Package 'flexmix'

Description

Compute the Akaike Information Criterion.

Methods

object = flexmix:

Compute the AIC of a flexmix object

object = stepFlexmix:

Compute the AIC of all models contained in the stepFlexmix object.

Description

22-centre clinical trial of beta-blockers for reducing mortality after myocardial infarction.

Usage

data("betablocker")

Format

A data frame with 44 observations on the following 4 variables.

Deaths

Number of deaths.

Total

Total number of patients.

Center

Number of clinical centre.

Treatment

A factor with levels Control and Treated.

Source

G. McLachlan and D. Peel. Finite Mixture Models, 2000. John Wiley and Sons Inc. http://www.maths.uq.edu.au/~gjm/DATA/mmdata.html

References

M. Aitkin. Meta-analysis by random effect modelling in generalized linear models. Statistics in Medicine, 18, 2343–2351, 1999.

S. Yusuf, R. Peto, J. Lewis, R. Collins and P. Sleight. Beta blockade during and after myocardial infarction: an overview of the randomized trials. Progress in Cardiovascular Diseases, 27, 335–371, 1985.

Examples

data("betablocker", package = "flexmix")
betaMix <- initFlexmix(cbind(Deaths, Total - Deaths) ~ 1 | Center,
                       data = betablocker, k = 3, nrep = 5,
                       model = FLXMRglmfix(family = "binomial",
                         fixed = ~Treatment))

Description

Compute the Bayesian Information Criterion.

Methods

object = flexmix:

Compute the BIC of a flexmix object

object = stepFlexmix:

Compute the BIC of all models contained in the stepFlexmix object.

Description

A sample of 915 biochemistry graduate students.

Usage

data("bioChemists")

Format

art

count of articles produced during last 3 years of Ph.D.

fem

factor indicating gender of student, with levels Men and Women

mar

factor indicating marital status of student, with levels Single and Married

kid5

number of children aged 5 or younger

phd

prestige of Ph.D. department

ment

count of articles produced by Ph.D. mentor during last 3 years

Details

This data set is taken from package pscl provided by Simon Jackman.

Source

found in Stata format at https://jslsoc.sitehost.iu.edu/stata/spex_data/couart2.dta

References

Long, J. Scott. The origins of sex difference in science. Social Forces, 68, 1297–1315, 1990.

Long, J. Scott. Regression Models for Categorical and Limited Dependent Variables, 1997. Thousand Oaks, California: Sage.

Description

Given a flexmix object perform parametric or empirical bootstrap.

Usage

boot(object, ...)
## S4 method for signature 'flexmix'
boot(object, R, sim = c("ordinary", "empirical", "parametric"),
    initialize_solution = FALSE, keep_weights = FALSE,
    keep_groups = TRUE, verbose = 0, control,
    k, model = FALSE, ...)
LR_test(object, ...)
## S4 method for signature 'flexmix'
LR_test(object, R, alternative = c("greater", "less"), control, ...)

Arguments

Value

boot returns an object of class FLXboot which contains the fitted parameters, the fitted priors, the log likelihoods, the number of components of the fitted mixtures and the information if the EM algorithm has converged.

LR_test returns an object of class htest containing the number of valid bootstrap replicates, the p-value, the - twice log likelihood ratio test statistics for the original data and the bootstrap replicates.

Author(s)

Bettina Gruen

Examples

data("NPreg", package = "flexmix")
fitted <- initFlexmix(yn ~ x + I(x^2) | id2, data = NPreg, k = 2)
## Not run: 
lrtest <- LR_test(fitted, alternative = "greater", R = 20,
                  verbose = 1)

## End(Not run)

Description

A simple artificial regression example data set with 3 latent classes, one independent variable x and a concomitant variable w.

Usage

data("BregFix")

Format

A data frame with 200 observations on the following 5 variables.

yes

number of successes

no

number of failures

x

independent variable

w

concomitant variable, a factor with levels 0 1

class

latent class memberships

Examples

data("BregFix", package = "flexmix")
Model <- FLXMRglmfix(family="binomial",
                     nested = list(formula = c(~x, ~0), k = c(2, 1)))
Conc <- FLXPmultinom(~w)
FittedBin <- initFlexmix(cbind(yes, no) ~ 1, data = BregFix,
                         k = 3, model = Model, concomitant = Conc)
summary(FittedBin)

Description

The data is from a new product and concept test where the number of individual packs of hard candy purchased within the past 7 days is recorded.

Usage

data("candy")

Format

A data frame with 21 observations on the following 2 variables.

Packages

a numeric vector

Freq

a numeric vector

Source

D. Boehning, E. Dietz and P. Schlattmann. Recent Developments in Computer-Assisted Analysis of Mixtures. Biometrics 54(2), 525–536, 1998.

References

J. Magidson and J. K. Vermunt. Latent Class Models. In D. W. Kaplan (ed.), The Sage Handbook of Quantitative Methodology for the Social Sciences, 175–198, 2004. Thousand Oakes: Sage Publications.

D. Boehning, E. Dietz and P. Schlattmann. Recent Developments in Computer-Assisted Analysis of Mixtures. Biometrics, 54(2), 525–536, 1998.

W. R. Dillon and A. Kumar. Latent structure and other mixture models in marketing: An integrative survey and overview. In R. P. Bagozzi (ed.), Advanced methods of marketing research, 352–388, 1994. Cambridge, UK: Blackwell.

Description

Count data from a dental epidemiological study for evaluation of various programs for reducing caries collected among school children from an urban area of Belo Horizonte (Brazil).

Usage

data("dmft")

Format

A data frame with 797 observations on the following 5 variables.

End

Number of decayed, missing or filled teeth at the end of the study.

Begin

Number of decayed, missing or filled teeth at the beginning of the study.

Gender

A factor with levels male and female.

Ethnic

A factor with levels brown, white and black.

Treatment

A factor with levels control, educ, enrich, rinse, hygiene and all.

Details

The aim of the caries prevention study was to compare four methods to prevent dental caries. Interventions were carried out according to the following scheme:

control

Control group

educ

Oral health education

enrich

Enrichment of the school diet with rice bran

rinse

Mouthwash with 0.2% sodium floride (NaF) solution

hygiene

Oral hygiene

all

All four methods together

Source

D. Boehning, E. Dietz, P. Schlattmann, L. Mendonca and U. Kirchner. The zero-inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology. Journal of the Royal Statistical Society A, 162(2), 195–209, 1999.

Examples

data("dmft", package = "flexmix")
dmft_flx <- initFlexmix(End ~ 1, data = dmft, k = 2,
                        model = FLXMRglmfix(family = "poisson", 
                        fixed = ~ Gender + Ethnic + Treatment))

Description

Compute the entropic measure information criterion for model selection.

Usage

## S4 method for signature 'flexmix'
EIC(object, ...)
## S4 method for signature 'stepFlexmix'
EIC(object, ...)

Arguments

Value

Returns a numeric vector with the corresponding EIC value(s).

Methods

object = "flexmix":

Compute the EIC of a flexmix object.

object = "stepFlexmix":

Compute the EIC of all models contained in the stepFlexmix object.

Author(s)

Bettina Gruen

References

V. Ramaswamy, W. S. DeSarbo, D. J. Reibstein, and W. T. Robinson. An empirical pooling approach for estimating marketing mix elasticities with PIMS data. Marketing Science, 12(1), 103–124, 1993.

Examples

data("NPreg", package = "flexmix")
ex1 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2)
EIC(ex1)

Description

Generate random data mixed from k generalized linear regressions (GLMs).

Usage

ExLinear(beta, n, xdist = "runif", xdist.args = NULL,
         family = c("gaussian","poisson"), sd = 1, ...)

Arguments

Details

First, arguments n (and sd for Gaussian response) are recycled to the number of mixture components ncol(beta), and arguments xdist and xdist.args are recycled to the number of explanatory variables nrow(beta)-1. Then a design matrix is created for each mixture component by drawing random numbers from xdist. For each component, the design matrix is multiplied by the regression coefficients to form the linear predictor. For Gaussian responses the identity link is used, for Poisson responses the log link.

The true cluster memberships are returned as attribute "clusters".

