SIMEX variance component tests in generalized linear mixed measurement error models.

In the analysis of clustered data with covariates measured with error, a problem of common interest is to test for correlation within clusters and heterogeneity across clusters. We examined this problem in the framework of generalized linear mixed measurement error models. We propose using the simulation extrapolation (SIMEX) method to construct a score test for the null hypothesis that all variance components are zero. A key feature of this SIMEX score test is that no assumptions need to be made regarding the distributions of the random effects and the unobserved covariates. We illustrate this test by analyzing Framingham heart disease data and evaluate its performance by simulation. We also propose individual SIMEX score tests for testing the variance components separately. Both tests can be easily implemented using existing statistical software.