response variable has to be specified in the argument rev, e.g., rev = c("y").

By default, proportional odds are assumed and only the intercepts differ per category of the ordinal response. To allow for non-proportional odds, i.e., \[\log\left(\frac{P(y_i > k)}{P(y_i \leq k)}\right) = \gamma_k + \eta_i + \eta_{ki}, \quad k = 1, \ldots, K-1,\] the argument nonprop can be specified. It takes a one-sided formula or a list of one-sided formulas. When a single formula is supplied, or a unnamed list with just one element, it is assumed that the formula corresponds to the main model. To specify non-proportional effects for linear predictors in models for ordinal covariates, the list has to be named with the names of the ordinal response variables.

For example, the following three specifications are equivalent and assume a non-proportional effect of C1 on O1, but C1 is assumed to have a proportional effect on the incomplete ordinal covariate O2:

clm_imp(O1 ~ C1 + C2 + B2 + O2, data = wideDF, nonprop = ~ C1)
clm_imp(O1 ~ C1 + C2 + B2 + O2, data = wideDF, nonprop = list(~ C1))
clm_imp(O1 ~ C1 + C2 + B2 + O2, data = wideDF, nonprop = list(O1 = ~ C1))

To specify non-proportional effects on O2, a named list has to be provided:

clm_imp(O1 ~ C1 + C2 + B2 + O2 + B1, data = wideDF,
        nonprop = list(O1 = ~ C1,
                       O2 = ~ C1 + B1))

The variables for which a non-proportional effect is assumed also have to be part of the regular model formula.

Custom model parts

(Note: This feature is experimental and has not been fully tested yet.)

Via the argument custom it is possible to provide custom sub-models that replace the sub-models that are automatically generated by JointAI.

Using this feature it is, for instance, possible to use the value of a repeatedly measured variable at a specific time point as covariate in another model. An example would be the use of "baseline" cholesterol (chol at day = 0) as covariate in a survival model.

First, the variable chol0 is added to the PBC data. For most patients the value of cholesterol at baseline is observed, but not for all. It is important that the data has a row with day = 0 for each patient.

PBC <- merge(PBC,
             subset(PBC, day == 0, select = c("id", "chol")),
             by = "id", suffixes = c("", "0"))

Next, the custom piece of JAGS model syntax needs to be specified. We loop here only over the patients for which the baseline cholesterol is missing.

calc_chol0 <- "
for (ii in 1:28) {
  M_id[row_chol0_id[ii], 3] <- M_lvlone[row_chol0_lvlone[ii], 1]
  }"

To be able to run the model with the custom imputation "model" for baseline cholesterol we need to provide the numbers of the rows in the data matrices that contain the missing values of baseline cholesterol and the rows that contain the imputed cholesterol at day = 0:

row_chol0_lvlone <- which(PBC$day == 0 & is.na(PBC$chol0))
row_chol0_id <- match(PBC$id, unique(PBC$id))[row_chol0_lvlone]

Then we pass both the custom sub-model and the additional data to the analysis function coxph_imp(). Note that we explicitly need to specify the model for chol.

coxph_imp(list(Surv(futime, status != "censored") ~ age + sex + chol0,
               chol ~ age + sex + day + (day | id)),
          no_model = "day", data = PBC,
          append_data_list = list(row_chol0_lvlone = row_chol0_lvlone,
                                  row_chol0_id = row_chol0_id),
          custom = list(chol0 = calc_chol0))

Note

Coding of variables:

The default covariate (imputation) models are chosen based on the class of each of the variables, distinguishing between numeric, factor with two levels, unordered factor with >2 levels and ordered factor with >2 levels.

When a continuous variable has only two different values it is assumed to be binary and its coding and default (imputation) model will be changed accordingly. This behaviour can be overwritten specifying a model type via the argument models.

Variables of type logical are automatically converted to unordered factors.

