A simulation-based goodness-of-fit test for random effects in generalized linear mixed models

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21 Citations (Scopus)

Abstract

The goodness-of-fit of the distribution of random effects in a generalized linear mixed model is assessed using a conditional simulation of the random effects conditional on the observations. Provided that the specified joint model for random effects and observations is correct, the marginal distribution of the simulated random effects coincides with the assumed random effects distribution. In practice, the specified model depends on some unknown parameter which is replaced by an estimate. We obtain a correction for this by deriving the asymptotic distribution of the empirical distribution function obtained from the conditional sample of the random effects. The approach is illustrated by simulation studies and data examples.
Original languageEnglish
JournalScandinavian Journal of Statistics
Volume33
Issue number4
Pages (from-to)721-731
Number of pages11
ISSN1467-9469
Publication statusPublished - 2006

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Generalized Linear Mixed Model
Goodness of Fit Test
Random Effects
Simulation
Conditional Simulation
Empirical Distribution Function
Joint Model
Marginal Distribution
Goodness of fit
Unknown Parameters
Asymptotic distribution
Goodness of fit test
Generalized linear mixed model
Random effects
Simulation Study
Estimate

Cite this

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title = "A simulation-based goodness-of-fit test for random effects in generalized linear mixed models",
abstract = "The goodness-of-fit of the distribution of random effects in a generalized linear mixed model is assessed using a conditional simulation of the random effects conditional on the observations. Provided that the specified joint model for random effects and observations is correct, the marginal distribution of the simulated random effects coincides with the assumed random effects distribution. In practice, the specified model depends on some unknown parameter which is replaced by an estimate. We obtain a correction for this by deriving the asymptotic distribution of the empirical distribution function obtained from the conditional sample of the random effects. The approach is illustrated by simulation studies and data examples.",
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A simulation-based goodness-of-fit test for random effects in generalized linear mixed models. / Waagepetersen, Rasmus.

In: Scandinavian Journal of Statistics, Vol. 33, No. 4, 2006, p. 721-731.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - A simulation-based goodness-of-fit test for random effects in generalized linear mixed models

AU - Waagepetersen, Rasmus

PY - 2006

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N2 - The goodness-of-fit of the distribution of random effects in a generalized linear mixed model is assessed using a conditional simulation of the random effects conditional on the observations. Provided that the specified joint model for random effects and observations is correct, the marginal distribution of the simulated random effects coincides with the assumed random effects distribution. In practice, the specified model depends on some unknown parameter which is replaced by an estimate. We obtain a correction for this by deriving the asymptotic distribution of the empirical distribution function obtained from the conditional sample of the random effects. The approach is illustrated by simulation studies and data examples.

AB - The goodness-of-fit of the distribution of random effects in a generalized linear mixed model is assessed using a conditional simulation of the random effects conditional on the observations. Provided that the specified joint model for random effects and observations is correct, the marginal distribution of the simulated random effects coincides with the assumed random effects distribution. In practice, the specified model depends on some unknown parameter which is replaced by an estimate. We obtain a correction for this by deriving the asymptotic distribution of the empirical distribution function obtained from the conditional sample of the random effects. The approach is illustrated by simulation studies and data examples.

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JO - Scandinavian Journal of Statistics

JF - Scandinavian Journal of Statistics

SN - 1467-9469

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