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A Simulation‐based Goodness‐of‐fit Test for Random Effects in Generalized Linear Mixed Models
Author(s) -
WAAGEPETERSEN RASMUS
Publication year - 2006
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2006.00504.x
Subject(s) - mathematics , goodness of fit , random effects model , marginal distribution , conditional probability distribution , statistics , joint probability distribution , random variable , medicine , meta analysis
. 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.