[2] Common use cases for latent variable models include applications in psychometrics (e.g., summarizing responses to a set of survey questions with a factor analysis model positing a smaller number of psychological attributes, such as the trait extraversion, that are presumed to cause the survey question responses),[3] and natural language processing (e.g., a topic model summarizing a corpus of texts with a number of "topics").
Different types of the latent variable models can be grouped according to whether the manifest and latent variables are categorical or continuous:[5] The Rasch model represents the simplest form of item response theory.
Mixture models are central to latent profile analysis.
[7] The manifest variables in factor analysis and latent profile analysis are continuous and in most cases, their conditional distribution given the latent variables is assumed to be normal.
Their conditional distributions are assumed to be binomial or multinomial.