A robust score test of homogeneity for zero-inflated count data

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Score tests are commonly used to assess heterogeneity in zero-inflated models.
• Traditional score tests rely on accurate null hypothesis model specification.
• Model misspecification can lead to unreliable inferences in standard score tests.

Purpose of the Study:

• To develop a score test for zero-inflated models that is robust to model misspecification.
• To provide a reliable method for testing population heterogeneity when the true model is unknown.

Main Methods:

• Proposed a score test for homogeneity within a general framework of mixture models.
• Introduced a layer of randomness into the model to handle uncertainty in specification.
• Applied the approach to zero-inflated Poisson models, incorporating a random term in the Poisson mean.

Main Results:

• Simulations demonstrated that the proposed score test maintains empirical size across all levels.
• The test shows robustness against certain model misspecifications.
• A slight loss of power was observed for well-specified non-random mean models under the null hypothesis.

Conclusions:

• The developed score test offers a more reliable approach for evaluating heterogeneity in zero-inflated models.
• The method's robustness is valuable in practical settings where true model specifications are often uncertain.
• The procedure was effectively illustrated using real-world data on health promotion activities and dental caries.