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

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Computation of the asymptotic null distribution of goodness-of-fit tests for multi-state models. / Titman, Andrew C.
In: Lifetime Data Analysis, Vol. 15, No. 4, 12.2009, p. 519-533.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Titman, AC 2009, 'Computation of the asymptotic null distribution of goodness-of-fit tests for multi-state models.', Lifetime Data Analysis, vol. 15, no. 4, pp. 519-533. https://doi.org/10.1007/s10985-009-9133-5

APA

Titman, A. C. (2009). Computation of the asymptotic null distribution of goodness-of-fit tests for multi-state models. Lifetime Data Analysis, 15(4), 519-533. https://doi.org/10.1007/s10985-009-9133-5

Vancouver

Titman AC. Computation of the asymptotic null distribution of goodness-of-fit tests for multi-state models. Lifetime Data Analysis. 2009 Dec;15(4):519-533. doi: 10.1007/s10985-009-9133-5

Author

Titman, Andrew C. / Computation of the asymptotic null distribution of goodness-of-fit tests for multi-state models. In: Lifetime Data Analysis. 2009 ; Vol. 15, No. 4. pp. 519-533.

Bibtex

@article{21003a33c33241e08804110564feb8b5,
title = "Computation of the asymptotic null distribution of goodness-of-fit tests for multi-state models.",
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.",
keywords = "Multi-state model - Goodness-of-fit - Panel observation - Hidden Markov model",
author = "Titman, {Andrew C.}",
year = "2009",
month = dec,
doi = "10.1007/s10985-009-9133-5",
language = "English",
volume = "15",
pages = "519--533",
journal = "Lifetime Data Analysis",
issn = "1380-7870",
publisher = "Springer Netherlands",
number = "4",

}

RIS

TY - JOUR

T1 - Computation of the asymptotic null distribution of goodness-of-fit tests for multi-state models.

AU - Titman, Andrew C.

PY - 2009/12

Y1 - 2009/12

N2 - 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.

AB - 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.

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

U2 - 10.1007/s10985-009-9133-5

DO - 10.1007/s10985-009-9133-5

M3 - Journal article

VL - 15

SP - 519

EP - 533

JO - Lifetime Data Analysis

JF - Lifetime Data Analysis

SN - 1380-7870

IS - 4

ER -