Lifetime Data Analysis

, 15:519 | Cite as

Computation of the asymptotic null distribution of goodness-of-fit tests for multi-state models

  • Andrew C. Titman


We develop an improved approximation to the asymptotic null distribution of the goodness-of-fit tests for panel observed multi-state Markov models (Aguirre-Hernandez and Farewell, Stat Med 21:1899–1911, 2002) and hidden Markov models (Titman and Sharples, Stat Med 27:2177–2195, 2008). By considering the joint distribution of the grouped observed transition counts and the maximum likelihood estimate of the parameter vector it is shown that the distribution can be expressed as a weighted sum of independent \({\chi^2_1}\) random variables, where the weights are dependent on the true parameters. The performance of this approximation for finite sample sizes and where the weights are calculated using the maximum likelihood estimates of the parameters is considered through simulation. In the scenarios considered, the approximation performs well and is a substantial improvement over the simple χ 2 approximation.


Multi-state model Goodness-of-fit Panel observation Hidden Markov model 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsLancaster UniversityLancasterUK

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