# poLCA.entropy: Entropy of a fitted latent class model In poLCA: Polytomous Variable Latent Class Analysis

 poLCA.entropy R Documentation

## Entropy of a fitted latent class model

### Description

Calculates the entropy of a cross-classification table produced as a density estimate using a latent class model.

### Usage

` poLCA.entropy(lc) `

### Arguments

 `lc` A model object estimated using the `poLCA` function.

### Details

Entropy is a measure of dispersion (or concentration) in a probability mass function. For multivariate categorical data it is calculated

H = -∑_c p_c log(p_c)

where p_c is the share of the probability in the cth cell of the cross-classification table. A fitted latent class model produces a smoothed density estimate of the underlying distribution of cell percentages in the multi-way table of the manifest variables. This function calculates the entropy of that estimated probability mass function.

### Value

A number taking a minumum value of 0 (representing complete concentration of probability on one cell) and a maximum value equal to the logarithm of the total number of cells in the fitted cross-classfication table (representing complete dispersion, or equal probability for outcomes across every cell).

`poLCA`

### Examples

```data(carcinoma)
f <- cbind(A,B,C,D,E,F,G)~1
lca2 <- poLCA(f,carcinoma,nclass=2) # log-likelihood: -317.2568
lca3 <- poLCA(f,carcinoma,nclass=3) # log-likelihood: -293.705
lca4 <- poLCA(f,carcinoma,nclass=4,nrep=10,maxiter=5000) # log-likelihood: -289.2858

# Maximum entropy (if all cases equally dispersed)
log(prod(sapply(lca2\$probs,ncol)))

# Sample entropy ("plug-in" estimator, or MLE)
p.hat <- lca2\$predcell\$observed/lca2\$N
H.hat <- -sum(p.hat * log(p.hat))
H.hat   # 2.42

# Entropy of fitted latent class models
poLCA.entropy(lca2)
poLCA.entropy(lca3)
poLCA.entropy(lca4)
```

poLCA documentation built on April 25, 2022, 5:06 p.m.