Date of Award
Morgridge College of Education, Research Methods and Information Science, Research Methods and Statistics
Developmental studies, Functional form analysis, Growth mixture modeling, Growth trajectories, Latent growth curve modeling, Trend analysis
Growth mixture modeling (GMM) is a methodological tool used to represent heterogeneity in longitudinal datasets through the identification of unobserved subgroups following qualitatively and quantitatively distinct trajectories in a population. These growth trajectories or functional forms are informed by the underlying developmental theory, are distinct to each subgroup, and form the core assumptions of the model. Therefore, the accuracy of the assumed functional forms of growth strongly influences substantive research and theories of growth. While there is evidence of mis-specified functional forms of growth in GMM literature, the weight of this violation has been largely overlooked. Current solutions to circumvent assumption violations to functional forms of growth are reliant on theory and inferences yielded from previous research. However, the low frequency of systematic replications of study assumptions implies that developmental theories may not always suggest the correct functional form for a given growth phenomenon. The current dissertation is an examination of GMM assumption violation to the functional form of growth. The simulation study quantitatively contrasted the measured differences between the true population model to a series of mis-specified models where the outcome appropriateness was measured using latent classes and model fit indices. Results of the simulation study revealed two key takeaways. Firstly, that the fit indices of the mis-specified models consistently selected the correct number of classes present in the sample. However, closer examination of the mixing proportion of these latent classes revealed that individual’s probability of membership to the latent classes was compromised for the mis-specified models. Secondly, the type of functional form mis-specified (i.e., a simple linear or quadratic or complex Gompertz) determined how visible the effects of the mis-specification would be to the researcher. The implications of these findings are further discussed in this paper along with directions for future research.
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Received from ProQuest
Ghevarghese, Richa, "Mis-Specification of Functional Forms in Growth Mixture Modeling: A Monte Carlo Simulation" (2022). Electronic Theses and Dissertations. 2048.
Developmental psychology, Statistics, Higher education