The consequences of ignoring assessment date heterogeneity within waves for latent growth models

In traditional latent growth modeling, researchers assume that assessment dates within waves from longitudinal studies are homogeneous, although they are nearly always heterogeneous. In this study, we present a pedagogical illustration of assessing the consequences of ignoring time-point variability within a wave using the Math Item Response Theory scores from the Early Childhood Longitudinal Study for Kindergarten (ECLS -- K). By comparing latent growth change and prediction models for time invariant and time varying latent growth models, we found some changes in parameter estimates, particularly in the variance and residual variance in the linear effect. We found slight differences on the mean of the linear and quadratic effect, as well as the direct effect of our predictor on the linear and quadratic effect. However, further substantive claims about parameter estimates changes are limited due to missing data and a possible model misspecification.