It assumes that the data arise from a mixture of discrete distributions, within each of which the variables are independent.
Latent class analysis (LCA) is a subset of structural equation modeling, used to find groups or subtypes of cases in multivariate categorical data.
As in factor analysis, the LCA can also be used to classify case according to their maximum likelihood class membership.
The probability model used in LCA is closely related to the Naive Bayes classifier.
Cluster analysis is, like LCA, used to discover taxon-like groups of cases in data.
If a multivariate mixture estimation is constrained so that measures must be uncorrelated within each distribution, it is termed latent profile analysis.
The data in this case consists of a N-way contingency table with answers to the items for a number of respondents.
LCA may be used in many fields, such as: collaborative filtering,[4] Behavior Genetics[5] and Evaluation of diagnostic tests.