# bootstrap.lca

##### Bootstrap Samples of LCA Results

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.

- Keywords
- multivariate

##### Usage

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

##### Arguments

- l
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.

##### 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.

##### Value

An object of class `bootstrap.lca`

is returned, containing

The LogLikelihood of the models and of the corresponding saturated models

Likelihood quotient of the models and the corresponding saturated models

Mean and Standard deviation of
`lratio`

Likelihood quotient of the original model and the corresponding saturated model

Z-Statistics of `lratioorg`

P-Values for `zratio`

, computed via normal
distribution and empirical distribution

Pearson's Chisq of the models

Mean and Standard deviation of
`chisq`

Pearson's Chisq of the original model

Z-Statistics of `chisqorg`

P-Values for `zchisq`

, computed via normal
distribution and empirical distribution

Number of bootstrap samples

Number of LCA Iterations

##### References

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

##### See Also

##### Examples

```
# NOT RUN {
## 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
# }
```

*Documentation reproduced from package e1071, version 1.7-3, License: GPL-2 | GPL-3*