A score test for testing a zero-inflated Poisson regression model against zero-inflated negative binomial...

Area of Science:

• Biostatistics
• Statistical Modeling
• Epidemiology

Background:

• Count data frequently exhibit excess zeros, exceeding expectations for a standard Poisson distribution.
• Zero-inflated Poisson (ZIP) regression models are commonly used for such data.
• However, ZIP models can yield biased parameter estimates when non-zero counts display overdispersion relative to the Poisson distribution.

Purpose of the Study:

• To address potential bias in zero-inflated Poisson regression models.
• To develop a statistical test for model selection in the presence of excess zeros and overdispersion.
• To compare zero-inflated Poisson models against more flexible zero-inflated negative binomial alternatives.

Main Methods:

• Development of a score test statistic.
• The test evaluates the null hypothesis of a ZIP model against the alternative of a zero-inflated negative binomial (ZINB) model.
• Focus on assessing overdispersion in the non-zero component of the count data.

Main Results:

• The proposed score test provides a method for distinguishing between ZIP and ZINB models.
• This test is crucial when overdispersion is suspected in the non-zero counts.
• The test helps to identify situations where ZIP model assumptions are violated, leading to biased estimates.

Conclusions:

• The score test is a valuable tool for selecting appropriate models for zero-inflated count data with potential overdispersion.
• Using the test can lead to more accurate parameter estimates compared to standard ZIP models when overdispersion is present.
• This facilitates more reliable statistical inference in fields utilizing count data analysis.