What is a latent variable?

It is a variable that is not directly observed but is inferred from observed indicators, such as a trait measured by several test items or a construct measured by several survey questions.

How does this area relate to factor analysis?

Factor analysis is the measurement core; these models extend it by adding structural relationships among latent variables and by allowing categorical or trait-like latent variables.

Structural and Latent Variable Models

Structural and latent variable models represent relationships among unobserved constructs and the observed indicators that measure them, generalizing factor analysis to systems of equations.

Definition

Structural and latent variable models are multivariate models that posit unobserved variables, link them to observed indicators through a measurement model, and specify relationships among the latent and observed variables through a structural model.

Scope

This area covers models in which latent variables are inferred from measured indicators and related to one another and to observed variables. It includes structural equation modeling with continuous latent factors, latent class analysis with categorical latent variables, and item response theory for latent traits underlying item responses. The emphasis is on the measurement of constructs and the modeling of structural relations among them.

Sub-topics

Core questions

How can unobserved constructs be measured from observed indicators?
How are relationships among latent variables specified and estimated?
When are latent variables best treated as continuous, categorical, or trait-like?
How is the fit and identification of such models assessed?

Key theories

Measurement and structural decomposition: These models separate a measurement component, relating latent variables to observed indicators, from a structural component, specifying relationships among the latent variables, unifying factor analysis and path analysis.
Unified latent variable framework: Continuous-factor, categorical-class, and trait models can be viewed as instances of a general latent variable framework distinguished by the assumed distribution of the latent and observed variables.

Clinical relevance

These models are central to the social and behavioral sciences for measuring constructs such as ability, attitude, or socioeconomic status and for testing theories about how such constructs relate, and they support test development and the analysis of survey and questionnaire data.

History

The area synthesizes the factor-analytic tradition in psychometrics with path analysis from biometrics, brought together in the structural equation modeling framework in the 1970s. Latent class analysis and item response theory developed in parallel for categorical latent variables and latent traits, and a unifying latent variable perspective emerged later.

Debates

Causal interpretation of structural models: Structural models are often given causal readings, but whether path coefficients estimated from observational data can be interpreted causally depends on strong assumptions, and this interpretation remains contested.

Key figures

Kenneth Bollen
Karl Joreskog
Paul Lazarsfeld

Seminal works

bollen1989
skrondal2004
bartholomew2011

Frequently asked questions

What is a latent variable?: It is a variable that is not directly observed but is inferred from observed indicators, such as a trait measured by several test items or a construct measured by several survey questions.
How does this area relate to factor analysis?: Factor analysis is the measurement core; these models extend it by adding structural relationships among latent variables and by allowing categorical or trait-like latent variables.