Factors Affecting the Adequacy and Preferability of Semiparametric Groups-Based Approximations of Continuous Growth Trajectories

Abstract

Psychologists have long been interested in characterizing individual differences in change over time. It is often plausible to assume that the distribution of these individual differences is continuous in nature, yet theory is seldom so specific as to designate its parametric form (e.g., normal). Semiparametric groups-based trajectory models (SPGMs) were thus developed to provide a discrete approximation for continuously distributed growth of unknown form. Previous research has demonstrated the adequacy of the approximation provided by SPGM but only under relatively narrow, theoretically optimal conditions. Under alternative conditions, which may be more common in practice (e.g., higher dimension random effects, smaller sample sizes), this study shows that approximation adequacy can suffer. Furthermore, this study also evaluates whether SPGM's discrete approximation is preferable to a parametric trajectory model that assumes normally distributed random effects when in fact the distribution is modestly nonnormal. The answer is shown to depend on distributional characteristics of both repeated measures (binary or continuous) and random effects (bimodal or skewed). Implications for practice are discussed in light of empirical examples on externalizing behavior.

Understanding Linkages Among Mixture Models

“…Muthén, 2001;Nagin, 1999; also called a latent class growth model) longitudinal panel data (J repeated measures on a single outcome) are required. Most GBT applications employ conditionally normal repeated measures (see Sterba, Baldasaro, & Bauer, 2012), as we do here; however, it has been applied with other within-class distributions (e.g., Poisson or Bernoulli). The GBT model accounts for the pattern of means and (co)variances of repeated measures in the population via a mixing of homogeneous classes of persons who, within class, follow the same trajectory of change apart from pure error.…”

Latent trajectories of infant breast milk consumption in the United States

“…This specific technique was less useful for converging on what might be the “true” number of trajectories but, along with domain knowledge, was instrumental in determining what might be a useful number of trajectories to describe. Using BIC as a metric of model fit was poorly suited to this data structure because of the large number of time points; similar issues have been reported for other researchers using GBTM (Sterba, Baldasaro, & Bauer, ). It may also be that there are simply a large number of latent breastfeeding trajectories that exist, beyond what might be practically useful.…”

A discrete-time Multiple Event Process Survival Mixture (MEPSUM) model.

“…Simulation research on the SPGM conducted by Brame et al (2006), Nagin (2005), and Muthén and Asparouhov (2008) has demonstrated that a discrete-point finite mixture can reasonably approximate various random effects distributions of low dimensionality. More recently, however, Sterba, Baldasaro and Bauer (2012) determined that the adequacy of the approximation suffers when the random effects distribution is of higher dimensionality, particularly for binary outcomes at low sample sizes. The latter results give greater emphasis to our caution that the MEPSUM model is likely to perform best in large samples.…”