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<p>In count data regression, the phenomena of overdispersion and excess counts at specific values often occur, which standard models may not adequately address. The <i>l</i>-inflated power series regression model extends conventional count models by incorporating inflation at a specific count <i>l</i>. A significant challenge in fitting these regression models is the presence of outliers and collinearity among covariates. These issues can substantially complicate the model fitting process, leading to unstable parameter estimates, an unstable fitted model, and ultimately, prediction errors. To mitigate their impact, we introduce comprehensive methods for parameter estimation utilizing robust, shrinkage, and combination techniques. We provide detailed derivations, explanations, and practical considerations to facilitate understanding and implementation.</p>

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Robustness and Collinearity Resistance l-Inflated Power Series Regression

  • 期刊论文

  • 发表日期：

    2025年11月22日

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  • Hadi Saboori,
  • Omid Shojaee

摘要

In count data regression, the phenomena of overdispersion and excess counts at specific values often occur, which standard models may not adequately address. The l-inflated power series regression model extends conventional count models by incorporating inflation at a specific count l. A significant challenge in fitting these regression models is the presence of outliers and collinearity among covariates. These issues can substantially complicate the model fitting process, leading to unstable parameter estimates, an unstable fitted model, and ultimately, prediction errors. To mitigate their impact, we introduce comprehensive methods for parameter estimation utilizing robust, shrinkage, and combination techniques. We provide detailed derivations, explanations, and practical considerations to facilitate understanding and implementation.