Brief Report: Polynomial Regression Mixture Modeling for Heterogeneous Effects of Informant Congruence

Abstract

Using data from multiple informants has long been considered best practice in education. However, multiple informants often disagree on similar constructs, complicating decision-making. Polynomial regression and response-surface analysis (PRA) is often used to test the congruence effect between multiple informants on an outcome. However, PRA assumes the congruence effect on the outcome is homogeneous across individuals. To investigate unknown heterogeneity in the congruence effect, we introduce polynomial regression mixture modeling (PRMix). We demonstrate how PRMix enhances congruence research by allowing researchers to investigate individual differences in the congruence effect. The differential congruence effects between latent classes are illustrated with response-surface plots. We provide practical suggestions for using PRMix and discuss future research directions in methodology.

Keywords:

• Congruence
• latent class
• mixture
• multiple informants
• polynomial regression
• response surface

Notes

1 Structural equation modeling can be used to conduct multiple group polynomial regression analysis.

2 The formulas to obtain the intercept and slope of the first principal axis can be found in Edwards and Parry (1993).

3 The correlation between student ratings and teacher ratings was .42, and we did not observe essential multicollinearity (VIF = 1.21). It is recommended to check essential multicollinearity of congruence predictors.

4 The intercept and slope of the first principal axis should be 0 and 1, respectively, for Y to be maximized along the congruence line (X = Z).