Response Surface Analysis With Multilevel Data: Illustration for the Case of Congruence Hypotheses

Response surface analysis (RSA) is a statistical approach that enables researchers to test congruence hypotheses; the proposition that the degree of congruence between people's values in 2 psychological constructs should be positively or negatively related to their value in an outcome variable. This is done by estimating a polynomial regression model and using the graph of the model and several parameters as a guide to interpret the resulting regression coefficients in terms of the congruence hypothesis. One problem with using RSA in applied research is that the model and the interpretation of the model's parameters in terms of congruence effects have only been thoroughly developed for single-level data. Here, we present an extension of RSA to multilevel data. Among other things we show how the standard errors can be computed and how researchers can decide whether the occurrence of a congruence effect depends on a Level 2 covariate. We illustrate the suggested extension with 2 examples that guide readers through the test of congruence effects in the case of multilevel data. We also provide R scripts that researchers can adopt to conduct multilevel RSA. Translational Abstract Many psychological theories propose that the amount of congruence between two psychological variables is related to an outcome variable (e.g., that the congruence between competence demands of a person's job and the person's competence relates to job satisfaction). The present article introduces an extension of RSA that can be applied to multilevel data and provide R scripts to facilitate these analyses. The suggested approach allows researchers to examine their congruence hypotheses and other RSA effects when they have multilevel data.