BIAS ANALYSIS AND SIMEX APPROACH IN GENERALIZED LINEAR MIXED MEASUREMENT ERROR MODELS

We consider generalized linear mixed models (GLMMs) for clustered data when one of the predictors is measured with error. When the measureme nt error is additive and normally distributed and the error-prone pred ictor is itself normally distributed, we show that the observed data a lso follow a GLMM but with a different fixed effects structure from th e original model, a different and more complex random effects structur e, and restrictions on the parameters. This characterization enables u s to compute the biases that result in common GLMMs when one ignores m easurement error For instance, in one common situation the biases in p arameter estimates become larger as the number of observations within a cluster increases, both for regression coefficients and for variance components. Parameter estimation is described using the SIMEX method, a relatively new functional method that makes no assumptions about th e structure of the unobservable predictors. Simulations and an example illustrate the results.