Resarch Reports
No 2011:7:
Tests of Markov Order and Homogeneity in a Markov Chain
Robert Jonsson ()
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; (follow links to similar papers)
JEL-Codes: C10; (follow links to similar papers)
30 pages, October 31, 2011
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