Proportion data falling in the continuum (0, 1) are very common in practice. It can also happen that an inflated number of zeros (or ones) occur with proportion data. There are extensive studies of zero-inflated data in the literature. Almost all of them, however, focus on zero-inflated count data. Furthermore,...
This dissertation is concerned with hypothesis testing for
fixed effects in mixed linear models. Our primary emphasis is on
mixed models when the class of covariance matrices has what we
call a rich linear structure. Such models include mixed ANOVA
models and regression models with heteroscedastic variances. For
the majority...
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...
This thesis considers likelihood inferences for generalized linear models with additional
random effects. The likelihood function involved ordinarily cannot be evaluated
in closed form and numerical integration is needed. The theme of the thesis is
a closed-form approximation based on Laplace's method. We first consider a special
yet important case...
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...
Geostatistical linear interpolation procedures such as kriging require knowledge of the
covariance structure of the spatial process under investigation. In practice, the covariance of the
process is unknown, and must be estimated from the available data. As the quality of the
resulting predictions, and associated mean square prediction errors, depends...
Mixed linear models are a time honored method of analyzing correlated data. However, there is still no method of calculating exact confidence intervals or p-values for an arbitrary parameter in any mixed linear model. Instead, researchers must use either specialized approximate and exact tests that have been developed for particular...