Investigating the effects of congruence between within-person associations: A comparison of two extensions of response surface analysis

Humberg, S.; Kuper, N.; Rentzsch, K.; Gerlach, T. M.; Back, M. D.; Nestler, S.

Zusammenfassung

Response Surface Analysis (RSA) allows researchers to study whether the degree of congruence between two predictor variables is related to a potential psychological outcome. Here, we adapt RSA to the case in which the two predictor variables whose congruence is of interest refer to individual differences in within-person associations (WPAs) between variables that fluctuate over time. For example, a WPA-congruence hypothesis in research on romantic relationships could posit that partners are happier when they have similar social reactivities – that is, when they have similarly strong WPAs between the quantity of their social interactions and their momentary well-being. One method for testing a WPA-congruence hypothesis is a 2-step approach in which the individuals’ WPAs are first estimated as random slopes in respective multilevel models, and then these estimates are used as predictors in a regular RSA. As an alternative, we suggest combining RSA with multilevel structural equation modeling (MSEM) by specifying the WPAs as random slopes in the structural equation and using their latent second-order terms to predict the outcome on Level 2. We introduce both approaches and provide and explain their corresponding computer code templates. We also compared the two approaches with a simulation study and found that the MSEM model – despite its complexities (e.g., nonlinear functions of latent slopes) – has advantages over the 2-step approach. We conclude that the MSEM approach should be used in practice. We demonstrate its application using data from a daily diary study and offer guidance for important decisions (e.g., about standardization).