Examples

## simple example in 2d
beta <- matrix(c(1, 2, 3, -1), ncol = 2)
sigma <- c(.5, 1)
df1 <- ExLinear(beta, 100, sd = sigma, min = -1, max = 2)
plot(y~x1, df1, col = attr(df1, "clusters"))

## add a second explanatory variable with exponential distribution
beta2 <- rbind(beta, c(-2, 2))
df2 <-  ExLinear(beta2, 100, sd = c(.5, 1),
                 xdist = c("runif", "rexp"),
                 xdist.args = list(list(min = -1, max = 2),
                                   list(rate = 3)))

summary(df2)

opar = par("mfrow")
par(mfrow = 1:2)
hist(df2$x1)
hist(df2$x2)
par(opar)

f1 <- flexmix(y ~ ., data = df2, k = 2)

## sort components on Intercept
f1 <- relabel(f1, "model", "Intercept")

## the parameters should be close to the true beta and sigma
round(parameters(f1), 3)
rbind(beta2, sigma)

### A simple Poisson GLM
df3 <- ExLinear(beta/2, 100, min = -1, max = 2, family = "poisson")
plot(y ~ x1, df3, col = attr(df3, "clusters"))

f3 <- flexmix(y ~ ., data = df3, k = 2,
              model = FLXMRglm(family = "poisson"))
round(parameters(relabel(f3, "model", "Intercept")), 3)
beta/2

Description

A simple artificial example for normal clustering with 4 latent classes, all of them having a Gaussian distribution. See the function definition for true means and covariances.

Usage

ExNclus(n)
data("Nclus")

Arguments

Details

The Nclus data set can be re-created by ExNclus(100) using set.seed(2602), it has been saved as a data set for simplicity of examples only.

Examples

data("Nclus", package = "flexmix")
require("MASS")
eqscplot(Nclus, col = rep(1:4, c(100, 100, 150, 200)))

Description

A simple artificial regression example with 2 latent classes, one independent variable (uniform on $[0,10]$), and three dependent variables with Gaussian, Poisson and Binomial distribution, respectively.

Usage

ExNPreg(n)
data("NPreg")

Arguments

Details

The NPreg data frame can be re-created by ExNPreg(100) using set.seed(2602), it has been saved as a data set for simplicity of examples only.

Examples

data("NPreg", package = "flexmix")
plot(yn ~ x, data = NPreg, col = class)
plot(yp ~ x, data = NPreg, col = class)
plot(yb ~ x, data = NPreg, col = class)

Description

Number of faults in rolls of a textile fabric.

Usage

data("fabricfault")

Format

A data frame with 32 observations on the following 2 variables.

Length

Length of role (m).

Faults

Number of faults.

Source

G. McLachlan and D. Peel. Finite Mixture Models, 2000, John Wiley and Sons Inc. http://www.maths.uq.edu.au/~gjm/DATA/mmdata.html

References

A. F. Bissell. A Negative Binomial Model with Varying Element Sizes Biometrika, 59, 435–441, 1972.

M. Aitkin. A general maximum likelihood analysis of overdispersion in generalized linear models. Statistics and Computing, 6, 251–262, 1996.

Examples

data("fabricfault", package = "flexmix")
fabricMix <- initFlexmix(Faults ~ 1, data = fabricfault, k = 2,
                         model = FLXMRglmfix(family = "poisson",
                           fixed = ~ log(Length)), 
                         nrep = 5)

Description

Extract fitted values for each component from a flexmix object.

Usage

## S4 method for signature 'flexmix'
fitted(object, drop = TRUE, aggregate = FALSE, ...)

Arguments

Author(s)

Friedrich Leisch and Bettina Gruen

Examples

data("NPreg", package = "flexmix")
ex1 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2)
matplot(NPreg$x, fitted(ex1), pch = 16, type = "p")
points(NPreg$x, NPreg$yn)

Description

FlexMix implements a general framework for finite mixtures of regression models. Parameter estimation is performed using the EM algorithm: the E-step is implemented by flexmix, while the user can specify the M-step.

Usage

flexmix(formula, data = list(), k = NULL, cluster = NULL, 
        model = NULL, concomitant = NULL, control = NULL,
        weights = NULL)
## S4 method for signature 'flexmix'
summary(object, eps = 1e-4, ...)

Arguments

Details

FlexMix models are described by objects of class FLXM, which in turn are created by driver functions like FLXMRglm or FLXMCmvnorm. Multivariate responses with independent components can be specified using a list of FLXM objects.

The summary method lists for each component the prior probability, the number of observations assigned to the corresponding cluster, the number of observations with a posterior probability larger than eps and the ratio of the latter two numbers (which indicates how separated the cluster is from the others).

Value

Returns an object of class flexmix.

Author(s)

Friedrich Leisch and Bettina Gruen

References

Friedrich Leisch. FlexMix: A general framework for finite mixture models and latent class regression in R. Journal of Statistical Software, 11(8), 2004. doi:10.18637/jss.v011.i08

Bettina Gruen and Friedrich Leisch. Fitting finite mixtures of generalized linear regressions in R. Computational Statistics & Data Analysis, 51(11), 5247-5252, 2007. doi:10.1016/j.csda.2006.08.014

Bettina Gruen and Friedrich Leisch. FlexMix Version 2: Finite mixtures with concomitant variables and varying and constant parameters Journal of Statistical Software, 28(4), 1-35, 2008. doi:10.18637/jss.v028.i04

See Also

plot-methods

Examples

data("NPreg", package = "flexmix")

## mixture of two linear regression models. Note that control parameters
## can be specified as named list and abbreviated if unique.
ex1 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2,
               control = list(verb = 5, iter = 100))

ex1
summary(ex1)
plot(ex1)

## now we fit a model with one Gaussian response and one Poisson
## response. Note that the formulas inside the call to FLXMRglm are
## relative to the overall model formula.
ex2 <- flexmix(yn ~ x, data = NPreg, k = 2,
               model = list(FLXMRglm(yn ~ . + I(x^2)), 
                            FLXMRglm(yp ~ ., family = "poisson")))
plot(ex2)

ex2
table(ex2@cluster, NPreg$class)

## for Gaussian responses we get coefficients and standard deviation
parameters(ex2, component = 1, model = 1)

## for Poisson response we get only coefficients
parameters(ex2, component = 1, model = 2)

## fitting a model only to the Poisson response is of course
## done like this
ex3 <- flexmix(yp ~ x, data = NPreg, k = 2,
               model = FLXMRglm(family = "poisson"))

## if observations are grouped, i.e., we have several observations per
## individual, fitting is usually much faster:
ex4 <- flexmix(yp~x|id1, data = NPreg, k = 2,
               model = FLXMRglm(family = "poisson"))

## And now a binomial example. Mixtures of binomials are not generically
## identified, here the grouping variable is necessary:
set.seed(1234)
ex5 <- initFlexmix(cbind(yb,1 - yb) ~ x, data = NPreg, k = 2,
                   model = FLXMRglm(family = "binomial"), nrep = 5)
table(NPreg$class, clusters(ex5))

ex6 <- initFlexmix(cbind(yb, 1 - yb) ~ x | id2, data = NPreg, k = 2,
                   model = FLXMRglm(family = "binomial"), nrep = 5)
table(NPreg$class, clusters(ex6))

Description

A fitted flexmix model.

Slots

model:

List of FLXM objects.

prior:

Numeric vector with prior probabilities of clusters.

posterior:

Named list with elements scaled and unscaled, both matrices with one row per observation and one column per cluster.

iter:

Number of EM iterations.

k:

Number of clusters after EM.

k0:

Number of clusters at start of EM.

cluster:

Cluster assignments of observations.

size:

Cluster sizes.

logLik:

Log-likelihood at EM convergence.

df:

Total number of parameters of the model.

components:

List describing the fitted components using FLXcomponent objects.

formula:

Object of class "formula".

control:

Object of class "FLXcontrol".

call:

The function call used to create the object.

group:

Object of class "factor".

converged:

Logical, TRUE if EM algorithm converged.

concomitant:

Object of class "FLXP"..

weights:

Optional weights of the observations.

Extends

Class FLXdist, directly.

Accessor Functions

The following functions should be used for accessing the corresponding slots:

cluster:

Cluster assignments of observations.

posterior:

A matrix of posterior probabilities for each observation.

Author(s)

Friedrich Leisch and Bettina Gruen

Description

A fitted component of a flexmix model.

Objects from the Class

Objects can be created by calls of the form new("FLXcomponent", ...).

