A Two-Step Robust Estimation Approach for Inferring Within-person Relations in Longitudinal Design: Tutorial and Simulations

Psychological researchers have shown an interest in disaggregating within-person variability from between-person differences. Especially for inferring reciprocal relations among variables at the within-person level, applications of the random-intercept cross-lagged panel model (RI-CLPM) with stable trait factors has increased rapidly. This paper provides a tutorial, simulation, and illustrative example of another recent approach proposed by Usami (2023). This approach consists of a two-step procedure: within-person variability scores (WPVS) for each person, which are disaggregated from the stable traits of that person, are predicted using structural equation modeling, and causal parameters are then estimated via a potential outcome approach, such as by using structural nested mean models (SNMMs). This method assumes a data-generating process similar to that in RI-CLPM, and has several advantages: (i) the flexible inclusion of curvilinear and interaction effects for WPVS as latent variables in treatment and outcome models, (ii) more accurate estimates of causal parameters for reciprocal relations can be obtained under certain conditions owing to them being doubly robust, even if unobserved time-varying confounders and model misspecifications exist, (iii) no models for (the distributions of) observed time-varying confounders are needed for estimation, and (iv) the risk of obtaining improper solutions is reduced. After explaining the data-generating process and the analysis procedure using the R package DTRreg for SNMMs, estimation performances are compared with RI-CLPM through large-scale simulations. We show that the proposed approach works well in many conditions if longitudinal data with T≧4 are available, and that the accuracy increases as T becomes larger. An analytic example using data regarding sleep habits and mental health statuses from the Tokyo Teen Cohort (TTC) study is also provided.