Contrasts

JointAI version \(\geq\) 1.0.0 uses the globally (via options("contrasts")) specified contrasts. However, for incomplete categorical variables, for which the contrasts need to be re-calculated within the JAGS model, currently only contr.treatment and contr.sum are possible. Therefore, when an in complete ordinal covariate is used and the default contrasts (contr.poly()) are set to be used for ordered factors, a warning message is printed and dummy coding (contr.treatment()) is used for that variable instead.

Non-linear effects and transformation of variables:

JointAI handles non-linear effects, transformation of covariates and interactions the following way:
When, for instance, a model formula contains the function log(x) and x has missing values, x will be imputed and used in the linear predictor of models for which no formula was specified, i.e., it is assumed that the other variables have a linear association with x. The log() of the observed and imputed values of x is calculated and used in the linear predictor of the main analysis model.

If, instead of using log(x) in the model formula, a pre-calculated variable logx is used, this variable is imputed directly and used in the linear predictors of all models, implying that variables that have logx in their linear predictors have a linear association with logx but not with x.

When different transformations of the same incomplete variable are used in one model it is strongly discouraged to calculate these transformations beforehand and supply them as different variables. If, for example, a model formula contains both x and x2 (where x2 = x^2), they are treated as separate variables and imputed with separate models. Imputed values of x2 are thus not equal to the square of imputed values of x. Instead, x and I(x^2) should be used in the model formula. Then only x is imputed and x^2 is calculated from the imputed values of x internally.

The same applies to interactions involving incomplete variables.

Sequence of models:

Models generated automatically (i.e., not mentioned in formula or fixed are specified in a sequence based on the level of the outcome of the respective model in the multi-level hierarchy and within each level according to the number of missing values. This means that level-1 variables have all level-2, level-3, ... variables in their linear predictor, and variables on the highest level only have variables from the same level in their linear predictor. Within each level, the variable with the most missing values has the most variables in its linear predictor.

Not (yet) possible:

• prediction (using predict) conditional on random effects

• the use of splines for incomplete variables

• the use of (or equivalents for) pspline, or strata in survival models

• left censored or interval censored data

See Also

set_refcat, traceplot, densplot, summary.JointAI, MC_error, GR_crit, predict.JointAI, add_samples, JointAIObject, add_samples, parameters, list_models

Vignettes

• Minimal Example

• Model Specification

• Parameter Selection

• MCMC Settings

• After Fitting

• Theoretical Background

Examples

# Example 1: Linear regression with incomplete covariates
mod1 <- lm_imp(y ~ C1 + C2 + M1 + B1, data = wideDF, n.iter = 100)


# Example 2: Logistic regression with incomplete covariates
mod2 <- glm_imp(B1 ~ C1 + C2 + M1, data = wideDF,
                family = binomial(link = "logit"), n.iter = 100)

## Not run: 

# Example 3: Linear mixed model with incomplete covariates
mod3 <- lme_imp(y ~ C1 + B2 + c1 + time, random = ~ time|id,
                data = longDF, n.iter = 300)


# Example 4: Parametric Weibull survival model
mod4 <- survreg_imp(Surv(time, status) ~ age + sex + meal.cal + wt.loss,
                    data = survival::lung, n.iter = 100)


# Example 5: Proportional hazards survival model
mod5 <- coxph_imp(Surv(time, status) ~ age + sex + meal.cal + wt.loss,
                    data = survival::lung, n.iter = 200)

# Example 6: Joint model for longitudinal and survival data
mod6 <- JM_imp(list(Surv(futime, status != 'censored') ~ age + sex +
                    albumin + copper + trig + (1 | id),
                    albumin ~ day + age + sex + (day | id)),
                    timevar = 'day', data = PBC, n.iter = 100)

# Example 7: Proportional hazards  model with a time-dependent covariate
mod7 <- coxph_imp(Surv(futime, status != 'censored') ~ age + sex + copper +
                  trig + stage + (1 | id),
                  timevar = 'day', data = PBC, n.iter = 100)



