bootstrap.lca: Bootstrap Samples of LCA Results

Description

This function draws bootstrap samples from a given LCA model and refits a new LCA model for each sample. The quality of fit of these models is compared to the original model.

Usage

bootstrap.lca(l, nsamples=10, lcaiter=30, verbose=FALSE)

Arguments

An LCA model as created by lca

nsamples

Number of bootstrap samples

lcaiter

Number of LCA iterations

verbose

If TRUE some output is printed during the computations.

Value

An object of class bootstrap.lca is returned, containing
logl, loglsatThe LogLikelihood of the models and of the corresponding saturated models
lratioLikelihood quotient of the models and the corresponding saturated models
lratiomean, lratiosdMean and Standard deviation of lratio
lratioorgLikelihood quotient of the original model and the corresponding saturated model
zratioZ-Statistics of lratioorg
pvalzratio, pvalratioP-Values for zratio, computed via normal distribution and empirical distribution
chisqPearson's Chisq of the models
chisqmean, chisqsdMean and Standard deviation of chisq
chisqorgPearson's Chisq of the original model
zchisqZ-Statistics of chisqorg
pvalzchisq, pvalchisqP-Values for zchisq, computed via normal distribution and empirical distribution
nsamplesNumber of bootstrap samples
lcaiterNumber of LCA Iterations

Details

From a given LCA model l, nsamples bootstrap samples are drawn. For each sample a new LCA model is fitted. The goodness of fit for each model is computed via Likelihood Ratio and Pearson's Chisquare. The values for the fitted models are compared with the values of the original model l. By this method it can be tested whether the data to which l was originally fitted come from an LCA model.

References

Anton K. Formann: ``Die Latent-Class-Analysis'', Beltz Verlag 1984

Examples

Run this code

## Generate a 4-dim. sample with 2 latent classes of 500 data points each.
## The probabilities for the 2 classes are given by type1 and type2.
type1 <- c(0.8,0.8,0.2,0.2)
type2 <- c(0.2,0.2,0.8,0.8)
x <- matrix(runif(4000),nr=1000)
x[1:500,] <- t(t(x[1:500,])<type1)*1
x[501:1000,] <- t(t(x[501:1000,])<type2)*1

l <- lca(x, 2, niter=5)
bl <- bootstrap.lca(l,nsamples=3,lcaiter=5)
bl

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