Latent class model

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In statistics the latent class model (LCM) relates a set of discrete multivariate variables to a set of latent variables. It is a type of latent variable model. Latent class analysis (LCA) on this model can be used to analyze a N-way contingency table, and "explain" 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^n_{i_n, t},

where T is the number of latent classes and pt are the so-called recruitment probabilities that should sum to one. p^n_{i_n, t} 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.

[edit] 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.
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