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Abstract:
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The linear spline growth model (LSGM) is a popular tool for examining nonlinear change patterns over time. It approximates more complex patterns by attaching at least two linear pieces. Besides examining within-person changes and between-person differences of trajectories simultaneously, it poses interesting statistical challenges, such as learning the location of a change point (i.e., knot), the knot’s variance, prediction of the knot location using covariates, and analyzing data with individually-varying time 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 for individual differences of trajectories in the ITPs framework. Our simulation studies demonstrate that the proposed BLSGMs-TICs are capable of estimating and testing the knot variance while correctly controlling type I error rates. More importantly, they generally estimated the parameters of interest unbiasedly, precisely and exhibited appropriate confidence interval coverage.
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