In the section Regression with Measurement Errors in X and Y, outcome variables and predictor variables are assumed to have been measured with errors. In order to study the true relationships among the true scores variables, models for measurement errors are also incorporated into the estimation. The context of applications is that of regression or econometric analysis.

In the social and behavioral sciences, the same kind of model is developed in the context of test theory or item construction for measuring cognitive abilities, personality traits, or other latent variables. This kind of modeling is better-known as measurement models or confirmatory factor analysis (these two terms are interchangeable) in the psychometric field. Usually, applications in the social and behavioral sciences involve a much larger number of observed variables. This section considers some of these measurement or confirmatory factor-analytic models. For illustration purposes, only a handful of variables are used in the examples. Applications that use the PATH modeling language in PROC CALIS are described.