On group-based trajectory modelling
Date
2018
Authors
Davies, Christopher Edward
Editors
Advisors
Glonek, Garique Francis Vladimir
Giles, Lynne Catherine
Giles, Lynne Catherine
Journal Title
Journal ISSN
Volume Title
Type:
Theses
Citation
Statement of Responsibility
Conference Name
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.
School/Discipline
School of Mathematical Sciences
Dissertation Note
Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Mathematical Sciences, 2018
Provenance
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