Normal and nonnormal polynomial regression mixture modeling for differential congruence effects: A simulation and tutorial.

Polynomial regression with response surface analysis (PRRSA) has been widely adopted in congruence research when the relation of congruence to an outcome is examined. However, PRRSA assumes that the congruence effects are homogeneous across all individuals. Polynomial regression mixture analysis (PRMix) allows for heterogeneity in the effect of congruence on an outcome across individuals and identifies latent classes of differential congruence effects. In this study, through Monte Carlo simulation, we examined bias in response surface parameters when differential congruence effects were not modeled correctly in PRRSA. We found that the size of the bias depended on the proportion of ignored classes. When evaluating PRMix and nonnormal PRMix, we found that PRMix generally performed well in detecting two latent classes of differential congruence effects when the assumption of residual normality within class was satisfied, but led to severe over-extraction when this assumption was violated. Nonnormal PRMix provided an adequate solution for the generated skew t residual distribution within class. We provide an empirical data example with annotated software syntax to demonstrate the normal and nonnormal PRMix procedures, including model specification and the construction of confidence intervals for the response surface parameters. Practical implications are discussed for applied researchers.