| For many years, statisticians have recognized the improvement in efficiency of many inference problems as a result of implementing the prior ordering of parameters or restrictions in the analysis. These restrictions often arise naturally, and have applications to many scientific and non-scientific disciplines. Moreover, as it is often the case that observations are not normally distributed and are sometimes observed in a cluster, Generalized Linear Models (GLMs) or Generalized Linear Mixed Models (GLMMs) are employed. Furthermore, many studies involve analysis of data for which some observations are unobserved, or missing. Previous research has indicated that omitting these incomplete values may lead to inefficient, and often biased results. A full unrestricted maximum likelihood estimation based on the likelihood of the responses has been well studied for estimation in clustered and missing-data situations. The present thesis will extend maximum likelihood estimation and likelihood ratio hypothesis testing techniques for these popular models under linear inequality constraints on the parameters of interest. Such methods will improve upon previous results to incorporate general linear comparisons to nonlinear models, and allow for a wider variety of hypothesis tests. The innovative procedures avail of the gradient projection technique for maximum likelihood estimation, and chi-bar-square statistics for likelihood ratio tests. Theoretical and empirical results demonstrate the effectiveness of the maximum likelihood estimators and likelihood ratio tests under parameter constraints. The research is motivated by applications to clustered smoking data among Canadian youth, and an examination of missing variables in relation to contaminant detection of pregnant women for the Canadian government's Northern Contaminants Programme. |
