A latent variable model is a statistical model that relates a set of observable variables (also called manifest variables or indicators) to a set of latent variables. Latent variable models are applied across a wide range of fields such as biology, computer science, and social science. 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), and natural language processing (e.g., a topic model summarizing a corpus of texts with a number of "topics").
It is assumed that the responses on the indicators or manifest variables are the result of an individual's position on the latent variable(s), and that the manifest variables have nothing in common after controlling for the latent variable (local independence).