Extending Latent Basis Growth Model to Explore Joint Development in the Framework of Individual Measurement Occasions

Longitudinal processes in multiple domains are often theorized to be nonlinear, which poses unique statistical challenges. Empirical researchers often select a nonlinear longitudinal model by weighing how specific the model must be regarding the nature of the nonlinearity, whether the model provides efficient estimation and interpretable coefficients. Latent basis growth models (LBGMs) are one method that can get around these tradeoffs: it does not require specification of any functional form; additionally, its estimation process is expeditious, and estimates are straightforward to interpret. We propose a novel specification for LBGMs that allows for (1) unequally-spaced study waves and (2) individual measurement occasions around each wave. We then extend LBGMs to explore multiple repeated outcomes because longitudinal processes rarely unfold in isolation. We present the proposed model by simulation studies and real-world data analyses. Our simulation studies demonstrate that the proposed model can provide unbiased and accurate estimates with target coverage probabilities of a 95% confidence interval. With the real-world analyses using longitudinal reading and mathematics scores, we demonstrate that the proposed parallel LBGM can capture the underlying developmental patterns of these two abilities and that the novel specification of LBGMs is helpful in joint development where longitudinal processes have different time structures. We also provide the corresponding code for the proposed model.