# Example 8: Parallel computation
# If no strategy how the "future" should be handled is specified, the
# MCMC chains are run sequentially.
# To run MCMC chains in parallel, a strategy can be specified using the
# package \pkg{future} (see ?future::plan), for example:
future::plan(future::multisession, workers = 4)
mod8 <- lm_imp(y ~ C1 + C2 + B2, data = wideDF, n.iter = 500, n.chains = 8)
mod8$comp_info$future
# To re-set the strategy to sequential computation, the sequential strategy
# can be specified:
future::plan(future::sequential)


## End(Not run)

Description

This data is a small subset of the data collected within the 2011-2012 wave of the NHANES study, a study designed to assess the health and nutritional status of adults and children in the United States, conduced by the National Center for Health Statistics.

Usage

data(NHANES)

Format

A data frame with 186 rows and 13 variables:

SBP

systolic blood pressure

gender

male or female

age

in years

race

race / Hispanic origin (5 categories)

WC

waist circumference in cm

alc

alcohol consumption (binary: <1 drink per week vs. >= 1 drink per week)

educ

educational level (binary: low vs. high)

creat

creatinine concentration in mg/dL

albu

albumin concentration in g/dL

uricacid

uric acid concentration in mg/dL

bili

bilirubin concentration in mg/dL

occup

occupational status (3 categories)

smoke

smoking status (3 ordered categories)

Note

The subset provided here was selected and re-coded to facilitate demonstration of the functionality of the JointAI package, and no clinical conclusions should be derived from it.

Source

National Center for Health Statistics (NCHS) (2011 - 2012). National Health and Nutrition Examination Survey Data. URL https://www.cdc.gov/nchs/nhanes/.

Examples

summary(NHANES)

Description

Returns the names of the parameters/nodes of an object of class 'JointAI' for which a monitor is set.

Usage

parameters(object, expand_ranef = FALSE, mess = TRUE, warn = TRUE, ...)

Arguments

Examples

# (This function does not need MCMC samples to work, so we will set
# n.adapt = 0 and n.iter = 0 to reduce computational time)
mod1 <- lm_imp(y ~ C1 + C2 + M2 + O2 + B2, data = wideDF, n.adapt = 0,
               n.iter = 0, mess = FALSE)

parameters(mod1)

Description

Data from the Mayo Clinic trial in primary biliary cirrhosis (PBC) of the liver. This dataset was obtained from the survival package: the variables copper and trig from survival::pbc were merged into survival::pbcseq and several categorical variables were re-coded.

Format

PBC: A data frame of 312 individuals in long format with 1945 rows and 21 variables.

Survival outcome and id

id

case number

futime

number of days between registration and the earlier of death, transplantation, or end of follow-up

status

status at endpoint ("censored", "transplant" or "dead")

Baseline covariates

trt

D-pen (D-penicillamine) vs placebo

age

in years

sex

male or female

copper

urine copper ($\mu$g/day)

trig

triglycerides (mg/dl)

Time-varying covariates

day

number of days between enrolment and this visit date; all measurements below refer to this date

albumin

serum albumin (mg/dl)

alk.phos

alkaline phosphatase (U/liter)

ascites

presence of ascites

ast

aspartate aminotransferase (U/ml)

bili

serum bilirubin (mg/dl)

chol

serum cholesterol (mg/dl)

edema

"no": no oedema, "(un)treated": untreated or successfully treated 1 oedema, "edema": oedema despite diuretic therapy

hepato

presence of hepatomegaly (enlarged liver)

platelet

platelet count

protime

standardised blood clotting time

spiders

blood vessel malformations in the skin

stage

histologic stage of disease (4 levels)

Examples

summary(PBC)

Description

This function plots a grid of histograms (for continuous variables) and bar plots (for categorical variables) and labels it with the proportion of missing values in each variable.

