Estimation and tests for a longitudinal regression model based on the Markov chain |
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| Authors: | M Ataharul Islam Khalaf S Sultan Rafiqul I Chowdhury |
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| Institution: | aDepartment of Statistics, Biostatistics & Informatics, University of Dhaka, Dhaka 1000, Bangladesh;bDepartment of Statistics and OR, College of Science, King Saud University, PO Box 2455, Riyadh 11451, Saudi Arabia;cDepartment of Health Information Administration, Kuwait University, Kuwait |
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| Abstract: | In this paper, the dependence of transition probabilities on covariates and a test procedure for covariate dependent Markov models are examined. The nonparametric test for the role of waiting time proposed by Jones and Crowley M. Jones, J. Crowley, Nonparametric tests of the Markov model for survival data Biometrika 79 (3) (1992) 513–522] has been extended here to transitions and reverse transitions. The limitation of the Jones and Crowley method is that it does not take account of other covariates that might have association with the probabilities of transition. A simple test procedure is proposed that can be employed for testing: (i) the significance of association between covariates and transition probabilities, and (ii) the impact of waiting time on the transition probabilities. The procedure is illustrated using panel data on hospitalization of the elderly population in the USA from the Health and Retirement Survey (HRS). |
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| Keywords: | Markov model Covariate dependence Transition Test for model Test for waiting time |
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