The impact of covariance misspecification in group-based trajectory models for longitudinal data with non-stationary covariance structure

Abstract

One purpose of a longitudinal study is to gain a better understanding of how an outcome of interest changes among a given population over time. In what follows, a trajectory will be taken to mean the series of measurements of the outcome variable for an individual. Group-based trajectory modelling methods seek to identify subgroups of trajectories within a population, such that trajectories that are grouped together are more similar to each other than to trajectories in distinct groups. Group-based trajectory models generally assume a certain structure in the covariances between measurements, for example conditional independence, homogeneous variance between groups or stationary variance over time. Violations of these assumptions could be expected to result in poor model performance. We used simulation to investigate the effect of covariance misspecification on misclassification of trajectories in commonly used models under a range of scenarios. To do this we defined a measure of performance relative to the ideal Bayesian correct classification rate. We found that the more complex models generally performed better over a range of scenarios. In particular, incorrectly specified covariance matrices could significantly bias the results but using models with a correct but more complicated than necessary covariance matrix incurred little cost.

Identifying typical trajectories in longitudinal data: modelling strategies and interpretations

“…If, the assumed covariance structure is too simple, the number of classes may be greater because more are needed to capture the variability in the data [32]. For this reason, and as demonstrated in simulations [33], when selecting the number of classes for growth mixture models, one should in principle allow for general specifications,…”

“…e.g., with class-specific covariance matrices Ω c u . and timespecific residual error variance 2 j [33]. How general these matrices can be, will be limited by the study size and may not be suitable with binary outcome data when their prevalence is low [33].…”

“…The assumption of independence for the residual errors e s ij , conditional on class s, which is usually made when performing latent class growth analysis, is most likely to be incorrect, especially when there are several observations per individual. Violations may lead to biased estimates of the class-specific regression coefficients [33] unless the classes are well separated, e.g. entropy > 0.8 [32].…”

“…Mixed effects models can be viewed as single class growth mixture model. Hence, their goodness of fit can be compared with that obtained from growth mixture models with increasing numbers of classes, allowing for class-specific covariance structures [33]. We compared growth mixture models with up to six classes using the criteria described in "Growth mixture models".…”

Identification of developmental trajectory classes: Comparing three latent class methods using simulated and real data

“…Although the use of LCA, LCGA or GMM can result in different outcomes (Morin et al 2011;Kooken et al 2018), it is unknown which of these three methods performs best. The relative performances of LCA, LCGA and GMM has previously been assessed (Twisk and Hoekstra 2012;Martin and von Oertzen 2015;Diallo et al 2016;Davies et al 2017), but the three methods have not yet been compared together in one simulation study, nor have they been compared in terms of bias.…”