Assessing Mediational Processes in Parallel Bilinear Spline Growth Curve Models in the Framework of Individual Measurement Occasions

Multiple existing studies have developed multivariate growth models with nonlinear functional forms to explore joint development where two longitudinal records are associated over time. However, multiple repeated outcomes are not necessarily synchronous. Accordingly, it is of interest to investigate an association between two repeated variables on different occasions, for example, how a short-term change of one variable affects a long-term change of the other(s). One statistical tool for such analyses is longitudinal mediation models. In this study, we extend latent growth mediation models with linear trajectories (Cheong et al., 2003) and develop two models to evaluate mediational processes where the bilinear spline (i.e., the linear-linear piecewise) growth model is utilized to capture the change patterns. We define the mediational process as either the baseline covariate or the change of covariate influencing the change of the mediator, which, in turn, affects the change of the outcome. We present the proposed models by simulation studies. Our simulation studies demonstrate that the proposed mediational models can provide unbiased and accurate point estimates with target coverage probabilities with a 95% confidence interval. To illustrate modeling procedures, we analyze empirical longitudinal records of multiple disciplinary subjects, including reading, mathematics, and science test scores, from Grade K to Grade 5. The empirical analyses demonstrate that the proposed model can estimate covariates' direct and indirect effects on the change of the outcome. Through the real-world data analyses, we also provide a set of feasible recommendations for empirical researchers. We also provide the corresponding code for the proposed models.