Generalised linear model selection by the predictive least quasi-deviance criterion

• Published in: Biometrika Vol. 83; no. 1; pp. 41 - 54
• Main Authors: QIAN, GUOQI, GABOR, GEORGE, GUPTA, R. P.
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.03.1996; Biometrika Trust
• Subjects: Consistency; Error rates; Exact sciences and technology; Least squares; Linear inference, regression; Linear models; Linear regression; Martingales; Mathematical functions; Mathematics; Model selection; Modeling; Nonparametric inference; Prediction; Predictive least quasi-deviance; Predictive modeling; Predictive stochastic complexity; Prequential analysis; Probability and statistics; Quasi-likelihood function; Regression analysis; Sciences and techniques of general use; Statistics; Stochastic models; Selection problem; Generalized linear model; Deviance; Selection; Likelihood; Consistency; Prediction; Selection criterion; Complexity
• ISSN: 0006-3444; 1464-3510
• DOI: 10.1093/biomet/83.1.41

We consider the problem of selecting a model with the best predictive ability in a class of generalised linear models. A predictive least quasi-deviance criterion is proposed to measure the predictive ability of a model. This criterion is obtained by applying the idea of the predictive minimum description length principle and the theory of quasi-likelihood functions. The resulting predictive quasi-deviance function is an extension of the predictive stochastic complexity of the model. Under rather weak conditions the predictive least quasi-deviance method is shown to be consistent in the sense that the probability of selecting the right model converges to one as the number of observations goes to infinity. Also we show that the selected model converges to the optimal model in expectation. The method is then modified for finite sample applications. Examples and simulation results are presented.