GOODNESS OF FIT TESTS FOR GENERALIZED LINEAR MIXED MODELS
GOODNESS OF FIT TESTS FOR GENERALIZED LINEAR MIXED MODELS
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Date
2010
Authors
Tang, Min
Advisor
Slud, Eric V
Pfeiffer, Ruth M
Pfeiffer, Ruth M
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DRUM DOI
Abstract
Generalized Linear mixed models (GLMMs) are widely used for regression analysis of data, continuous or discrete, that are
assumed to be clustered or correlated. Assessing model fit is
important for valid inference. We therefore propose a class of
chi-squared goodness-of-fit tests for GLMMs. Our test
statistic is a quadratic form in the differences between observed
values and the values expected under the estimated model in cells
defined by a partition of the covariate space. We show that this
test statistic has an asymptotic chi-squared distribution. We study
the power of the test through simulations for two special cases of
GLMMs, linear mixed models (LMMs) and logistic mixed models. For
LMMs, we further derive the analytical power of the test under
contiguous local alternatives and compare it with simulated
empirical power. Three examples are used to illustrate the proposed test.