The semiparametric group-based trajectory model (GBTM), a special case of the more general growth mixture model, has been and increasingly employed technique for modeling heterogeneous change over time. A benefit of the GBTM is the ability to uncover distinct classes in the population that are characterized by their developmental trajectories. The characteristics of the developmental trajectories are affected by the number of classes extracted during estimation which in turn can affect inference, future investigation, and treatment or intervention. Thus, it is important that the measure(s) being relied upon for class enumeration are as accurate as possible. Only a handful of over 20 measures for class enumeration have been assessed in the context of GBTM using Monte Carlo methods prompting the need for a more thorough investigation. The purpose of this study was to determine if there were differences in the studied enumeration measures (information criteria, likelihood ratio test derivatives, and entropy based statistics and classification indices) abilities to correctly identify a true number of latent classes and to determine the common extraction errors for select enumeration measures in the context of a GBTM. A Monte Carlo study was performed and data were generated for true 4-class censored normal and binary logit models. Manipulated factors were sample size, the number of repeated measures, class mixing proportions, percent missing, and separation among the classes. Data were analyzed using a classification and regression tree approach. The results demonstrated that there were differences in the enumeration measures abilities to correctly identify the true 4-class solution in both model types. Correct classification rates were highest when the separation among the classes was high, the class mixing proportions were either equal or moderately unequal, and the sample size was 800 or above. The information criteria had the most accurate classification rates while entropy statistics and classification indices had the least accurate classification rates. There were higher rates of under extraction errors overall but in certain conditions some of the enumeration measures showed a tendency to over extract classes. The Bayesian information criterion and the sample size adjusted Bayesian information criterion were the two measures recommended overall.
|Advisor:||Kim, Kevin H.|
|Commitee:||Chung, Tammy A., Stone, Clement, Ye, Feifei|
|School:||University of Pittsburgh|
|School Location:||United States -- Pennsylvania|
|Source:||DAI-A 76/02(E), Dissertation Abstracts International|
|Subjects:||Educational tests & measurements, Statistics|
|Keywords:||Censored normal regression, Class enumeration, Classification rates, Developmental trajectory, Information criteria|
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