A test of inflated zeros for Poisson regression models

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Excessive zeros in data can lead to overdispersion and invalidate Poisson regression models.
• Existing methods for testing excess zeros, like the Vuong test, often suffer from Type I error rate deviations.
• The development of robust methods for identifying inflated zeros is crucial for reliable statistical modeling.

Purpose of the Study:

• To develop a new, reliable approach for testing inflated zeros within the framework of Poisson regression.
• To provide a method that does not necessitate the use of a zero-inflated Poisson model for testing.
• To evaluate the performance of the new approach against the commonly used Vuong test.

Main Methods:

• A novel statistical approach was developed for testing inflated zeros.
• The proposed method operates directly within the Poisson model framework.
• Performance was assessed through simulation studies comparing Type I error rates and power.

Main Results:

• The new approach demonstrates superior control over the Type I error rate compared to the Vuong test.
• Simulations indicate that the developed method offers increased statistical power.
• The proposed test effectively identifies inflated zeros without requiring a zero-inflated Poisson model.

Conclusions:

• The new method provides a more valid and powerful alternative for testing inflated zeros in Poisson regression.
• This approach addresses the limitations of existing tests, particularly the Vuong test's Type I error issues.
• Researchers can confidently use this new method for more accurate statistical inference in the presence of excessive zeros.