Latent Class Analysis (LCA)

A latent class analysis with k classes is performed on the data given by x.

Usage

lca(x, k, niter=100, matchdata=FALSE, verbose=FALSE)

Arguments

x: Either a data matrix of binary observations or a list of patterns as created by countpattern
k: Number of classes used for LCA
niter: Number of Iterations
matchdata: If TRUE and x is a data matrix, the class membership of every data point is returned, otherwise the class membership of every pattern is returned.
verbose: If TRUE some output is printed during the computations.

Value

An object of class "lca" is returned, containing

w: Probabilities to belong to each class
p: Probabilities of a `1' for each variable in each class
matching: Depending on matchdata either the class membership of each pattern or of each data point
logl, loglsat: The LogLikelihood of the model and of the saturated model
bic, bicsat: The BIC of the model and of the saturated model
chisq: Pearson's Chisq
lhquot: Likelihood quotient of the model and the saturated model
n: Number of data points.
np: Number of free parameters.

References

Anton K. Formann: “Die Latent-Class-Analysis”, Beltz Verlag 1984

Author

Andreas Weingessel

Examples

## 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), nrow = 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)
print(l)
#> LCA-Result
#> ----------
#> 
#> Datapoints: 1000 
#> Classes:    2 
#> Probability of classes
#> [1] 0.63 0.37
#> Itemprobabilities
#>      1    2    3    4
#> 1 0.29 0.28 0.72 0.71
#> 2 0.84 0.88 0.09 0.14
summary(l)
#> LCA-Result
#> ----------
#> 
#> Datapoints: 1000 
#> Classes:    2 
#> 
#> Goodness of fit statistics:
#> 
#> Number of parameters, estimated model: 9 
#> Number of parameters, saturated model: 15 
#> Log-Likelihood, estimated model:       -2488.88 
#> Log-Likelihood, saturated model:       -2471.916 
#> 
#> Information Criteria:
#> 
#> BIC, estimated model: 5039.931 
#> BIC, saturated model: 5047.448 
#> 
#> TestStatistics:
#> 
#> Likelihood ratio:   33.9292   p-val: 6.942523e-06 
#> Pearson Chi^2:      34.62364   p-val: 5.096803e-06 
#> Degress of freedom: 6 
p <- predict(l, x)
table(p, c(rep(1,500),rep(2,500)))
#>    
#> p     1   2
#>   1  85 492
#>   2 415   8