A Finite Mixture Approach to Covariance Structure Modeling With Unknown, Heterogeneous Populations
Hesson-Mcinnis, Matthew
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https://hdl.handle.net/2142/82207
Description
Title
A Finite Mixture Approach to Covariance Structure Modeling With Unknown, Heterogeneous Populations
Author(s)
Hesson-Mcinnis, Matthew
Issue Date
1997
Doctoral Committee Chair(s)
Hubert, Lawrence J.
Department of Study
Psychology
Discipline
Psychology
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Language
eng
Abstract
"The field of covariance structure modeling has included models for heterogeneous populations for some time (e.g., Muthen, 1989), but to date none have incorporated methods that allow for heterogeneity when the population membership is unknown. The field of finite mixture analysis, however, addresses the issues of unknown heterogeneous populations. The finite mixture methodology, therefore, is applied to the problem of covariance structure modeling when the sample represents an unknown mixture of heterogeneous populations. Using the EM algorithm for maximum likelihood estimation, a finite mixture covariance structure (FMCS) model is developed by replacing the usual finite mixture complete data log-likelihood function with a log-likelihood function that incorporates covariance structure within the multiple populations. Convergence theorems from the finite mixture literature are examined and validated for the new method, and the importance of good starting values is stressed. Additionally, standard error estimates are derived through the calculation of the observed Fisher information matrix of the FMCS model. The model was evaluated by assessing the accuracy of recovering known mixture and covariance structure parameters in synthetic (e.g., Monte Carlo) data as well as by judging the increase in interpretability of a non-synthetic (e.g., ""real world"") data set. The Monte Carlo simulations indicated that the model recovers the true parameters with a great deal of accuracy for most although not all models. Most importantly, models with too many parameters free to vary between the unknown populations exhibit a tendency to find spurious maximizers on the boundary of the allowable parameter space, a problem that has plagued finite mixtures with heterogeneous covariances. The analysis of an archival data set from the U.S.M.S.P.B. (1987) with the FMCS model provided a unique interpretation of the data not available with a traditional one-sample covariance structure model. Limitations and directions for future research are discussed."
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