Latent variable models are a broad subclass of latent structure models. They postulate some relationship between the statistical properties of observable variables (or “manifest variables”, or “indicators”) and latent variables. A special kind of statistical analysis corresponds to each kind of the latent variable models.
According to Bartholomew and Knott [1], the latent variable models (and corresponding areas of statistical analysis) can be categorized according to the types of the manifest and latent variables:
| Category | Latent variable | Manifest variable |
| Factor analysis | Continuous | Continuous |
| Latent profile analysis | Categorical | Continuous |
| Latent trait analysis | Continuous | Categorical |
| Latent class analysis | Categorical | Categorical |
A central assumption in these models is the local independence postulate.
In latent variable models the distribution of continuous variables is often assumed to be normal, distribution of categorical variables – binomial or multinomial.
[1] Bartholomew, D.J., and Knott, M. (1999). Latent Variable Models and Factor Analysis. London: Arnold.