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

Research output: Contribution to journalJournal article

Published

Journal publication date12/2009
JournalLifetime Data Analysis
Journal number4
Volume15
Number of pages15
Pages519-533
Original languageEnglish

Abstract

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 X^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 X^2_1 approximation.

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