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<p>An alternative for modeling count data with overdispersion or underdispersion is the use of the generalized Poisson distribution, which is flexible due to incorporating a parameter that allows diagnosing the degree of dispersion. Based on this argument, this article aimed to develop a generalized linear model for this distribution, considering covariates, and to propose adapting ridge estimators to provide better precision in statistical inference through the estimation of standard errors of the parameters and the mean squared error. To validate the proposal of this article, a Monte Carlo simulation was conducted considering scenarios with different degrees of dispersion (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\delta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>), sample sizes (<i>n</i>), and independent variables <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p = 3, 6, 9\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>=</mo> <mn>3</mn> <mo>,</mo> <mn>6</mn> <mo>,</mo> <mn>9</mn> </mrow> </math></EquationSource> </InlineEquation>, and 12, plus the intercept. Finally, two applications with illustrative data were performed, concluding that the adaptation of the ridge estimators was appropriate, as it discriminated the performance of the estimators at different degrees of overdispersion, yielding consistent results between the mean squared error and the standard error of the parameter estimates, as well as agreement between the results obtained through simulation and the illustration given in the applications.</p>

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Adapted Ridge Estimators in the Generalized Poisson Regression Model: Development, Simulation, and Application

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Diana Rebaza Fernández,
  • Marcelo Ângelo Cirillo

摘要

An alternative for modeling count data with overdispersion or underdispersion is the use of the generalized Poisson distribution, which is flexible due to incorporating a parameter that allows diagnosing the degree of dispersion. Based on this argument, this article aimed to develop a generalized linear model for this distribution, considering covariates, and to propose adapting ridge estimators to provide better precision in statistical inference through the estimation of standard errors of the parameters and the mean squared error. To validate the proposal of this article, a Monte Carlo simulation was conducted considering scenarios with different degrees of dispersion ( \(\delta \) δ ), sample sizes (n), and independent variables \(p = 3, 6, 9\) p = 3 , 6 , 9 , and 12, plus the intercept. Finally, two applications with illustrative data were performed, concluding that the adaptation of the ridge estimators was appropriate, as it discriminated the performance of the estimators at different degrees of overdispersion, yielding consistent results between the mean squared error and the standard error of the parameter estimates, as well as agreement between the results obtained through simulation and the illustration given in the applications.