title: Tests for detecting overdispersion in models with measurement error in covariates.
abstract: Measurement error in covariates can affect the accuracy in count data modeling and analysis. In overdispersion identification, the true mean-variance relationship can be obscured under the influence of measurement error in covariates. In this paper, we propose three tests for detecting overdispersion when covariates are measured with error: a modified score test and two score tests based on the proposed approximate likelihood and quasi-likelihood, respectively. The proposed approximate likelihood is derived under the classical measurement error model, and the resulting approximate maximum likelihood estimator is shown to have superior efficiency. Simulation results also show that the score test based on approximate likelihood outperforms the test based on quasi-likelihood and other alternatives in terms of empirical power. By analyzing a real dataset containing the health-related quality-of-life measurements of a particular group of patients, we demonstrate the importance of the proposed methods by showing that the analyses with and without measurement error correction yield significantly different results.
authors.affiliation: Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, China.
authors.forename: Yingsi
authors.initials: Y
authors.lastname: Yang
authors.affiliation: Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, China.
authors.forename: Man Yu
authors.initials: MY
authors.lastname: Wong
mesh_terms: D015982:Bias; D006302:Health Services Research / Q000706:statistics & numerical data; D016013:Likelihood Functions; D016012:Poisson Distribution
keywords: count data; measurement error; overdispersion test; quasi-likelihood; score test