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Latent Variable Models

Latent Variable Models:

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 analysisContinuousContinuous
Latent profile analysisCategoricalContinuous
Latent trait analysisContinuousCategorical
Latent class analysisCategoricalCategorical

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.

Latent variable models are covered in´s online course Introduction to Structural Equation Modeling.

[1] Bartholomew, D.J., and Knott, M. (1999). Latent Variable Models and Factor Analysis. London: Arnold.

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