A marginalized zero-truncated Poisson regression model and its model averaging prediction

Abstract

Counting data without zero category often occurs in many fields, such as social studies, clinical trials and economic phenomenon analyses. Researchers usually show interest in describing the characteristics of the observed counts and the Poisson distribution is often preferred to model the counted data. Nevertheless, making marginal inference on the population mean is a challenging job when missing zero class occurs and the Poisson mean is considered as an alternative. In this paper, based on a so-called marginalized zero-truncated Poisson (ZTP) regression model, a novel SR-based EM-FS algorithm is proposed to facilitate parameter estimation. To improve the prediction accuracy, this paper proposes a zero-truncated Poisson model averaging prediction that selects the optimal weight combination by minimizing a Kullback–Leibler (KL) divergence criterion. It is shown that the weight criterion is approximately unbiased about the expected KL loss. We further prove that the proposed prediction is asymptotically optimal in the sense that the KL-type loss and prediction risk are asymptotically identical to those of the infeasible best possible averaged prediction. Simulations and two empirical data applications are conducted to illustrate the proposed method.

Keywords

Marginalized ZTP regression model / SR-based EM-FS algorithm / Frequentist model averaging / Weight choice criterion / Kullback–Leibler divergence

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Funding

National Natural Science Foundation of China(61773401)

National Natural Science Foundation of China(11688101)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature