A Non-arbitrary Method of Identifying and Scaling Latent Variables in SEM and MACS Models

Abstract

A non-arbitrary method for the identification and scale setting of latent variables in general structural equation modeling is introduced. This particular technique provides identical model fit as traditional methods (e.g., the marker variable method), but it allows one to estimate the latent parameters in a nonarbitrary metric that reflects the metric of the measured indicators. This technique, therefore, is particularly useful for mean and covariance structures (MACS) analyses, where the means of the indicators and latent constructs are of key interest. By introducing this alternative method of identification and scale setting, researchers are provided with an additional tool for conducting MACS analyses that provides a meaningful and nonarbitrary scale for the estimates of the latent variable parameters. Importantly, this tool can be used with single-group single-occasion models as well as with multiple-group models, multiple-occasion models, or both.