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Tests for detecting overdispersion in models with measurement error in covariates
Author(s) -
Yang Yingsi,
Wong Man Yu
Publication year - 2015
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.6568
Subject(s) - overdispersion , covariate , statistics , computer science , econometrics , observational error , mathematics , count data , poisson distribution
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. Copyright © 2015 John Wiley & Sons, Ltd.