Slots

df:

Number of parameters used by the component.

logLik:

Function computing the log-likelihood of observations.

parameters:

List with model parameters.

predict:

Function predicting response for new data.

Author(s)

Friedrich Leisch and Bettina Gruen

Description

Hyperparameters for the EM algorithm.

Objects from the Class

Objects can be created by calls of the form new("FLXcontrol", ...). In addition, named lists can be coerced to FLXcontrol objects, names are completed if unique (see examples).

Slots

iter.max:

Maximum number of iterations.

minprior:

Minimum prior probability of clusters, components falling below this threshold are removed during the iteration.

tolerance:

The EM algorithm is stopped when the (relative) change of log-likelihood is smaller than tolerance.

verbose:

If a positive integer, then the log-likelihood is reported every verbose iterations. If 0, no output is generated during model fitting.

classify:

Character string, one of "auto", "weighted", "hard" (or "CEM"), "random" or ("SEM").

nrep:

Reports the number of random initializations used in stepFlexmix() to determine the mixture.

Run new("FLXcontrol") to see the default settings of all slots.

Author(s)

Friedrich Leisch and Bettina Gruen

Examples

## have a look at the defaults
new("FLXcontrol")

## corce a list
mycont <- list(iter = 200, tol = 0.001, class = "r")
as(mycont, "FLXcontrol")

Description

Constructs objects of class FLXdist which represent unfitted finite mixture models.

Usage

FLXdist(formula, k = NULL, model = FLXMRglm(), components,
         concomitant = FLXPconstant())

Arguments

Value

Returns an object of class FLXdist.

Author(s)

Bettina Gruen

See Also

FLXdist-class

Description

Objects of class FLXdist represent unfitted finite mixture models.

Usage

## S4 method for signature 'FLXdist'
parameters(object, component = NULL, model = NULL, which = c("model",
    "concomitant"), simplify = TRUE, drop = TRUE)
## S4 method for signature 'FLXdist'
predict(object, newdata = list(), aggregate = FALSE, ...)

Arguments

Slots

model

List of FLXM objects.

prior

Numeric vector with prior probabilities of clusters.

components

List describing the components using FLXcomponent objects.

concomitant:

Object of class "FLXP".

formula

Object of class "formula".

call

The function call used to create the object.

k

Number of clusters.

Accessor Functions

The following functions should be used for accessing the corresponding slots:

parameters:

The parameters for each model and component, return value depends on the model.

prior:

Numeric vector of prior class probabilities/component weights

Author(s)

Friedrich Leisch and Bettina Gruen

See Also

FLXdist

Description

This is the basic computing engine called by flexmix, it should usually not be used directly.

Usage

FLXfit(model, concomitant, control, postunscaled = NULL, groups,
       weights)

Arguments

Value

Returns an object of class flexmix.

Author(s)

Friedrich Leisch and Bettina Gruen

See Also

flexmix, flexmix-class

Description

FlexMix model specification.

Details

The most generic class is the virtual class FLXM. The classes FLXMC for model-based clustering and FLXMR for clusterwise regression extend the virtual class. Both have further more specific model classes which inherit from them.

Model class FLXMCsparse allows for model-based clustering with a sparse matrix as data input.

Objects from the Class

Objects can be created by calls of the form new("FLXM", ...), typically inside driver functions like FLXMRglm or FLXMCmvnorm.

Slots

fit:

Function returning an FLXcomponent object.

defineComponent:

Function or expression to determine the FLXcomponent object given the parameters.

weighted:

Logical indicating whether fit can do weighted likelihood maximization.

name:

Character string used in print methods.

formula:

Formula describing the model.

fullformula:

Resulting formula from updating the model formula with the formula specified in the call to flexmix.

x:

Model matrix.

y:

Model response.

terms, xlevels, contrasts:

Additional information for model matrix.

preproc.x:

Function for preprocessing matrix x before the EM algorithm starts, by default the identity function.

preproc.y:

Function for preprocessing matrix y before the EM algorithm starts, by default the identity function.

Author(s)

Friedrich Leisch and Bettina Gruen

Description

These are drivers for flexmix implementing model-based clustering of univariate data using different distributions for the component-specific models.

Usage

FLXMCdist1(formula = . ~ ., dist, ...)

Arguments

Details

Currently drivers for the following distributions are available:

1. Lognormal ("lnorm")

2. inverse Gaussian ("invGauss" using dinvGauss)

3. gamma ("gamma")

4. exponential ("exp")

5. Weibull ("weibull")

6. Burr ("burr" using dburr)

7. Inverse Burr ("invburr" using dinvburr)

Value

FLXMCdist1 returns an object of class FLXMC.

Author(s)

Friedrich Leisch and Bettina Gruen

References

Tatjana Miljkovic and Bettina Gruen. Modeling loss data using mixtures of distributions. Insurance: Mathematics and Economics, 70, 387-396, 2016. doi:10.1016/j.insmatheco.2016.06.019

See Also

flexmix

Examples

if (require("actuar")) {
    set.seed(123)
    y <- c(rexp(100, 10), rexp(100, 1))
    ex <- flexmix(y ~ 1, cluster = rep(1:2, each = 100), model = FLXMCdist1(dist = "exp"))    
    parameters(ex)
}

Description

This driver for flexmix implements estimation of mixtures of factor analyzers using ML estimation of factor analysis implemented in factanal in each M-step.

Usage

FLXMCfactanal(formula = . ~ ., factors = 1, ...)

Arguments

Value

FLXMCfactanal returns an object of class FLXM.

Warning

This does not implement the AECM framework presented in McLachlan and Peel (2000, p.245), but uses the available functionality in R for ML estimation of factor analyzers. The implementation therefore is only experimental and has not been well tested.

Please note that in general a good initialization is crucial for the EM algorithm to converge to a suitable solution for this model class.

Author(s)

Bettina Gruen

References

G. McLachlan and D. Peel. Finite Mixture Models, 2000. John Wiley and Sons Inc.

See Also

flexmix

Examples

## Reproduce (partly) Table 8.1. p.255 (McLachlan and Peel, 2000)
if (require("gclus")) {
  data("wine", package = "gclus")
  wine_data <- as.matrix(wine[,-1])
  set.seed(123)
  wine_fl_diag <- initFlexmix(wine_data ~ 1, k = 3, nrep = 10,
                              model = FLXMCmvnorm(diagonal = TRUE))
  wine_fl_fact <- lapply(1:4, function(q) flexmix(wine_data ~ 1, model =
                          FLXMCfactanal(factors = q, nstart = 3),
                          cluster = posterior(wine_fl_diag)))
  sapply(wine_fl_fact, logLik)
  ## FULL
  set.seed(123)
  wine_full <- initFlexmix(wine_data ~ 1, k = 3, nrep = 10,
                           model = FLXMCmvnorm(diagonal = FALSE))
  logLik(wine_full)
  ## TRUE
  wine_true <- flexmix(wine_data ~ 1, cluster = wine$Class,
                       model = FLXMCmvnorm(diagonal = FALSE))
  logLik(wine_true)
}

Description

This is a model driver for flexmix implementing model-based clustering of binary data.

Usage

FLXMCmvbinary(formula = . ~ ., truncated = FALSE)

Arguments

Details

This model driver can be used to cluster binary data. The only parameter is the column-wise mean of the data, which equals the probability of observing a 1.

Value

FLXMCmvbinary returns an object of class FLXMC.

Author(s)

Friedrich Leisch and Bettina Gruen

See Also

flexmix

Description

This is a model driver for flexmix implementing model-based clustering of a combination of binary and Gaussian data.

Usage

FLXMCmvcombi(formula = . ~ .)

Arguments

Details

This model driver can be used to cluster mixed-mode binary and Gaussian data. It checks which columns of a matrix contain only zero and ones, and does the same as FLXMCmvbinary for them. For the remaining columns of the data matrix independent Gaussian distributions are used (same as FLXMCmvnorm with diagonal = FALSE. The same could be obtained by creating a corresponding list of two models for the respective columns, but FLXMCmvcombi does a better job in reporting parameters.

Value

FLXMCmvcombi returns an object of class FLXMC.

