Equality in constraints and metric‐setting measurement models

Abstract

Researchers using structural equation models with latent variables know that they must set the metric of each latent variable in the model. Whether the metric is set by fixing the variance of the latent variable or by fixing a loading of one of its indicators to a nonzero constant is viewed by most researchers as a necessary but unimportant decision. We show, however, that when the loadings of two (or more) observed variables that load on different latent variables are constrained to be equal, then different choices for setting the metric define distinct models. These models can differ in important ways: (a) their fit to the same observed covariance matrix, (b) the estimated values of their unstandard‐ized and standardized parameters, and (c) their identification statuses.