This thesis considers the problem of estimating the linear
parameters of generalized linear models (GLM), especially binomial
and Poisson regression models, when the explanatory variable is
subject to measurement error. In this situation, the dependence of
the response variable on the observed explanatory variable cannot
typically be modeled as a...
Data in the form of counts or proportions often exhibit more
variability than that predicted by a Poisson or binomial
distribution. Many different models have been proposed to account
for extra-Poisson or extra-binomial variation. A simple model
includes a single heterogeneity factor (dispersion parameter) in the
variance. Other models that...
The Thurstone-Mosteller and Bradley-Terry Models are commonly used to rank items from paired comparisons experiments in which one item in each pair "wins," and to assess the importance of time-independent explanatory variables on such rankings. The first part of this thesis clarifies the use of probit and logistic regression models...
This thesis advocates the use of maximum likelihood analysis for generalized
regression models with measurement error in a single explanatory variable. This will be
done first by presenting a computational algorithm and the numerical details for carrying
out this algorithm on a wide variety of models. The computational methods will...
Semiparametric maximum likelihood analysis allows inference in errors-invariables models with small loss of efficiency relative to full likelihood analysis but with significantly weakened assumptions. In addition, since no distributional assumptions are made for the nuisance parameters, the analysis more nearly parallels that for usual regression. These highly desirable features and...
This dissertation is about the likelihood analysis of ordered categorical responses in a longitudinal/spatial study, meaning regression-like analysis when the response variable is categorical with ordered categories, and is measured repeatedly over time or space on the experimental or sampling units. Particular attention is given to the multivariate ordinal probit...
Regression calibration inference seeks to estimate regression models with measurement error in explanatory variables by replacing the mismeasured variable by its conditional expectation, given a surrogate variable, in an estimation procedure that would have been used if the true variable were available. This study examines the effect of the uncertainty...
RNA-Sequencing (RNA-Seq) has rapidly become the de facto technique in transcriptome studies. However, established statistical methods for analyzing experimental and observational microarray studies need to be revised or completely re-invented to accommodate RNA-Seq data's unique characteristics. In this dissertation, we focus on statistical analyses performed at two particular stages in...
This thesis proposes an approximate maximum likelihood estimator and
likelihood ratio test for parameters in a generalized linear model when two or
more random effects are present. Substantial progress in parameter estimation
for such models has been made with methods involving generalized least squares
based on the approximate marginal mean...
This dissertation is about statistical methods for data analysis using generalized linear mixed models (GLMMs) with censored covariates. Special attention in given to the particular problem of inference about age-specific reproductive success in wild animal populations using some animals with known ages and some animals with ages only known to...