Usage

plot_all(data, nrow = NULL, ncol = NULL, fill = grDevices::grey(0.8),
  border = "black", allNA = FALSE, idvars = NULL, xlab = "",
  ylab = "frequency", ...)

Arguments

See Also

Vignette: Visualizing Incomplete Data

Examples

op <- par(mar = c(2,2,3,1), mgp = c(2, 0.6, 0))
plot_all(wideDF)
par(op)

Description

Plots densities and bar plots of the observed and imputed values in a long-format dataset (multiple imputed datasets stacked onto each other).

Usage

plot_imp_distr(data, imp = "Imputation_", id = ".id", rownr = ".rownr",
  ncol = NULL, nrow = NULL, labeller = NULL)

Arguments

Examples

## Not run: 
mod <- lme_imp(y ~ C1 + c2 + B2 + C2, random = ~ 1 | id, data = longDF,
               n.iter = 200, monitor_params = c(imps = TRUE), mess = FALSE)
impDF <- get_MIdat(mod, m = 5)
plot_imp_distr(impDF, id = "id", ncol = 3)

## End(Not run)

Description

Plot an object object inheriting from class 'JointAI'

Usage

## S3 method for class 'JointAI'
plot(x, ...)

Arguments

Note

Currently, plot() can only be used with (generalized) linear (mixed) models.

Examples

mod <- lm_imp(y ~ C1 + C2 + B1, data = wideDF, n.iter = 100)
plot(mod)

Description

Obtains predictions and corresponding credible intervals from an object of class 'JointAI'.

Usage

## S3 method for class 'JointAI'
predict(object, outcome = 1L, newdata,
  quantiles = c(0.025, 0.975), type = "lp", start = NULL, end = NULL,
  thin = NULL, exclude_chains = NULL, mess = TRUE, warn = TRUE,
  return_sample = FALSE, ...)

Arguments

Details

A model.matrix $X$ is created from the model formula (currently fixed effects only) and newdata. $X\beta$ is then calculated for each iteration of the MCMC sample in object, i.e., $X\beta$ has n.iter rows and nrow(newdata) columns. A subset of the MCMC sample can be selected using start, end and thin.

Value

A list with entries dat, fit and quantiles, where fit contains the predicted values (mean over the values calculated from the iterations of the MCMC sample), quantiles contain the specified quantiles (by default 2.5% and 97.5%), and dat is newdata, extended with fit and quantiles (unless prediction for an ordinal outcome is done with type = "prob", in which case the quantiles are an array with three dimensions and are therefore not included in dat).

Note

• So far, predict cannot calculate predicted values for cases with missing values in covariates. Predicted values for such cases are NA.

• For repeated measures models prediction currently only uses fixed effects.

Functionality will be extended in the future.

See Also

predDF.JointAI, *_imp

Examples

# fit model
mod <- lm_imp(y ~ C1 + C2 + I(C2^2), data = wideDF, n.iter = 100)

# calculate the fitted values
fit <- predict(mod)

# create dataset for prediction
newDF <- predDF(mod, vars = ~ C2)

# obtain predicted values
pred <- predict(mod, newdata = newDF)

# plot predicted values and 95% confidence band
matplot(newDF$C2, pred$fitted, lty = c(1, 2, 2), type = "l", col = 1,
xlab = 'C2', ylab = 'predicted values')

Description

Obtain and print the summary, (fixed effects) coefficients (coef) and credible interval (confint) for an object of class 'JointAI'.

Usage

## S3 method for class 'Dmat'
print(x, digits = getOption("digits"),
  scientific = getOption("scipen"), ...)

## S3 method for class 'JointAI'
summary(object, start = NULL, end = NULL, thin = NULL,
  quantiles = c(0.025, 0.975), subset = NULL, exclude_chains = NULL,
  outcome = NULL, missinfo = FALSE, warn = TRUE, mess = TRUE, ...)

