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. This paper provides a tutorial, simulation, and illustrative example of a new approach proposed by Usami (2023). This approach consists of a two-step procedure: <i>within-person variability scores</i> (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 <i>via</i> a potential outcome approach, such as by using structural nested mean models (SNMMs). This method 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. Estimation performances are investigated through large-scale simulations and it shows that the proposed approach works well in many conditions if longitudinal data with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>T</mml:mi><mml:mo>≥</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math> are available. An analytic example using data from the Tokyo Teen Cohort (TTC) study is also provided.