Author(s)

Friedrich Leisch

See Also

flexmix, FLXMCmvbinary, FLXMCmvnorm

Examples

## create some artificial data
x1 <- cbind(rnorm(300),
            sample(0:1, 300, replace = TRUE, prob = c(0.25, 0.75)))
x2 <- cbind(rnorm(300, mean = 2, sd = 0.5),
            sample(0:1, 300, replace = TRUE, prob = c(0.75, 0.25)))
x <- rbind(x1, x2)

## fit the model
f1 <- flexmix(x ~ 1, k = 2, model = FLXMCmvcombi())
## should be similar to the original parameters
parameters(f1)
table(clusters(f1), rep(1:2, c(300,300)))

## a column with noise should not hurt too much
x <- cbind(x, rnorm(600))
f2 <- flexmix(x ~ 1, k = 2, model = FLXMCmvcombi())
parameters(f2)
table(clusters(f2), rep(1:2, c(300,300)))

Description

These are demo drivers for flexmix implementing model-based clustering of Gaussian data.

Usage

FLXMCmvnorm(formula = . ~ ., diagonal = TRUE)
FLXMCnorm1(formula = . ~ .)

Arguments

Details

This is mostly meant as a demo for FlexMix driver programming, you should also look at package mclust for real applications. FLXMCmvnorm clusters multivariate data, FLXMCnorm1 univariate data. In the latter case smart initialization is important, see the example below.

Value

FLXMCmvnorm returns an object of class FLXMC.

Author(s)

Friedrich Leisch and Bettina Gruen

References

Friedrich Leisch. FlexMix: A general framework for finite mixture models and latent class regression in R. Journal of Statistical Software, 11(8), 2004. doi:10.18637/jss.v011.i08

See Also

flexmix

Examples

data("Nclus", package = "flexmix")

require("MASS")
eqscplot(Nclus)

## This model is wrong (one component has a non-diagonal cov matrix)
ex1 <- flexmix(Nclus ~ 1, k = 4, model = FLXMCmvnorm())
print(ex1)
plotEll(ex1, Nclus)

## True model, wrong number of components
ex2 <- flexmix(Nclus ~ 1, k = 6, model = FLXMCmvnorm(diagonal = FALSE))  
print(ex2)

plotEll(ex2, Nclus)

## Get parameters of first component
parameters(ex2, component = 1)

## Have a look at the posterior probabilies of 10 random observations
ok <- sample(1:nrow(Nclus), 10)
p  <- posterior(ex2)[ok, ]
p

## The following two should be the same
max.col(p)
clusters(ex2)[ok]

## Now try the univariate case
plot(density(Nclus[, 1]))

ex3 <- flexmix(Nclus[, 1] ~ 1, cluster = cut(Nclus[, 1], 3),
               model = FLXMCnorm1())
ex3
parameters(ex3)

Description

This is a model driver for flexmix implementing model-based clustering of Poisson distributed data.

Usage

FLXMCmvpois(formula = . ~ .)

Arguments

Details

This can be used to cluster Poisson distributed data where given the component membership the variables are mutually independent.

Value

FLXMCmvpois returns an object of class FLXMC.

Author(s)

Friedrich Leisch and Bettina Gruen

See Also

flexmix

Description

Model driver for fitting mixtures of conditional logit models.

Usage

FLXMRcondlogit(formula = . ~ ., strata)

Arguments

Details

The M-step is performed using coxph.fit.

Value

Returns an object of class FLXMRcondlogit inheriting from FLXMRglm.

Warning

To ensure identifiability repeated measurements are necessary. Sufficient conditions are given in Gruen and Leisch (2008).

Author(s)

Bettina Gruen

References

Bettina Gruen and Friedrich Leisch. Identifiability of finite mixtures of multinomial logit models with varying and fixed effects. Journal of Classification, 25, 225–247. 2008.

See Also

FLXMRmultinom

Examples

if (require("Ecdat")) {
  data("Catsup", package = "Ecdat")
  ## To reduce the time needed for the example only a subset is used
  Catsup <- subset(Catsup, id %in% 1:100)
  Catsup$experiment <- seq_len(nrow(Catsup))
  vnames <- c("display", "feature", "price")
  Catsup_long <-
    reshape(Catsup,
            idvar = c("id", "experiment"),
            times = c(paste("heinz", c(41, 32, 28), sep = ""),
              "hunts32"),
            timevar = "brand",
            varying = matrix(colnames(Catsup)[2:13], nrow = 3, byrow = TRUE),
            v.names = vnames,
            direction = "long")
  Catsup_long$selected <- with(Catsup_long, choice == brand)
  Catsup_long <- Catsup_long[, c("id", "selected", "experiment", vnames, "brand")]
  Catsup_long$brand <- relevel(factor(Catsup_long$brand), "hunts32")
  set.seed(0808)
  flx1 <- flexmix(selected ~ display + feature + price + brand | id,
                  model = FLXMRcondlogit(strata = ~ experiment), 
                  data = Catsup_long, k = 1)
}

Description

This is the main driver for FlexMix interfacing the glm family of models.

Usage

FLXMRglm(formula = . ~ .,
         family = c("gaussian", "binomial", "poisson", "Gamma"),
         offset = NULL)

Arguments

Details

See flexmix for examples.

Value

Returns an object of class FLXMRglm inheriting from FLXMR.

Author(s)

Friedrich Leisch and Bettina Gruen

References

Friedrich Leisch. FlexMix: A general framework for finite mixture models and latent class regression in R. Journal of Statistical Software, 11(8), 2004. doi:10.18637/jss.v011.i08

See Also

flexmix, glm

Description

This implements a driver for FlexMix which interfaces the glm family of models and where it is possible to specify fixed (constant) or nested varying coefficients or to ensure that in the Gaussian case the variance estimate is equal for all components.

Usage

FLXMRglmfix(formula = . ~ ., fixed = ~0, varFix = FALSE, nested = NULL, 
       family = c("gaussian", "binomial", "poisson", "Gamma"),
       offset = NULL)

Arguments

Value

Returns an object of class FLXMRglmfix inheriting from FLXMRglm and FLXMRfix.

Author(s)

Friedrich Leisch and Bettina Gruen

See Also

FLXMRglm

Examples

data("NPreg", package = "flexmix")
ex <- flexmix(yn ~ x | id2, data = NPreg, k = 2,
              cluster = NPreg$class,
              model = FLXMRglm(yn ~ . + I(x^2)))
ex.fix <- flexmix(yn ~ x | id2, data = NPreg,
                  cluster = posterior(ex),
                  model = FLXMRglmfix(nested = list(k = c(1, 1),
                                      formula = c(~0, ~I(x^2)))))
summary(refit(ex))
## Not run: 
summary(refit(ex.fix))

## End(Not run)

Description

This is a driver which allows fitting of mixtures of GLMs where the coefficients are penalized using the (adaptive) lasso or the elastic net by reusing functionality from package glmnet.

Usage

FLXMRglmnet(formula = . ~ ., family = c("gaussian", "binomial", "poisson"),
              adaptive = TRUE, select = TRUE, offset = NULL, ...)

Arguments

Details

Some care is needed to ensure convergence of the algorithm, which is computationally more challenging than a standard EM. In the proposed method, not only are cluster allocations identified and component parameters estimated as commonly done in mixture models, but there is also variable selection via penalized regression using $k$-fold cross-validation to choose the penalty parameter. For the algorithm to converge, it is necessary that the same cross-validation partitioning be used across the EM iterations, i.e., the subsamples for cross-validation must be defined at the beginning This is accomplished using the foldid option as an additional parameter to be passed to cv.glmnet (see glmnet package documentation).

Value

Returns an object of class FLXMRglm.

Author(s)

Frederic Mortier and Nicolas Picard.

References

Frederic Mortier, Dakis-Yaoba Ouedraogo, Florian Claeys, Mahlet G. Tadesse, Guillaume Cornu, Fidele Baya, Fabrice Benedet, Vincent Freycon, Sylvie Gourlet-Fleury and Nicolas Picard. Mixture of inhomogeneous matrix models for species-rich ecosystems. Environmetrics, 26(1), 39-51, 2015. doi:10.1002/env.2320

See Also

FLXMRglm

Examples

set.seed(12)
    p <- 10
    beta <- matrix(0, nrow = p + 1, ncol = 2)
    beta[1,] <- c(-1, 1)
    beta[cbind(c(5, 10), c(1, 2))] <- 1

    nobs <- 100
    X <- matrix(rnorm(nobs * p), nobs, p)
    mu <- cbind(1, X) %*% beta
    z <- sample(1:ncol(beta), nobs, replace = TRUE)
    y <- mu[cbind(1:nobs, z)] + rnorm(nobs)
    data <- data.frame(y, X)
    ## The maximum number of iterations is reduced to
    ## avoid a long running time.
    fo <- sample(rep(seq(10), length = nrow(data)))
    ex1 <- flexmix(y ~ ., data = data, k = 2, cluster = z,
                   model = FLXMRglmnet(foldid = fo),
                   control = list(iter.max = 2))
    parameters(ex1)

Description

This is a driver which allows fitting of mixtures of linear models with random effects.

