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Tests of Markov Order and Homogeneity in a Markov Chain

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  • Jonsson, Robert

    ()
    (Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University)

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    Abstract

    A three-state non-homogeneous Markov chain (MC) of order m>=0, denoted M(m), was previously introduced by the author. The model was used to analyze work resumption among sick-listed patients. It was demonstrated that wrong assumptions about the Markov order m and about homogeneity can seriously invalidate predictions of future health states. In this paper focus is on tests (estimation) of m and of homogeneity. When testing for Markov order it is suggested to test M(m) against M(m+1) with m sequentially chosen as 0, 1, 2,…, until the null hypothesis can’t be rejected. Two test statistics are used, one based on the Maximum Likelihood ratio (MLR) and one based on a chi-square criterion. Also more formal test strategies based on Akaike’s and Baye’s information criteria are considered. Tests of homogeneity are based on MLR statistics. The performance of the tests is evaluated in simulation studies. The tests are applied to rehabilitation data where it is concluded that the rehabilitation process develops according to a non-homogeneous Markov chain of order 2, possibly changing to a homogeneous chain of order 1 towards the end of the period.

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    File URL: http://gupea.ub.gu.se/handle/2077/27931
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    Bibliographic Info

    Paper provided by Statistical Research Unit, Department of Economics, School of Business, Economics and Law, University of Gothenburg in its series Research Reports with number 2011:7.

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    Length: 30 pages
    Date of creation: 31 Oct 2011
    Date of revision:
    Handle: RePEc:hhs:gunsru:2011_007

    Contact details of provider:
    Postal: Statistical Research Unit, University of Gothenburg, Box 640, SE 40530 GÖTEBORG
    Web page: http://www.statistics.gu.se/

    Related research

    Keywords: Likelihood ratio; Test power; Bias of tests;

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