Modeling Change in the Presence of Nonrandomly Missing Data: Evaluating a Shared Parameter Mixture Model

Abstract

In longitudinal research, interest often centers on individual trajectories of change over time. When there is missing data, a concern is whether data are systematically missing as a function of the individual trajectories. Such a missing data process, termed random coefficient-dependent missingness, is statistically nonignorable and can bias parameter estimates obtained from conventional growth models that assume missing data are missing at random. This article describes a shared parameter mixture model (SPMM) for testing the sensitivity of growth model parameter estimates to a random coefficient-dependent missingness mechanism. Simulations show that the SPMM recovers trajectory estimates as well as or better than a standard growth model across a range of missing data conditions. The article concludes with practical advice for longitudinal data analysts.

Keywords:

• growth mixture models
• growth models
• longitudinal data
• missing data
• shared-parameter mixture models

Notes

1. ¹In the SPMM, covariates influence growth factors and missing data indicators directly, rather than indirectly via latent class probabilities. Although similar models presented in the literature allow covariates to affect class probabilities (e.g., Morgan-Lopez & Fals-Stewart, 2007), this practice is not recommended for the SPMM because it complicates computation of the aggregate model parameters. Allowing covariates to predict class membership implies that marginal covariate effects depend on the values of the covariates themselves (Dantan, Proust-Lima, Letenneur, & Jacqmin-Gadda, 2008). Although averaged effects of covariates could be computed with some effort, estimation of the standard errors for covariate effects is intractable (Dantan et al., 2008).

2. ²Rose, von Davier, and Xu (2010) found empirical support for the practice of using summary indicators when implemented with a traditional parameter mixture model and Gottfredson (2011) found similar support for their use in a SPMM context.

3. ³Solutions with small class proportions tend to produce very large standard error estimates that would in practice be rejected in favor of a solution with fewer classes, regardless of information criteria. Preliminary analyses indicated that solutions containing very small classes produced variance component estimates that were more upwardly biased than the estimates produced by solutions with more equal class proportions.