Tests of Markov Order and Homogeneity in a Markov Chain

Robert Jonsson ()
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Robert Jonsson: Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University, Postal: Statistical Research Unit, Göteborg University, Box 640, SE 40530 GÖTEBORG

No 2011:7, Research Reports from University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law

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.

Keywords: Likelihood ratio; Test power; Bias of tests (search for similar items in EconPapers)
JEL-codes: C10 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2011-10-31
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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