Estimating knots in bilinear spline growth models with time-invariant covariates in the framework of individual measurement occasions
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The linear spline growth model (LSGM) is a popular tool for examining nonlinear change patterns over time. It approximates complex patterns by attaching at least two linear trajectories. Besides examining within-person changes and between-person differences of trajectories simultaneously, it poses interesting statistical challenges, such as estimating the location of a change point (or knot), the knot's variance, prediction of the knot location using covariates, and analyzing data with individually-varying times points (ITPs). We developed a pair of bilinear spline growth models with time-invariant covariates (BLSGMs-TICs) to estimate a knot and its variability as well as to investigate predictors of individual trajectories in the ITPs framework. Our simulation studies demonstrate that the proposed models are capable of estimating and testing the knot variance while controlling Type I error rates. More importantly, they generally estimate the parameters of interest unbiasedly, precisely and exhibit appropriate confidence interval coverage.
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