Ren, Lulu
(2006)
PARAMETER ESTIMATION FOR LATENT MIXTURE MODELS WITHAPPLICATIONS TO PSYCHIATRY.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
Longitudinal and repeated measurement data commonly arise in many scientific researchareas. Traditional methods have focused on estimating single mean response as a function ofa time related variable and other covariates in a homogeneous population. However, in manysituations the homogeneity assumption may not be appropriate. Latent mixture modelscombine latent class modeling and conventional mixture modeling. They accommodate thepopulation heterogeneity by modeling each subpopulation with a mixing component. Inthis paper, we developed a hybrid Markov Chain Monte Carlo algorithm to estimate theparameters of the latent mixture model. We show through simulation studies that MCMCalgorithm is superior than the EM algorithm when missing value percentage is large.As an extension of latent mixture models, we also propose the use of cubic splines asa curve fitting technique instead of classic polynomial fitting. We show that this methodgives better fits to the data, and our MCMC algorithm estimates the model efficiently. Weapply the cubic spline technique to a data set which was collected in a study of alcoholism.Our MCMC algorithm shows several different P300 amplitude trajectory patterns amongchildren and adolescents.Other topics that are covered in this thesis include the identifiability of the latent mixturemodel and the use of such model to predict a binary outcome. We propose a bivariate versionof the latent mixture model, where two courses of longitudinal responses can be modeled atthe same time. Computational aspects of such models remain to be completed in the future.
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| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
6 July 2006 |
| Date Type: |
Completion |
| Defense Date: |
20 April 2006 |
| Approval Date: |
6 July 2006 |
| Submission Date: |
27 April 2006 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Statistics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Markov Chain Monte Carlo algorithm; EM algorithm; |
| Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-04272006-180326/, etd-04272006-180326 |
| Date Deposited: |
10 Nov 2011 19:42 |
| Last Modified: |
15 Nov 2016 13:42 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/7686 |
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