Inferences in dynamic logit models in semi-parametric setup for repeated binary data |
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Authors: | Nan Zheng Brajendra C Sutradhar |
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Institution: | 1. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, Canada;2. School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada |
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Abstract: | Binary dynamic fixed and mixed logit models are extensively studied in the literature. These models are developed to examine the effects of certain fixed covariates through a parametric regression function as a part of the models. However, there are situations where one may like to consider more covariates in the model but their direct effect is not of interest. In this paper we propose a generalization of the existing binary dynamic logit (BDL) models to the semi-parametric longitudinal setup to address this issue of additional covariates. The regression function involved in such a semi-parametric BDL model contains (i) a parametric linear regression function in some primary covariates, and (ii) a non-parametric function in certain secondary covariates. We use a simple semi-parametric conditional quasi-likelihood approach for consistent estimation of the non-parametric function, and a semi-parametric likelihood approach for the joint estimation of the main regression and dynamic dependence parameters of the model. The finite sample performance of the estimation approaches is examined through a simulation study. The asymptotic properties of the estimators are also discussed. The proposed model and the estimation approaches are illustrated by reanalysing a longitudinal infectious disease data. |
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Keywords: | Dynamic models for repeated binary responses non-parametric function in secondary covariates parametric regression in primary covariates semi-parametric conditional quasi-likelihood and semi-parametric likelihood estimation time-dependent covariates |
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