## S3 method for class 'summary.JointAI'
print(x, digits = max(3, .Options$digits - 4), ...)

## S3 method for class 'JointAI'
coef(object, start = NULL, end = NULL, thin = NULL,
  subset = NULL, exclude_chains = NULL, warn = TRUE, mess = TRUE, ...)

## S3 method for class 'JointAI'
confint(object, parm = NULL, level = 0.95,
  quantiles = NULL, start = NULL, end = NULL, thin = NULL,
  subset = NULL, exclude_chains = NULL, warn = TRUE, mess = TRUE, ...)

## S3 method for class 'JointAI'
print(x, digits = max(4, getOption("digits") - 4), ...)

Arguments

See Also

The model fitting functions lm_imp, glm_imp, clm_imp, lme_imp, glme_imp, survreg_imp and coxph_imp, and the vignette Parameter Selection for examples how to specify the parameter subset.

Examples

## Not run: 
mod1 <- lm_imp(y ~ C1 + C2 + M2, data = wideDF, n.iter = 100)

summary(mod1, missinfo = TRUE)
coef(mod1)
confint(mod1)

## End(Not run)

Description

Extract the random effects variance covariance matrix Returns the posterior mean of the variance-covariance matrix/matrices of the random effects in a fitted JointAI object.

Usage

rd_vcov(object, outcome = NULL, start = NULL, end = NULL, thin = NULL,
  exclude_chains = NULL, mess = TRUE, warn = TRUE)

Arguments

Description

Extract residuals from an object of class JointAI

Usage

## S3 method for class 'JointAI'
residuals(object, type = c("working", "pearson",
  "response"), warn = TRUE, ...)

Arguments

Note

• For mixed models residuals are currently calculated using the fixed effects only.

• For ordinal (mixed) models and parametric survival models only type = "response" is available.

• For Cox proportional hazards models residuals are not yet implemented.

Examples

mod <- glm_imp(B1 ~ C1 + C2 + O1, data = wideDF, n.iter = 100,
               family = binomial(), mess = FALSE)
summary(residuals(mod, type = 'response')[[1]])
summary(residuals(mod, type = 'working')[[1]])

Description

The function is a helper function that asks questions and, depending on the answers given by the user, returns the input for the argument refcats in the main analysis functions *_imp.

Usage

set_refcat(data, formula, covars, auxvars = NULL)

Arguments

Details

The arguments formula, covars and auxvars can be used to specify a subset of the data to be considered. If non of these arguments is specified, all variables in data will be considered.

Examples

## Not run: 
# Example 1: set reference categories for the whole dataset and choose
# answer option 3:
set_refcat(data = NHANES)
3

# insert the returned string as argument refcats
mod1 <- lm_imp(SBP ~ age + race + creat + educ, data = NHANES,
               refcats = 'largest')

# Example 2:
# specify a model formula
fmla <- SBP ~ age + gender + race + bili + smoke + alc

# write the output of set_refcat to an object
ref_mod2 <- set_refcat(data = NHANES, formula = fmla)
4
2
5
1
1

# enter the output in the model specification
mod2 <- lm_imp(formula = fmla, data = NHANES, refcats = ref_mod2,
               n.adapt = 0)

## End(Not run)

Description

Parameters used by several functions in JointAI

Arguments

Description

This data was simulated to mimic data from a longitudinal cohort study following mothers and their child from birth until approximately 4 years of age. It contains 2400 observations of 200 mother-child pairs. Children's BMI and head circumference was measured repeatedly and their age in months was recorded at each measurement. Furthermore, the data contain several baseline variables with information on the mothers' demographics and socio-economic status.

Usage

simLong

simWide

Format

simLong: A data frame in long format with 2400 rows and 16 variables

simWide: A data frame in wide format with 200 rows and 81 variables

An object of class data.frame with 2400 rows and 16 columns.

An object of class data.frame with 200 rows and 81 columns.

