Constrained inference for generalized linear models with incomplete covariate data

Abstract

Missing data are common in many experiments, including surveys, clinical trials, epidemiological studies, and environmental studies. Unconstrained likelihood inferences for generalized linear models (GLMs) with nonignorable missing covariates have been studied extensively in the literature. However, parameter orderings or constraints may occur naturally in practice, and thus the efficiency of a statistical method may be improved by incorporating parameter constraints into the likelihood function. In this paper, we consider constrained inference for analysing GLMs with nonignorable missing covariates under linear inequality constraints on the model parameters. Specifically, constrained maximum likelihood (ML) estimation is based on the gradient projection expectation maximization approach. Further, we investigate the asymptotic null distribution of the constrained likelihood ratio test (LRT). Simulations study the empirical properties of the constrained ML estimators and LRTs, which demonstrate improved precision of these constrained techniques. An application to contaminant levels in an environmental study is also presented.

Keywords:

• chi-bar-square distribution
• constrained inference
• EM algorithm
• environmental contaminants
• generalized linear model
• gradient projection

Acknowledgements

The authors thank the editor and a referee for their insightful comments which lead to an improved manuscript. The authors also thank Dr Jay van Oostdam and members of the Chemical Surveillance Bureau and the Environmental Health Science and Research Bureau of Health Canada for technical advice with respect to the NCP dataset. The authors also acknowledge Janet Brewster of the Government of Nunavut, and Duane Fleming of the Government of the Northwest Territories for their assistance.

Funding

This work was supported in part by the Natural Sciences and Engineering Research Council of Canada.