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

Titman, Andrew C. (2009) Computation of the asymptotic null distribution of goodness-of-fit tests for multi-state models. Lifetime Data Analysis, 15 (4). pp. 519-533. ISSN 1380-7870

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    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.

    Item Type: Article
    Journal or Publication Title: Lifetime Data Analysis
    Uncontrolled Keywords: Multi-state model - Goodness-of-fit - Panel observation - Hidden Markov model
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 23532
    Deposited By: Dr Andrew Titman
    Deposited On: 28 Jan 2009 14:00
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Oct 2013 14:49
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/23532

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