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Tests of Markov Order and Homogeneity in a Markov Chain

Listed author(s):
  • Jonsson, Robert

    ()

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

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    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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    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
    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/

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    1. P. J. Avery & D. A. Henderson, 1999. "Fitting Markov chain models to discrete state series such as DNA sequences," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(1), pages 53-61.
    2. J. P. Hughes & P Guttorp & S. P. Charles, 1999. "A non-homogeneous hidden Markov model for precipitation occurrence," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(1), pages 15-30.
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