On group-based trajectory modelling

Abstract

Group-based trajectory models are used for characteristics that, when followed longitudinally, may show subpopulations with distinct trajectories. This thesis describes three studies I undertook relating to these models. 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 may result in poor model performance, but the extent and nature of this is not well understood. In the first study, I used simulation to investigate the effect of covariance misspecification on misclassification of trajectories in commonly used models under a range of scenarios. I found that the more complex models generally performed better over a range of scenarios. In particular, incorrectly specified co- variance matrices could significantly bias the results, whereas using models with a correct but more complicated than necessary covariance matrix incurred little cost. An underlying assumption of the group-based trajectory model is that it applies to all trajectories, and this does not allow for the possibility that outliers may be present. Thus outlying trajectories may distort the estimated groups of these models and any subsequent analyses that use them. In the second study, I used simulations to assess the impact of outliers on group-based trajectory models. The presence of outliers tended to lead to an increased number of groups, and a reduction in the correct classification rate provided the group means were well separated. Following the simulations, I developed an algorithm for identifying outlying trajectories, and evaluated its performance on the simulated trajectory datasets. The application of my algorithm is recommended as part of sensitivity analyses to determine the effect that outliers may have. One approach to modelling the influence of prior covariates in the group-based setting is to consider models wherein these covariates affect the group member- ship probabilities. In the third study, I compared six different methods from the literature for estimating the effect of covariates in this way. I found that when investigating the effects of covariates, the full likelihood approach minimised the bias in the estimates of the covariate effects. In this ‘1-step’ approach, the estimation of the effect of covariates and the trajectory model are carried out simultaneously. Of the ‘3-step’ approaches, where the the effect of the covariates are assessed subsequent to the estimation of the group-based trajectory model, only Vermunt’s Improved 3-step resulted in bias estimates similar in size to the full likelihood approach. The remaining methods resulted in considerably higher bias in the covariate effect estimates, and should not be used. This thesis provides guidance in the use of group-based trajectory models for practising statisticians, focusing on the choice of covariance structures, the impact and identification of outlying trajectories, and the most appropriate methods for estimating the effects of covariates. Researchers should consider a wide range of models, and bearing in mind the assumptions they make, carefully choose that which fits best with the data.