Flexible Mixture Modeling

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

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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

formula

A symbolic description of the model to be fit. The general form is y~x|g where y is the response, x the set of predictors and g an optional grouping factor for repeated measurements.

data

An optional data frame containing the variables in the model.

k

Number of clusters (not needed if cluster is specified).

cluster

Either a matrix with k columns of initial cluster membership probabilities for each observation; or a factor or integer vector with the initial cluster assignments of observations at the start of the EM algorithm. Default is random assignment into k clusters.

weights

An optional vector of replication weights to be used in the fitting process. Should be NULL, an integer vector or a formula.

model

Object of class FLXM or list of FLXM objects. Default is the object returned by calling FLXMRglm().

concomitant

Object of class FLXP. Default is the object returned by calling FLXPconstant.

control

Object of class FLXcontrol or a named list.

object

Object of class flexmix.

eps

Probabilities below this threshold are treated as zero in the summary method.

...

Currently not used.

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. http://www.jstatsoft.org/v11/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. URL http://www.jstatsoft.org/v28/i04/

See Also

plot-methods

Examples

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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))

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