EVALUATING EMPIRICAL RELATIONSHIPS AMONG PREDICTION, MEASUREMENT, AND SCALING INVARIANCE

Abstract

The purpose of this study was to consider the relationships of prediction, measurement, and scaling invariance when these invariances were simultaneously evaluated in psychometric test data. An approach was developed to evaluate prediction, measurement, and scaling invariance based on linear and nonlinear prediction, measurement, and scaling functions. The approach was used to evaluate the relationships among 12 pairs of tests in 6 datasets for gender invariance. The prediction, measurement, and scaling invariance results were found to be similar for most of the test relationships evaluated, in that all 3 invariances were more likely to be established for highly correlated tests than for less highly correlated tests. The invariance results appeared to be well summarized by intercept differences in the linear prediction, measurement, and scaling functions. The implications of the results were discussed with respect to the relationships among prediction, measurement, and scaling invariances described in prior theoretical and empirical research. Suggestions for extending theoretical and empirical invariance research were provided.