Published
2020-11-01

Comparación del modelo COM-Poisson y el modelo Poisson

Comparison of the COM-Poisson model and the Poisson model

DOI: https://doi.org/10.15332/2422474x.6255
Álvaro Arley Castaño Colorado
Juan Carlos Correa Morales
PDF (Spanish)

Abstract (en)

When modeling count data, the poisson model is typically used, in which the equidispersion (ED) assumption is assumed, where the mean and variance are equal. When this condition is not easy to justify, different alternatives have been proposed, some more flexible than others in terms of accounting for both overdispersion (OD) and underdispersion (UN). One of them is the COM-Poisson model which was recently proposed and has been evaluated in inferential terms. The investigation presented here aims to compare the COM-Poisson model predictive quality with respect to the Poisson model and establish the loss in efficiency that occurs when the inadequate model is fitted when the property of equidispersion is not satisfactory. A simulation study determined that adjusting the inappropriate model either over or underdispersion does not represent in most cases, a gain or loss of the predictive quality. Two case studies illustrate ours findings obtained here.

Keywords (en): Count Data, Generalized Linear Models, Relative Efficiency, Poisson regression, Conway-Maxwell-Poisson regression, Predictive Power, Dispersion

Abstract (es)

La modelación de datos de conteo se hace típicamente usando el modelo Poisson, en el cual se asume equidispersión (ED), en donde la media y la varianza son iguales. Cuando esta condición no es fácil de justificar, han surgido diferentes alternativas, unas más flexibles que otras, en cuanto a la capacidad de manejar tanto sobredispersión (OD) como subdispersión (UD). Una de ellas es el modelo COM-Poisson el cual fue propuesto recientemente y ha sido evaluado en términos inferenciales (Sellers2010). Esta investigación quiere cuantificar la calidad predictiva del modelo COM-Poisson con respecto al modelo Poisson, y así establecer la pérdida en la eficiencia que se tiene al ajustar el modelo inadecuado cuando la propiedad de equidispersión no es satisfactoria. El estudio de simulación efectuado determinó que al ajustar el modelo inadecuado, ya sea en sobre o subdispersión, no representa, en la mayoría de los casos, ni una ganancia o pérdida en cuanto a la calidad predictiva de los valores ajustados. Dos estudios de caso aplicados a la ecología ilustran los resultados obtenidos

Keywords (es): Datos de Conteo, Modelos Lineales Generalizados, Eficiencia Relativa, Regresión Poisson, Regresión Conway-Maxwell-Poisson, Capacidad Predictiva, Dispersión

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How to Cite

Castaño Colorado , Álvaro A. ., & Correa Morales, J. C. (2020). Comparison of the COM-Poisson model and the Poisson model. Comunicaciones En Estadística, 13(2), 9-32. https://doi.org/10.15332/2422474x.6255

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