Latent structure models is a generic term for a broad set of categories of statistical models. This set includes factor analysis models, covariance structure models, latent profile analysis models, latent trait analysis models, latent class analysis models, and some others. Each category gives rise to a particular branch of statistical analysis.
Theoretical work is in progress to organize all these diverse classes of models into a unified framework. For a reasonable classification scheme covering a broad subset of the latent structure models see latent variable models.