Group Differences in Regression Intercepts: Implications for Factorial Invariance

Studies of differential prediction typically examine group differences in linear regression slopes or intercepts for predicting criterion scores from one or more test scores. When there are no group differences in slopes, what are the implications of differences in regression intercepts for the measurement equivalence of the tests or criterion across groups? Measurement equivalence is here defined as factorial invariance under a single-factor model for the tests and criterion. Two theorems are given that describe conditions under which intercept differences can exist under factorial invariance. In such cases, intercept differences do not result from measurement bias in either the tests or criterion. The conditions of the theorems are testable using multiple-group confirmatory factor analysis. These test procedures are illustrated in real data. The implications of the theorems and the test procedures for studies of differential prediction are discussed.