Estimating knots in bilinear spline growth mixture models with time-invariant covariates in the framework of individual measurement occasions
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The linear spline growth mixture model (LSGMM), which extends the linear spline growth model (LSGM) to the growth mixture model framework, is an appropriate tool for analyzing longitudinal data sets that come from a mixture of at least two latent classes and the underlying growth trajectories within each class are nonlinear. For each latent class, it approximates 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 estimating the location of a change point (or knot), grouping individuals into at least two unobserved classes, examining factors that may be associated with those latent groups, and analyzing data with individually-varying measurement occasions. We developed a two-step bilinear spline growth mixture model (BLSGMM) to cluster these linear piecewise individual trajectories as well as to associate time-invariant covariates (TICs) to the latent classes. Our simulation studies demonstrate that the proposed BLSGMM-TICs is capable of clustering the nonlinear change patterns well. More importantly, they generally estimate the parameters of interest unbiasedly, precisely, and exhibit appropriate confidence interval coverage.
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