Tests for detecting overdispersion in models with measurement error in covariates

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Measurement error in covariates can distort count data models.
• Overdispersion identification is particularly challenging with such errors, obscuring true relationships.

Purpose of the Study:

• To develop and evaluate novel statistical tests for detecting overdispersion in count data when covariates are subject to measurement error.
• To improve the accuracy and efficiency of statistical analyses in the presence of covariate measurement error.

Main Methods:

• Proposed three tests for overdispersion detection: a modified score test and two score tests using approximate likelihood and quasi-likelihood.
• Derived an approximate likelihood under the classical measurement error model.
• Evaluated methods through simulations and analysis of a real-world health-related quality-of-life dataset.

Main Results:

• The score test based on approximate likelihood demonstrated superior empirical power compared to quasi-likelihood and other methods.
• The approximate maximum likelihood estimator exhibited enhanced efficiency.
• Analysis of a real dataset confirmed significant differences between analyses with and without measurement error correction.

Conclusions:

• The proposed methods effectively detect overdispersion in the presence of covariate measurement error.
• Measurement error correction is crucial for accurate count data modeling, as demonstrated by significantly different results in real-world applications.