Thesis (Ph. D.)--University of Washington, 1993. / Vita. Includes bibliographical references (leaves [129]-133).

by Lam Man Kin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1990. / Bibliography: leaves 69-71. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Generalized Linear Models --- p.7 / Chapter §2.1 --- The Model --- p.7 / Chapter §2.2 --- Estimation of the Parameters --- p.10 / Chapter Chapter 3 --- Tests for the Dispersion Parameters --- p.15 / Chapter S3.1 --- Three Asymptotically Equivalent Tests based on MLE --- p.15 / Chapter §3.2 --- Application of the Tests for the Dispersion Parameters --- p.22 / Chapter Chapter 4 --- Finite Sample Study of the Three Tests based on Simulation --- p.29 / Chapter §4.1 --- Introduction --- p.29 / Chapter §4.2 --- The Simulation --- p.31 / Chapter §4.3 --- The Results --- p.34 / Chapter Chapter 5 --- An Example --- p.38 / Chapter Chapter 6 --- Conclusions and Discussions --- p.42 / Tables / References

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 and covariance matrix. However, tests and confidence intervals based on this approach have been limited to what is provided through asymptotic normality of estimates. The proposed solution is based on maximizing a Laplace approximation to the log-likelihood function. This approximation is remarkably accurate and has previously been demonstrated to work well for obtaining likelihood based estimates and inferences in generalized linear models with a single random effect. This thesis concentrates on extensions to the case of several random effects and the comparison of the likelihood ratio inference from this approximate likelihood analysis to the Wald-like inferences for existing estimators. The shapes of the Laplace approximate and true log-likelihood functions are practically identical, implying that maximum likelihood estimates and likelihood ratio inferences are obtained from the Laplace approximation to the log-likelihood. Use of the Laplace approximation circumvents the need for numerical integration, which can be practically impossible to compute when there are two random effects. However, both the Laplace and exact (via numerical integration) methods require numerical optimization, a sometimes slow process, for obtaining estimates and inferences. The proposed Laplace method for estimation and inference is demonstrated for three real (and some simulated) data sets, along with results from alternative methods which involve use of marginal means and covariances. The Laplace approximate method and another denoted as Restricted Maximum Likelihood (REML) performed rather similarly for estimation and hypothesis testing. The REML approach produced faster analyses and was much easier to implement while the Laplace implementation provided likelihood ratio based inferences rather than those relying on asymptotic normality. / Graduation date: 1995

Thesis (Ph. D.)--University of Queensland, 2001. / Includes bibliographical references.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 155-159). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references (leaves 155-159). Also available on the Internet.

When dealing with exponential family distributions, a constant dispersion is often assumed since it simplifies both model formulation and estimation. In contrast, heteroscedasticity is a common feature of almost every empirical data set. In this dissertation, the dispersion parameter is no longer considered as constant throughout the entire sample, but defined as the expected deviance of the individual response yi and its expected value _i such that it will be expressed as a linear combination of some covariates and their coefficients. At the same time, the dispersion regression is an essential part of a double Generalized Linear Model in which mean and dispersion are modelled in two interlinked and pseudo-simultaneously estimated submodels. In other words, the deviance is a function of the response mean which on the other hand depends on the dispersion. Due to the mutual dependency, the estimation algorithm will be iterated as long as the improvement of the one parameter leads to significant changes of the other until it is not the case. If appropriate covariates are chosen, the model’s goodness of fit should be improved by the property that the dispersion is estimated by external information instead of being a constant. In the following, the advantage of dispersion modelling will be shown by its application on three different types of data: a) zero-inflated data, b) non-linear time series data, and c) clinical trials data. All these data follow distributions of the exponential family for which the application of the Generalized Linear Model is justified, but require certain extensions of modelling methodologies. In this dissertation, The enhanced goodness of fit given that the constant dispersion assumption is dropped will be shown in the above listed examples. In fact, by formulating and carrying out score and Wald tests on testing for the possible occurrence of varying dispersion, evidence of heterogeneous dispersion could be found to be present in the data sets considered. Furthermore, although model formulation, asymptotic properties and computational effort are more extensive when dealing with the double models, the benefits and advantages in terms of improved fitting results and more efficient parameter estimates appear to justify the additional effort not only for the types of data introduced, but also generally for empirical data analysis, on different types of data as well. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

The general linear model, the weighted linear model, and the generalized linear model are presented in detail. Diagnostic tools for the linear models are considered. In general the standard analysis for linear models does not account for measurement error. / Thesis (M.Sc.) - University of KwaZulu-Natal, Pietermaritzburg, 2007.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1980. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 290-293).

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