Cubic response surface analysis: Investigating asymmetric and level-dependent congruence effects with third-order polynomial models.

Humberg S, Schönbrodt F D, Back M D & Nestler S

Research article (journal)

Abstract

Abstract Congruence hypotheses play a major role in many areas of psychology. They refer to, for example, the consequences of person-environment fit, similarity, or self-other agreement. For example, are people psychologically better adjusted when their self-view is in line with their reputation? A valid statistical approach that can be applied to investigate congruence hypotheses of this kind is quadratic Response Surface Analysis (RSA) in which a second-order polynomial model is fit to the data and appropriately interpreted. However, quadratic RSA does not allow researchers to investigate more precise expectations about a congruence effect. Do the data support an asymmetric congruence effect, in the sense that congruence leads to the highest (or lowest) outcome, but incongruence in one direction (e.g., self-view exceeds reputation) affects the outcome differently than incongruence in the other direction (e.g., self-view falls behind reputation)? Is there a level-dependent congruence effect, such that the amount of congruence is more strongly related to the outcome variable for some levels of the predictors (e.g., high self-view and reputation) than for others (e.g., low self-view and reputation)? Such complex congruence hypotheses have frequently been suggested in the literature, but they could not be investigated because an appropriate statistical approach has yet to be developed. Here, we present analytical strategies, based on third-order polynomial models, that enable users to investigate asymmetric and level-dependent congruence effects, respectively. To facilitate the correct application of the suggested approaches, we provide respective step-by-step guidelines, corresponding R syntax, and illustrative analyses using simulated and real data. (PsycInfo Database Record (c) 2022 APA, all rights reserved) Impact Statement Psychologists are often interested in examining whether the degree of congruence between 2 psychological variables is related to an outcome variable (e.g., whether people whose self-view is in line with the way they are seen by others are more satisfied with their social relationships than people whose reputation is discrepant from their self-view). To investigate whether such congruence effects are present in empirical data, one can analyze the data with quadratic Response Surface Analysis (RSA). However, researchers often have very nuanced expectations about congruence effects (e.g., that a discrepancy between self-view and reputation is especially detrimental when people see themselves in an overly positive light, whereas it is less detrimental when people hold a self-view that falls behind their reputation). These nuances could not yet be examined empirically. In the present article, we present cubic RSA, an extension of quadratic RSA, which can be used to detect such complex congruence effects. We also show how these analyses can be conducted with the software R and demonstrate it with 3 examples. (PsycInfo Database Record (c) 2022 APA, all rights reserved)

Details zur Publikation

Release year: 2022
Language in which the publication is written: English