On Effect Size Measures for Nested Measurement Models

A class of effect size indices are discussed that evaluate the degree to which two nested confirmatory factor analysis models differ from each other in terms of fit to a set of observed variables. These descriptive effect measures can be used to quantify the impact of parameter restrictions imposed in an initially considered model and are free from an explicit relationship to sample size. The described indices represent the extent to which respective linear combinations of the proportions of explained variance in the manifest variables are changed as a result of introducing the constraints. The indices reflect corresponding aspects of the impact of the restrictions and are independent of their statistical significance or lack thereof. The discussed effect size measures are readily point and interval estimated, using popular software, and their application is illustrated with numerical examples.

Automated summary

This article discusses a class of effect size indices that evaluate the differences between two nested confirmatory factor analysis models in terms of fit to observed variables. These indices quantify the impact of parameter restrictions on the initially considered model and are independent of sample size. The described indices measure the changes in linear combinations of the proportions of explained variance in the manifest variables as a result of introducing constraints. They are not influenced by the statistical significance of these restrictions. The discussed effect size measures can be easily estimated using popular software and their application is illustrated with numerical examples.