Usage

FLXMRlmm(formula = . ~ ., random, lm.fit = c("lm.wfit",
          "smooth.spline"), varFix = c(Random = FALSE, Residual =
          FALSE), ...)
FLXMRlmer(formula = . ~ ., random, weighted = TRUE,
          control = list(), eps = .Machine$double.eps)

Arguments

Details

FLXMRlmm allows only one random effect. FLXMRlmer allows an arbitrary number of random effects if weighted = FALSE; a certain structure of the model matrix of the random effects has to be given for weighted ML estimation, i.e. where weighted = TRUE.

Value

Returns an object of class FLXMRlmer and FLXMRlmm inheriting from FLXMRglm and FLXMR, respectively.

Warning

For FLXMRlmer the weighted ML estimation is only correct if the covariate matrix of the random effects is the same for each observation. By default weighted ML estimation is made and the condition on the covariate matrix of the random effects is checked. If this fails, only estimation with weighted = FALSE is possible which will maximize the classification likelihood.

Author(s)

Bettina Gruen

Examples

id <- rep(1:50, each = 10)
x <- rep(1:10, 50)
sample <- data.frame(y = rep(rnorm(unique(id)/2, 0, c(5, 2)), each = 10) +
                         rnorm(length(id), rep(c(3, 8), each = 10)) +
                         rep(c(0, 3), each = 10) * x,
                     x = x,
                     id = factor(id))
fitted <- flexmix(.~.|id, k = 2, model = FLXMRlmm(y ~ x, random = ~ 1),
                  data = sample, control = list(tolerance = 10^-3),
                  cluster = rep(rep(1:2, each = 10), 25))
parameters(fitted)

fitted1 <- flexmix(.~.|id, k = 2, model = FLXMRlmer(y ~ x, random = ~ 1),
                  data = sample, control = list(tolerance = 10^-3),
                  cluster = rep(rep(1:2, each = 10), 25))
parameters(fitted1)

fitted2 <- flexmix(.~.|id, k = 2,
                   model = FLXMRlmm(y ~ 0 + x, random = ~ 1,
                     lm.fit = "smooth.spline"),
                  data = sample, control = list(tolerance = 10^-3),
                  cluster = rep(rep(1:2, each = 10), 25))
parameters(fitted2)

Description

This is a driver which allows fitting of mixtures of linear models with random effects and left-censored observations.

Usage

FLXMRlmmc(formula = . ~ ., random, censored, varFix, eps = 10^-6, ...)

Arguments

Value

Returns an object of class FLXMRlmmc, FLXMRlmmcfix, FLXMRlmc or FLXMRlmcfix inheriting from FLXMR.

Author(s)

Bettina Gruen

Description

This is a driver which allows fitting of mixtures of GAMs.

Usage

FLXMRmgcv(formula = . ~ ., family = c("gaussian", "binomial", "poisson"),
          offset = NULL, control = NULL, optimizer = c("outer", "newton"),
          in.out = NULL, eps = .Machine$double.eps, ...)

Arguments

Value

Returns an object of class FLXMRmgcv inheriting from FLXMRglm.

Author(s)

Bettina Gruen

See Also

FLXMRglm

Examples

set.seed(2012)
x <- seq(0, 1, length.out = 100)
z <- sample(0:1, length(x), replace = TRUE)
y <- rnorm(length(x), ifelse(z, 5 * sin(x * 2 * pi), 10 * x - 5))
fitted_model <- flexmix(y ~ s(x), model = FLXMRmgcv(),
                        cluster = z + 1,
                        control = list(tolerance = 10^-3))
plot(y ~ x, col = clusters(fitted_model))
matplot(x, fitted(fitted_model), type = "l", add = TRUE)

Description

Model driver for fitting mixtures of multinomial logit models.

Usage

FLXMRmultinom(formula = . ~ ., ...)

Arguments

Details

The M-step is performed using nnet.default.

Value

Returns an object of class FLXMRmultinom inheriting from FLXMRglm.

Warning

To ensure identifiability repeated measurements are necessary. Sufficient conditions are given in Gruen and Leisch (2008).

Author(s)

Bettina Gruen

References

Bettina Gruen and Friedrich Leisch. Identifiability of finite mixtures of multinomial logit models with varying and fixed effects. Journal of Classification, 25, 225–247. 2008.

See Also

FLXMRcondlogit

Description

This driver adds a noise component to the mixture model which can be used to model background noise in the data. See the Compstat paper Leisch (2008) cited below for details.

Usage

FLXMRrobglm(formula = . ~ ., family = c("gaussian", "poisson"),
            bgw = FALSE, ...)

Arguments

Value

Returns an object of class FLXMRrobglm inheriting from FLXMRglm.

Note

The implementation of this model class is currently under development, and some methods like refit are still missing.

Author(s)

Friedrich Leisch and Bettina Gruen

References

Friedrich Leisch. Modelling background noise in finite mixtures of generalized linear regression models. In Paula Brito, editor, Compstat 2008–Proceedings in Computational Statistics, 385–396. Physica Verlag, Heidelberg, Germany, 2008.
Preprint available at http://epub.ub.uni-muenchen.de/6332/.

Examples

## Example from Compstat paper, see paper for detailed explanation:
data("NPreg", package = "flexmix")
DATA <- NPreg[, 1:2]
set.seed(3)
DATA2 <- rbind(DATA, cbind(x = -runif(3), yn = 50 + runif(3)))

## Estimation without (f2) and with (f3) background component
f2 <- flexmix(yn ~ x + I(x^2), data = DATA2, k = 2)
f3 <- flexmix(yn ~ x + I(x^2), data = DATA2, k = 3,
              model = FLXMRrobglm(), 
              control = list(minprior = 0))

## Predict on new data for plots
x <- seq(-5,15, by = .1)
y2 <- predict(f2, newdata = data.frame(x = x))
y3 <- predict(f3, newdata = data.frame(x = x))

## f2 was estimated without background component:
plot(yn ~ x, data = DATA2, pch = clusters(f2), col = clusters(f2))
lines(x, y2$Comp.1, col = 1)
lines(x, y2$Comp.2, col = 2)

## f3 is with background component:
plot(yn ~ x, data = DATA2, pch = 4 - clusters(f3),
     col = 4 - clusters(f3))
lines(x, y3$Comp.2, col = 2)
lines(x, y3$Comp.3, col = 1)

Description

This is a driver which allows fitting of zero inflated poisson and binomial models.

Usage

FLXMRziglm(formula = . ~ ., family = c("binomial", "poisson"), ...)

Arguments

Value

Returns an object of class FLXMRziglm inheriting from FLXMRglm.

Note

In fact this only approximates zero inflated models by fixing the coefficient of the intercept at -Inf and the other coefficients at zero for the first component.

Author(s)

Friedrich Leisch and Bettina Gruen

Examples

data("dmft", package = "flexmix")
  Model <- FLXMRziglm(family = "poisson")
  Fitted <- flexmix(End ~ log(Begin + 0.5) + Gender + Ethnic + Treatment, 
                    model = Model, k = 2 , data = dmft, 
                    control = list(minprior = 0.01))
  summary(refit(Fitted))

Description

Specification of nesting structure for regression coefficients.

Objects from the Class

Objects can be created by calls of the form new("FLXnested", formula, k, ...). In addition, named lists can be coerced to FLXnested objects, names are completed if unique.

Slots

formula:

Object of class "list" containing the formula for determining the model matrix for each nested parameter.

k:

Object of class "numeric" specifying the number of components in each group.

Author(s)

Friedrich Leisch and Bettina Gruen

Description

Creator functions for the concomitant variable model. FLXPconstant specifies constant priors and FLXPmultinom multinomial logit models for the priors.

Usage

FLXPconstant()
FLXPmultinom(formula = ~1)

Arguments

Details

FLXPmultinom uses nnet.default from nnet to fit the multinomial logit model.

