Approximate conditional likelihood for generalized linear models with general missing data mechanism

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• 作者：Jiwei Zhao ; Jun Shao
• 关键词：Asymptotic normality ; generalized linear model ; identifiability ; missing data mechanism ; non ; canonical link function ; nonignorable missingness
• 刊名：Journal of Systems Science and Complexity
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：30
• 期：1
• 页码：139-153
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Systems Theory, Control; Operation Research/Decision Theory; Mathematics of Computing; Complex Systems; Statistics, general;
• 出版者：Academy of Mathematics and Systems Science, Chinese Academy of Sciences
• ISSN：1559-7067
• 卷排序：30

文摘

The generalized linear model is an indispensable tool for analyzing non-Gaussian response data, with both canonical and non-canonical link functions comprehensively used. When missing values are present, many existing methods in the literature heavily depend on an unverifiable assumption of the missing data mechanism, and they fail when the assumption is violated. This paper proposes a missing data mechanism that is as generally applicable as possible, which includes both ignorable and nonignorable missing data cases, as well as both scenarios of missing values in response and covariate. Under this general missing data mechanism, the authors adopt an approximate conditional likelihood method to estimate unknown parameters. The authors rigorously establish the regularity conditions under which the unknown parameters are identifiable under the approximate conditional likelihood approach. For parameters that are identifiable, the authors prove the asymptotic normality of the estimators obtained by maximizing the approximate conditional likelihood. Some simulation studies are conducted to evaluate finite sample performance of the proposed estimators as well as estimators from some existing methods. Finally, the authors present a biomarker analysis in prostate cancer study to illustrate the proposed method.