Document Type


Date of Degree

Fall 2016

Access Restrictions

Access restricted until 02/23/2019

Degree Name

PhD (Doctor of Philosophy)

Degree In


First Advisor

Michael P. Jones

First Committee Member

Gideon K.D. Zamba

Second Committee Member

Kai Wang

Third Committee Member

Jeffrey D. Long

Fourth Committee Member

Kung-Sik Chan


A semiparametric proportional likelihood ratio model was proposed by Luo and Tsai (2012) which is suitable for modeling a nonlinear monotonic relationship between the response variable and a covariate. Extending the generalized linear model, this model leaves the probability distribution unspecified but estimates it from the data. In this thesis, we propose to extend this model into analyzing the longitudinal data by incorporating random effects into the linear predictor. By using this model as the conditional density of the response variable given the random effects, we present a maximum likelihood approach for model estimation and inference. Two numerical estimation procedures were developed for response variables with finite support, one based on the Newton-Raphson algorithm and the other one based on generalized expectation maximization (GEM) algorithm. In both estimation procedures, Gauss-Hermite quadrature is employed to approximate the integrals.

Upon convergence, the observed information matrix is estimated through the second-order numerical differentiation of the log likelihood function. Asymptotic properties of the maximum likelihood estimator are established under certain regularity conditions and simulation studies are conducted to assess its finite sample properties and compare the proposed model to the generalized linear mixed model. The proposed method is illustrated in an analysis of data from a multi-site observational study of prodromal Huntington's disease.


GLMM, Longitudinal data, Misspecification, Mixed Model, Porportional likelihood ratio model


x, 112 pages


Includes bibliographical references (pages 108-112).


Copyright © 2016 Hongqian Wu

Available for download on Saturday, February 23, 2019

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