Value

Object of class FLXP. FLXPmultinom returns an object of class FLXPmultinom which extends class FLXP directly and is used for method dispatching.

Author(s)

Friedrich Leisch and Bettina Gruen

Description

Concomitant model class.

Objects from the Class

Objects can be created by calls of the form new("FLXP", ...), typically inside driver functions like FLXPconstant or FLXPmultinom.

Slots

name:

Character string used in print methods.

formula:

Formula describing the model.

x:

Model matrix.

fit:

Function returning the fitted prior probabilities.

refit:

Function returning the fitted concomitant model.

coef:

Matrix containing the fitted parameters.

df:

Function for determining the number of degrees of freedom used.

Author(s)

Friedrich Leisch and Bettina Gruen

Description

Extract grouping variable for all observations.

Usage

## S4 method for signature 'flexmix'
group(object)
## S4 method for signature 'FLXM'
group(object)
## S4 method for signature 'FLXMRglmfix'
group(object)

Arguments

Author(s)

Bettina Gruen

Description

Compute the Integrated Completed Likelihood criterion for model selection.

Usage

## S4 method for signature 'flexmix'
ICL(object, ...)
## S4 method for signature 'stepFlexmix'
ICL(object, ...)

Arguments

Value

Returns a numeric vector with the corresponding ICL value(s).

Methods

object = "flexmix":

Compute the ICL of a flexmix object.

object = "stepFlexmix":

Compute the ICL of all models contained in the stepFlexmix object.

Author(s)

Friedrich Leisch and Bettina Gruen

References

C. Biernacki, G. Celeux, and G. Govaert. Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(7), 719–725, 2000.

Examples

data("NPreg", package = "flexmix")
ex1 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2)
ICL(ex1)

Description

Estimate the Kullback-Leibler divergence of several distributions.

Usage

## S4 method for signature 'matrix'
KLdiv(object, eps = 10^-4, overlap = TRUE,...)
## S4 method for signature 'flexmix'
KLdiv(object, method = c("continuous", "discrete"), ...)

Arguments

Details

Estimates

$\int f(x) (\log f(x) - \log g(x)) dx$

for distributions with densities $f()$ and $g()$.

Value

A matrix of KL divergences where the rows correspond to using the respective distribution as $f()$ in the formula above.

Methods

object = "matrix":

Takes as input a matrix of density values with one row per observation and one column per distribution.

object = "flexmix":

Returns the Kullback-Leibler divergence of the mixture components.

Note

The density functions are modified to have equal support. A weight of at least eps is given to each observation point for the modified densities.

Author(s)

Friedrich Leisch and Bettina Gruen

References

S. Kullback and R. A. Leibler. On information and sufficiency.The Annals of Mathematical Statistics, 22(1), 79–86, 1951.

Friedrich Leisch. Exploring the structure of mixture model components. In Jaromir Antoch, editor, Compstat 2004–Proceedings in Computational Statistics, 1405–1412. Physika Verlag, Heidelberg, Germany, 2004. ISBN 3-7908-1554-3.

Examples

## Gaussian and Student t are much closer to each other than
## to the uniform:

x <- seq(-3, 3, length = 200)
y <- cbind(u = dunif(x), n = dnorm(x), t = dt(x, df = 10))

matplot(x, y, type = "l")
KLdiv(y)

if (require("mlbench")) {
set.seed(2606)
x <-  mlbench.smiley()$x
model1 <- flexmix(x ~ 1, k = 9, model = FLXmclust(diag = FALSE),
                  control  =  list(minprior = 0))
plotEll(model1, x)
KLdiv(model1)
}

Description

Apply a function to each component of a finite mixture

Usage

## S4 method for signature 'FLXRmstep'
Lapply(object, FUN, model = 1, component = TRUE, ...)

Arguments

Details

FUN is found by a call to match.fun and typically is specified as a function or a symbol (e.g. a backquoted name) or a character string specifying a function to be searched for from the environment of the call to Lapply.

Value

A list of the length equal to the number of components specified is returned, each element of which is the result of applying FUN to the specified component of the refitted mixture model.

Methods

object = FLXRmstep:

Apply a function to each component of a refitted flexmix object using method = "mstep".

Author(s)

Friedrich Leisch and Bettina Gruen

Examples

data("NPreg", package = "flexmix")
ex2 <- flexmix(yn ~ x, data = NPreg, k = 2, model = list(FLXMRglm(yn ~ 
    . + I(x^2)), FLXMRglm(yp ~ ., family = "poisson")))
ex2r <- refit(ex2, method = "mstep")
Lapply(ex2r, "vcov", 2)

Description

Evaluate the log-likelihood. This function is defined as an S4 generic in the stats4 package.

Methods

object = flexmix

Evaluate the log-likelihood of an flexmix object

Description

For a 22-centre trial the number of responses and the total number of patients is reported for the control group and the group receiving a new drug.

Usage

data("Mehta")

Format

A data frame with 44 observations on the following 4 variables.

Response

Number of responses.

Total

Total number of observations.

Drug

A factor indicating treatment with levels New and Control.

Site

A factor indicating the site/centre.

Source

M. Aitkin. Meta-analysis by random effect modelling in generalized linear models. Statistics in Medicine, 18, 2343–2351, 1999.

References

C.R. Mehta, N.R. Patel and P. Senchaudhuri. Importance sampling for estimating exact probabilities in permutational inference. Journal of the American Statistical Association, 83, 999–1005, 1988.

Examples

data("Mehta", package = "flexmix")
mehtaMix <- initFlexmix(cbind(Response, Total-Response) ~ 1|Site, 
                        data = Mehta, nrep = 5, k = 3,
                        model = FLXMRglmfix(family = "binomial",
                          fixed = ~ Drug), 
                        control = list(minprior = 0.04))

Description

A simple artificial regression example with 3 latent classes, two independent variables, one concomitant variable and a dependent variable which follows a Gaussian distribution.

Usage

data("NregFix")

Format

A data frame with 200 observations on the following 5 variables.

x1

Independent variable: numeric variable.

x2

Independent variable: a factor with two levels: 0 and 1.

w

Concomitant variable: a factor with two levels: 0 and 1.

y

Dependent variable.

class

Latent class memberships.

Examples

data("NregFix", package = "flexmix")
library("lattice")
xyplot(y ~ x1 | x2 * w, data = NregFix, groups = class)
Model <- FLXMRglmfix(~ 1, fixed = ~ x2, 
                     nested = list(k = c(2, 1),
                     formula = c(~x1, ~0)))
fittedModel <- initFlexmix(y ~ 1, model = Model, data = NregFix, k = 3,
                           concomitant = FLXPmultinom(~ w), nrep = 5)
fittedModel

Description

Number of patents, R&D spending and sales in millions of dollar for 70 pharmaceutical and biomedical companies in 1976.

Usage

data("patent")

Format

A data frame with 70 observations on the following 4 variables.

Company

Name of company.

Patents

Number of patents.

RDS

R&D spending per sales.

lgRD

Logarithmized R&D spendings (in millions of dollars).

Details

The data is taken from the National Bureau of Economic Research R&D Masterfile.

Source

P. Wang, I.M. Cockburn and M.L. Puterman. Analysis of Patent Data – A Mixed-Poisson-Regression-Model Approach. Journal of Business & Economic Statistics, 16(1), 27–41, 1998.

References

B.H. Hall, C. Cummins, E. Laderman and J. Mundy. The R&D Master File Documentation. Technical Working Paper 72, National Bureau of Economic Research, 1988. Cambridge, MA.

Examples

data("patent", package = "flexmix")
patentMix <- initFlexmix(Patents ~ lgRD, k = 3,
                         model = FLXMRglm(family = "poisson"),
                         concomitant = FLXPmultinom(~RDS),
                         nrep = 5, data = patent)
plot(Patents ~ lgRD, data = patent,
     pch = as.character(clusters(patentMix)))
ordering <- order(patent$lgRD)
apply(fitted(patentMix), 2, function(y)
      lines(sort(patent$lgRD), y[ordering]))

Description

The plot method for flexmix-class objects gives a rootogram or histogram of the posterior probabilities.

Usage

## S4 method for signature 'flexmix,missing'
plot(x, y, mark = NULL, markcol = NULL,
  col  =  NULL, eps = 1e-4, root = TRUE, ylim = TRUE, main = NULL, xlab = "",
  ylab = "", as.table = TRUE, endpoints = c(-0.04, 1.04), ...)

