Latent class model

In statistics the latent class model seeks to explain a set of discrete multivariate observed variables from a set of latent variables. Latent class analysis on this model can be used to analyze a N-way contingency table, and "explain" the observed variables from a number of latent classes. In one form the latent class model is written as

$p_{i_{1},i_{2},\ldots ,i_{N}}\approx \sum _{t}^{T}p_{t}\,\prod _{n}^{N}p_{i_{n},t}^{n},$

where T is the number of latent classes and p_t are the so-called recruitment probabilities that should sum to one. $p_{i_{n},t}^{n}$ are the marginal probabilities.

For a two-way latent class model the form is

$p_{ij}\approx \sum _{t}^{T}p_{t}\,p_{it}\,p_{jt}.$

This two-way model is related to probabilistic latent semantic analysis and non-negative matrix factorization.

References

• Paul F. Lazarfeld, Neil W. Henry, Latent Structure Analysis, 1968.
• Leo A. Goodman, "Exploratory latent structure analysis using both identifiable and unidentifiable models", Biometrika, 61:215-231, 1974.