Baseline covariates

(in simLong and simWide)

GESTBIR

gestational age at birth (in weeks)

ETHN

ethnicity (binary: European vs. other)

AGE_M

age of the mother at intake

HEIGHT_M

height of the mother (in cm)

PARITY

number of times the mother has given birth (binary: 0 vs. >=1)

SMOKE

smoking status of the mother during pregnancy (3 ordered categories: never smoked during pregnancy, smoked until pregnancy was known, continued smoking in pregnancy)

EDUC

educational level of the mother (3 ordered categories: low, mid, high)

MARITAL

marital status (3 categories)

ID

subject identifier

Long-format variables

(only in simLong)

time

measurement occasion/visit (by design, children should be measured at/around 1, 2, 3, 4, 7, 11, 15, 20, 26, 32, 40 and 50 months of age)

age

child age at measurement time in months

bmi

child BMI

hc

child head circumference in cm

hgt

child height in cm

wgt

child weight in gram

sleep

sleeping behaviour of the child (3 ordered categories)

Wide-format variables

(only in simWide)

age1, age2, age3, age4, age7, age11, age15, age20, age26, age32, age40, age50

child age at the repeated measurements in months

bmi1, bmi2, bmi3, bmi4, bmi7, bmi11, bmi15, bmi20, bmi26, bmi32, bmi40, bmi50

repeated measurements of child BMI

hc1, hc2, hc3, hc4, hc7, hc11, hc15, hc20, hc26, hc32, hc40, hc50

repeated measurements of child head circumference in cm

hgt1, hgt2, hgt3, hgt4, hgt7, hgt11, hgt15, hgt20, hgt26, hgt32, hgt40, hgt50

repeated measurements of child height in cm

wgt1, wgt2, wgt3, wgt4, wgt7, wgt11, wgt15, wgt20, wgt26, wgt32, wgt40, wgt50

repeated measurements of child weight in gram

sleep1, sleep2, sleep3, sleep4, sleep7, sleep11, sleep15, sleep20, sleep26, sleep32, sleep40, sleep50

repeated measurements of child sleep behaviour (3 ordered categories)

Examples

summary(simLong)
 summary(simWide)

Description

Calculate the sum of the computational duration of a JointAI object

Usage

sum_duration(object, by = NULL)

Arguments

Description

Creates a set of traceplots from the MCMC sample of an object of class 'JointAI'.

Usage

traceplot(object, ...)

## S3 method for class 'JointAI'
traceplot(object, start = NULL, end = NULL,
  thin = NULL, subset = c(analysis_main = TRUE), outcome = NULL,
  exclude_chains = NULL, nrow = NULL, ncol = NULL, use_ggplot = FALSE,
  warn = TRUE, mess = TRUE, ...)

Arguments

See Also

summary.JointAI, *_imp, densplot
The vignette Parameter Selection contains some examples how to specify the parameter subset.

Examples

# fit a JointAI model
mod <- lm_imp(y ~ C1 + C2 + M1, data = wideDF, n.iter = 100)


# Example 1: simple traceplot
traceplot(mod)


# Example 2: ggplot version of traceplot
traceplot(mod, use_ggplot = TRUE)


# Example 5: changing how the ggplot version looks (using ggplot syntax)
library(ggplot2)

traceplot(mod, use_ggplot = TRUE) +
  theme(legend.position = 'bottom') +
  xlab('iteration') +
  ylab('value') +
  scale_color_discrete(name = 'chain')

Description

A simulated cross-sectional dataset.

Usage

data(wideDF)

Format

A simulated data frame with 100 rows and 13 variables:

C1

continuous, complete variable

C2

continuous, incomplete variable

B1

binary, complete variable

B2

binary, incomplete variable

M1

unordered factor; complete variable

M2

unordered factor; incomplete variable

O1

ordered factor; complete variable

O2

ordered factor; incomplete variable

L1

continuous, complete variable

L2

continuous incomplete variable

id

id (grouping) variable

time

continuous complete variable

y

continuous, complete variable