Background: Longitudinal studies enable the study of within person change over time in addition to between person differences. In longitudinal studies of older adult populations even when not the question of interest, identifying participants with dementia is desirable, and often necessary. Yet in practice, the time to collect information from each participant may be limited. Therefore, some studies include only a brief general cognitive measure of which the Mini Mental State Examination (MMSE) is the most commonly used (Raina et al., 2009). The current study explores whether group-based trajectory modeling of MMSE scores with a selection of covariates can identify individuals who have or will develop dementia in an 8 year longitudinal study. Methods: The sample included 651 individuals from the Origins of Variance in the Oldest Old study of Swedish twins 80 years old or older (OCTO-Twin). Participants had completed the MMSE every two years, and cases of dementia were diagnosed according to DSM-III criteria. The accuracy of using the classes formed in growth mixture modeling and latent class growth modeling as indicative of dementia status was compared to that of more standard methods, the typical 24/30 cut score and a logistic regression. Results: A three-class quadratic model with covariate effects on class membership was found to best characterize the data. The classes were characterized as High Performing Late Decline, Rapidly Declining, and Decreasing Low Performance, and were labeled as such. Comparing the diagnostic accuracy of the latent trajectory groups against simple methods; the sensitivity of the final model was lower but it was the same or superior in specificity, positive predictive value, negative predictive value, and allowed a more fine-grained analysis of participant risk. Conclusions: Group-based trajectory models may be helpful for grouping longitudinal study participants, particularly if sensitivity is not the primary concern. / Graduate

The number of longitudinal studies has increased steadily in various social science disciplines over the last decade. Growth Mixture Modeling (GMM) has emerged among the new approaches for analyzing longitudinal data. It can be viewed as a combination of Hierarchical Linear Modeling, Latent Growth Curve Modeling and Finite Mixture Modeling. The combination of both continuous and categorical latent variables makes GMM a flexible analysis procedure. However, when researchers analyze their data using GMM, some may assume that the units are independent of each other even though it may not always be the case. The purpose of this dissertation was to examine the impact of ignoring a higher nesting structure in Multilevel Growth Mixture Modeling on the accuracy of classification of individuals and the accuracy on tests of significance (i.e., Type I error rate and statistical power) of the parameter estimates for the model in each subpopulation. Two simulation studies were conducted. In the first study, the impact of misspecifying the multilevel mixture model is investigated by ignoring a level of nesting structure in cross-sectional data. In the second study, longitudinal clustered data (e.g., repeated measures nested within units and units nested within clusters) are analyzed correctly and with a misspecification ignoring the highest level of the nesting structure. Results indicate that ignoring a higher level nesting structure results in lower classification accuracy, less accurate fixed effect estimates, inflation of lower-level variance estimates, and less accurate standard error estimates, the latter result which in turn affects the accuracy of tests of significance for the fixed effects. The magnitude of the intra-class correlation (ICC) coefficient has a substantial impact when a higher level nesting structure is ignored; the higher the ICC, the more variance at the highest level is ignored, and the worse the performance of the model. The implication for applied researchers is that it is important to model the multilevel data structure in (growth) mixture modeling. In addition, researchers should be cautious in interpreting their results if ignoring a higher level nesting structure is inevitable. Limitations concerning appropriate use of latent class analysis in growth modeling include unknown effects of incorrect estimation of the number of latent classes, non-normal distribution effects, and different growth patterns within-group and between-group.

Growth mixture models (GMMs) are used to model intra-individual change and inter-individual differences in change and to detect underlying group structure in longitudinal studies. Regularly, these models are fitted under the assumption of normality, an assumption that is frequently invalid. To this end, this thesis focuses on the development of novel non-elliptical growth mixture models to better fit real data. Two non-elliptical growth mixture models, via the multivariate skew-t distribution and the generalized hyperbolic distribution, are developed and applied to simulated and real data. Furthermore, these two non-elliptical growth mixture models are extended to accommodate missing values, which are near-ubiquitous in real data. Recently, finite mixtures of non-elliptical distributions have flourished and facilitated the flexible clustering of the data featuring longer tails and asymmetry. However, in practice, real data often have missing values, and so work in this direction is also pursued. A novel approach, via mixtures of the generalized hyperbolic distribution and mixtures of the multivariate skew-t distributions, is presented to handle missing values in mixture model-based clustering context. To increase parsimony, families of mixture models have been developed by imposing constraints on the component scale matrices whenever missing data occur. Next, a mixture of generalized hyperbolic factor analyzers model is also proposed to cluster high-dimensional data with different patterns of missing values. Two missingness indicator matrices are also introduced to ease the computational burden. The algorithms used for parameter estimation are presented, and the performance of the methods is illustrated on simulated and real data. / Thesis / Doctor of Philosophy (PhD)

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