Impact of Time Intervals on Lagged Moderated Regression Effects

(a) Background: Moderated regression analysis is the most frequently applied statistical method to analyze interaction/moderation effects in the applied psychology literature, and one of the most common statistical techniques of any kind (e.g., Aguinis, & Stone-Romero, 1997; Cohen, Cohen, West, & Aiken, 2003). Further, appreciation of the need for longitudinal studies has led to an increase in the number of studies that used lagged moderated regression analysis or related methods such as multi-sample structural equation models. It is, however, not well-known that results of lagged moderation analysis could be misleading if time intervals are not appropriately modelled. This was shown, e.g., in a recent meta-analysis of longitudinal studies (Guthier, Dormann, & Voelkle, 2020), but it also applies to primary studies. (b) Objectives/Research question(s): The objective is to identify conditions that lead to misleading results (e.g., wrong signs) from lagged moderation analysis and provide a solution. (d) Method/Approach: Monte Carlo Simulation of longitudinal data and analysis of generated data with different multiple regression models and moderated ctsem (e) Results/Findings: If more than a single effect in a causal system is moderated, length of interval is particularly consequential. Truly positive moderating effects can manifest as negative moderating effects and vice versa (sign-flipping) if moderated regression models are used. In particular, this happens if more than the focal lagged effect is moderated (e.g., a lagged effect in the 'reversed' causal direction) but with a different sign. Contrary, moderated ctsem yields less biased and in some cases unbiased estimates. (f) Conclusions and implications: Interpretations of previously published longitudinal moderation analyses should be treated with caution, and moderated ctsem instead of moderated regression analysis should be to analyze moderation with longitudinal data. unknown unknown