Arguments

Details

For each mixture component a rootogram or histogram of the posterior probabilities of all observations is drawn. Rootograms are very similar to histograms, the only difference is that the height of the bars correspond to square roots of counts rather than the counts themselves, hence low counts are more visible and peaks less emphasized. Please note that the y-axis denotes the number of observations in each bar in any case.

Usually in each component a lot of observations have posteriors close to zero, resulting in a high count for the corresponding bin in the rootogram which obscures the information in the other bins. To avoid this problem, all probabilities with a posterior below eps are ignored.

A peak at probability one indicates that a mixture component is well seperated from the other components, while no peak at one and/or significant mass in the middle of the unit interval indicates overlap with other components.

Author(s)

Friedrich Leisch and Bettina Gruen

References

Friedrich Leisch. FlexMix: A general framework for finite mixture models and latent class regression in R. Journal of Statistical Software, 11(8), 2004. doi:10.18637/jss.v011.i08

Jeremy Tantrum, Alejandro Murua and Werner Stuetzle. Assessment and pruning of hierarchical model based clustering. Proceedings of the 9th ACM SIGKDD international conference on Knowledge Discovery and Data Mining, 197–205. ACM Press, New York, NY, USA, 2003.

Friedrich Leisch. Exploring the structure of mixture model components. In Jaromir Antoch, editor, Compstat 2004–Proceedings in Computational Statistics, 1405–1412. Physika Verlag, Heidelberg, Germany, 2004. ISBN 3-7908-1554-3.

Description

Plot 50% and 95% confidence ellipses for mixtures of Gaussians fitted using FLXMCmvnorm.

Usage

plotEll(object, data, which = 1:2, model = 1, project = NULL, points = TRUE,
        eqscale = TRUE, col = NULL, number = TRUE, cex = 1.5, numcol = "black", 
        pch = NULL, ...)

Arguments

Author(s)

Friedrich Leisch and Bettina Gruen

See Also

FLXMCmvnorm

Description

Determine posterior probabilities or cluster memberships for a fitted flexmix or unfitted FLXdist model.

Usage

## S4 method for signature 'flexmix,missing'
posterior(object, newdata, unscaled = FALSE, ...)
## S4 method for signature 'FLXdist,listOrdata.frame'
posterior(object, newdata, unscaled = FALSE, ...)
## S4 method for signature 'flexmix,missing'
clusters(object, newdata, ...)
## S4 method for signature 'FLXdist,ANY'
clusters(object, newdata, ...)

Arguments

Author(s)

Friedrich Leisch and Bettina Gruen

Description

Refits an estimated flexmix model to obtain additional information like coefficient significance p-values for GLM regression.

Usage

## S4 method for signature 'flexmix'
refit(object, newdata, method = c("optim",
"mstep"), ...)
## S4 method for signature 'FLXRoptim'
summary(object, model = 1, which = c("model",
"concomitant"), ...)
## S4 method for signature 'FLXRmstep'
summary(object, model = 1, which = c("model",
"concomitant"), ...)

## S4 method for signature 'FLXRoptim,missing'
plot(x, y, model = 1, which = c("model", "concomitant"),
         bycluster = TRUE, alpha = 0.05, components, labels = NULL,
         significance = FALSE, xlab = NULL, ylab = NULL, ci = TRUE,
         scales = list(), as.table = TRUE, horizontal = TRUE, ...)

Arguments

Details

The refit method for FLXMRglm models in combination with the summary method can be used to obtain the usual tests for significance of coefficients. Note that the tests are valid only if flexmix returned the maximum likelihood estimator of the parameters. If refit is used with method = "mstep" for these component specific models the returned object contains a glm object for each component where the elements model which is the model frame and data which contains the original dataset are missing.

Value

An object inheriting form class FLXR is returned. For the method using optim the object has class FLXRoptim and for the M-step method it has class FLXRmstep. Both classes give similar results for their summary methods. Objects of class FLXRoptim have their own plot method. Lapply can be used to further analyse the refitted component specific models of objects of class FLXRmstep.

Warning

For method = "mstep" the standard deviations are determined separately for each of the components using the a-posteriori probabilities as weights without accounting for the fact that the components have been simultaneously estimated. The derived standard deviations are hence approximative and should only be used in an exploratory way, as they are underestimating the uncertainty given that the missing information of the component memberships are replaced by the expected values.

The newdata argument can only be specified when using method = "mstep" for refitting FLXMRglm components. A variant of glm for weighted ML estimation is used for fitting the components and full glm objects are returned. Please note that in this case the data and the model frame are stored for each component which can significantly increase the object size.

Author(s)

Friedrich Leisch and Bettina Gruen

References

Friedrich Leisch. FlexMix: A general framework for finite mixture models and latent class regression in R. Journal of Statistical Software, 11(8), 2004. doi:10.18637/jss.v011.i08

Examples

data("NPreg", package = "flexmix")
ex1 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2)
ex1r <- refit(ex1)

## in one component all coefficients should be highly significant,
## in the other component only the linear term
summary(ex1r)

Description

The components are sorted by the value of one of the parameters or according to an integer vector containing the permutation of the numbers from 1 to the number of components.

Usage

relabel(object, by, ...)
## S4 method for signature 'FLXdist,character'
relabel(object, by, which = NULL, ...)

Arguments

Author(s)

Friedrich Leisch and Bettina Gruen

Examples

set.seed(123)
    beta <- matrix(1:16, ncol = 4)
    beta
    df1 <- ExLinear(beta, n = 100, sd = .5)
    f1 <- flexmix(y~., data = df1, k = 4)

    ## There was label switching, parameters are not in the same order
    ## as in beta:
    round(parameters(f1))
        
    betas <- rbind(beta, .5)
    betas

    ## This makes no sense:
    summary(abs(as.vector(betas-parameters(f1))))

    ## We relabel the components by sorting the coefficients of x1:
    r1 <- relabel(f1, by = "model", which = "x1")
    round(parameters(r1))

    ## Now we can easily compare the fit with the true parameters:
    summary(abs(as.vector(betas-parameters(r1))))

Description

Given a finite mixture model generate random numbers from it.

Usage

rflexmix(object, newdata, ...)

Arguments

Details

rflexmix provides the creation of the model matrix for new data and the sampling of the cluster memberships. The sampling of the component distributions given the classification is done by calling rFLXM. This step has to be provided for the different model classes.

Value

A list with components

Author(s)

Bettina Gruen

Examples

example(flexmix)
sample <- rflexmix(ex1)

Description

Data on Ames Salmonella reverse mutagenicity assay.

Usage

data("salmonellaTA98")

Format

This data frame contains the following columns:

x

Dose levels of quinoline.

y

Numbers of revertant colonies of TA98 Salmonella observed on each of three replicate plates tested at each of six dose levels of quinoline diameter.

Details

This data set is taken from package dispmod provided by Luca Scrucca.

Source

Margolin, B.J., Kaplan, N. and Zeiger, E. Statistical analysis of the Ames Salmonella/microsome test, Proc. Natl. Acad. Sci. USA, 76, 3779–3783, 1981.

References

Breslow, N.E. Extra-Poisson variation in log-linear models, Applied Statistics, 33, 38–44, 1984.

Wang, P., Puterman, M.L., Cockburn, I.M., and Le, N.D. Mixed Poisson regression models with covariate dependent rates, Biometrics, 52, 381–400, 1996.

Examples

data("salmonellaTA98", package = "flexmix")
salmonMix <- initFlexmix(y ~ 1,
                         data = salmonellaTA98, 
                         model = FLXMRglmfix(family = "poisson", 
                           fixed = ~ x + log(x + 10)),                        
                         k = 2, nrep = 5)
salmonMix.pr <- predict(salmonMix, newdata = salmonellaTA98)
plot(y ~ x, data = salmonellaTA98, 
     pch = as.character(clusters(salmonMix)), 
     ylim = range(c(salmonellaTA98$y, unlist(salmonMix.pr))))
for (i in 1:2) lines(salmonellaTA98$x, salmonMix.pr[[i]], lty = i)

Description

Data from a clinical trial where the effect of intravenous gamma-globulin on suppression of epileptic seizures is studied. Daily observations for a period of 140 days on one patient are given, where the first 27 days are a baseline period without treatment, the remaining 113 days are the treatment period.

