A new modified biased estimator for Zero inflated Poisson regression model.

Area of Science:

• Statistics
• Econometrics
• Biostatistics

Background:

• The Zero-Inflated Poisson (ZIP) model is prevalent for analyzing count data with excess zeros.
• Multicollinearity among explanatory variables often compromises the performance of standard Maximum Likelihood Estimation (MLE) in ZIP models, leading to inflated Mean Squared Error (MSE).
• Ridge regression is a common technique to mitigate multicollinearity, but its application within the ZIP framework requires specific adaptations.

Purpose of the Study:

• To propose a novel modified Zero-Inflated Poisson ridge regression model.
• To enhance the estimation of parameters in the presence of multicollinearity for count data with excess zeros.
• To evaluate the performance of the proposed model against existing methods using simulation and real-world data.

Main Methods:

• Development of a modified Zero-Inflated Poisson ridge regression estimator.
• Implementation of a simulation strategy to assess estimator behavior under multicollinearity.
• Application of the proposed estimator to a real-life count data set.

Main Results:

• The proposed modified ZIP ridge regression model effectively reduces the impact of multicollinearity.
• Simulation results demonstrate improved estimator performance compared to standard ZIP-MLE.
• The real-life data application confirms the practical utility and robustness of the new model.

Conclusions:

• The modified Zero-Inflated Poisson ridge regression offers a valuable solution for count data analysis when multicollinearity is present.
• This approach provides more reliable estimates, particularly in fields dealing with complex count data, such as epidemiology and environmental science.
• The study highlights the importance of addressing multicollinearity for accurate modeling of zero-inflated count data.