Usage

data("seizure")

Format

A data frame with 140 observations on the following 4 variables.

Seizures

A numeric vector, daily counts of epileptic seizures.

Hours

A numeric vector, hours of daily parental observation.

Treatment

A factor with levels No and Yes.

Day

A numeric vector.

Source

P. Wang, M. Puterman, I. Cockburn, and N. Le. Mixed poisson regression models with covariate dependent rates. Biometrics, 52, 381–400, 1996.

References

B. Gruen and F. Leisch. Bootstrapping finite mixture models. In J. Antoch, editor, Compstat 2004–Proceedings in Computational Statistics, 1115–1122. Physika Verlag, Heidelberg, Germany, 2004. ISBN 3-7908-1554-3.

Examples

data("seizure", package = "flexmix")
plot(Seizures/Hours ~ Day, col = as.integer(Treatment),
     pch = as.integer(Treatment), data = seizure)
abline(v = 27.5, lty = 2, col = "grey")
legend(140, 9, c("Baseline", "Treatment"),
       pch = 1:2, col = 1:2, xjust = 1, yjust = 1)

set.seed(123)

## The model presented in the Wang et al paper: two components for
## "good" and "bad" days, respectively, each a Poisson GLM with hours of
## parental observation as offset

seizMix <- flexmix(Seizures ~ Treatment * log(Day),
                   data = seizure, k = 2,
                   model = FLXMRglm(family = "poisson",
                     offset = log(seizure$Hours)))

summary(seizMix)
summary(refit(seizMix))

matplot(seizure$Day, fitted(seizMix)/seizure$Hours, type = "l",
        add = TRUE, col = 3:4)

Description

Runs flexmix repeatedly for different numbers of components and returns the maximum likelihood solution for each.

Usage

initFlexmix(..., k, init = list(), control = list(), nrep = 3L,
            verbose = TRUE, drop = TRUE, unique = FALSE)
initMethod(name = c("tol.em", "cem.em", "sem.em"),
           step1 = list(tolerance = 10^-2),
           step2 = list(), control = list(), nrep = 3L)

stepFlexmix(..., k = NULL, nrep = 3, verbose = TRUE, drop = TRUE,
            unique = FALSE)

## S4 method for signature 'stepFlexmix,missing'
plot(x, y, what = c("AIC", "BIC", "ICL"),
  xlab = NULL, ylab = NULL, legend = "topright", ...)

## S4 method for signature 'stepFlexmix'
getModel(object, which = "BIC")

## S4 method for signature 'stepFlexmix'
unique(x, incomparables = FALSE, ...)

Arguments

Value

An object of class "stepFlexmix" containing the best models with respect to the log likelihood for the different number of components in a slot if length(k)>1, else directly an object of class "flexmix".

If unique = FALSE, then the resulting object contains one model per element of k (which is the number of clusters the EM algorithm started with). If unique = TRUE, then the result is resorted according to the number of clusters contained in the fitted models (which may be less than the number with which the EM algorithm started), and only the maximum likelihood solution for each number of fitted clusters is kept. This operation can also be done manually by calling unique() on objects of class "stepFlexmix".

Author(s)

Friedrich Leisch and Bettina Gruen

References

Friedrich Leisch. FlexMix: A general framework for finite mixture models and latent class regression in R. Journal of Statistical Software, 11(8), 2004. doi:10.18637/jss.v011.i08

Christophe Biernacki, Gilles Celeux and Gerard Govaert. Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models. Computational Statistics & Data Analysis, 41(3–4), 561–575, 2003.

Theresa Scharl, Bettina Gruen and Friedrch Leisch. Mixtures of regression models for time-course gene expression data: Evaluation of initialization and random effects. Bioinformatics, 26(3), 370–377, 2010.

Examples

data("Nclus", package = "flexmix")

## try 2 times for k = 4
set.seed(511)
ex1 <- initFlexmix(Nclus~1, k = 4, model = FLXMCmvnorm(diagonal = FALSE),
                   nrep = 2)
ex1

## now 2 times each for k = 2:5, specify control parameter
ex2 <- initFlexmix(Nclus~1, k = 2:5, model = FLXMCmvnorm(diagonal = FALSE),
                   control = list(minprior = 0), nrep = 2)
ex2
plot(ex2)

## get BIC values
BIC(ex2)

## get smallest model
getModel(ex2, which = 1)

## get model with 3 components
getModel(ex2, which = "3")

## get model with smallest ICL (here same as for AIC and BIC: true k = 4)
getModel(ex2, which = "ICL")

## now 1 time each for k = 2:5, with larger minimum prior
ex3 <- initFlexmix(Nclus~1, k = 2:5,
                   model = FLXMCmvnorm(diagonal = FALSE),
                   control = list(minprior = 0.1), nrep = 1)
ex3

## keep only maximum likelihood solution for each unique number of
## fitted clusters:
unique(ex3)

Description

The data investigates whether the adult Tribolium species Castaneum has developed an evolutionary advantage to recognize and avoid eggs of their own species while foraging.

Usage

data("tribolium")

Format

A data frame with 27 observations on the following 4 variables.

Remaining

A numeric vector.

Total

A numeric vector.

Replicate

A factor with levels 1, 2, 3.

Species

A factor with levels Castaneum Confusum Madens.

Details

Beetles of the genus Tribolium are cannibalistic in the sense that adults eat the eggs of their own species as well as those of closely related species. The experiment isolated a number of adult beetles of the same species and presented them with a vial of 150 eggs (50 of each type), the eggs being thoroughly mixed to ensure uniformity throughout the vial.

The data gives the consumption data for adult Castaneum species. It reports the number of Castaneum, Confusum and Madens eggs, respectively, that remain uneaten after two day exposure to the adult beetles. Replicates 1, 2, and 3 correspond to different occasions on which the experiment was conducted.

Source

P. Wang and M.L. Puterman. Mixed Logistic Regression Models. Journal of Agricultural, Biological, and Environmental Statistics, 3 (2), 175–200, 1998.

Examples

data("tribolium", package = "flexmix")
tribMix <- initFlexmix(cbind(Remaining, Total - Remaining) ~ Species, 
                   k = 2, nrep = 5, data = tribolium,
                   model = FLXMRglm(family = "binomial"))

Description

Trypanosome data from a dosage-response analysis to assess the proportion of organisms belonging to different populations. It is assumed that organisms belonging to different populations are indistinguishable other than in terms of their reaction to the stimulus.

Usage

data("trypanosome")

Format

A data frame with 426 observations on the following 2 variables.

Dead

A logical vector.

Dose

A numeric vector.

Details

The experimental technique involved inspection under the microscope of a representative aliquot of a suspension, all organisms appearing within two fields of view being classified either alive or dead. Hence the total numbers of organisms present at each dose and the number showing the quantal response were both random variables.

Source

R. Ashford and P.J. Walker. Quantal Response Analysis for a Mixture of Populations. Biometrics, 28, 981–988, 1972.

References

D.A. Follmann and D. Lambert. Generalizing Logistic Regression by Nonparametric Mixing. Journal of the American Statistical Association, 84(405), 195–300, 1989.

Examples

data("trypanosome", package = "flexmix")
trypMix <- initFlexmix(cbind(Dead, 1-Dead) ~ 1, k = 2, 
	               nrep = 5, data = trypanosome,
	               model = FLXMRglmfix(family = "binomial",
                           fixed = ~log(Dose)))

Description

The data set is from Simmons Study of Media and Markets and contains the incidence matrix for scotch brands used in last year for those households who report consuming scotch.

Usage

data("whiskey")

Format

A data frame whiskey with 484 observations on the following 2 variables.

Freq

a numeric vector

Incidence

a matrix with 21 columns

Additional information on the brands is contained in the data frame whiskey_brands which is simultaneously loaded. This data frame contains 21 observations on the following 3 variables.

Brand

a character vector

Type

a factor with levels Blend Single Malt

Bottled

a factor with levels Domestic Foreign

Details

The dataset is taken from the bayesm package.

Source

Peter Rossi and Rob McCulloch. bayesm: Bayesian Inference for Marketing/Micro-econometrics. R package version 2.0-8, 2006. http://gsbwww.uchicago.edu/fac/peter.rossi/research/bsm.html

References

Edwards, Y. and G. Allenby. Multivariate Analysis of Multiple Response Data, Journal of Marketing Research, 40, 321–334, 2003.