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Poisson-Tweedie Models for Count Data with Excessive Zeros. Comparison with the Negative Binomial Model
Modelos Poisson-Tweedie para datos de conteo con exceso de ceros. Comparación con el modelo binomial negativo
DOI:
https://doi.org/10.15446/rce.v47n1.101952Keywords:
Count data, Tweedie models, Zero - inflation (en)Datos de conteo, Exceso de ceros, Modelos Poisson - Tweedie (es)
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The presence of a large number of zero counts is quite common in studies involving count data. This causes overdispersion. Therefore, different types of models have been proposed as alternatives and a very frequent practice is to use the negative binomial model. In 2018, Bonat (2018) considered a new type of model, based on the Poisson-Tweedie dispersion models, hich can automatically adapt to different degrees of overdispersion in count data. This article presents a simulation study in order to compare the estimates derived from the Poisson- eedie model for a wide range of overdispersed data with estimates derived from the egative binomial model. In both models, the relative percent bias of the estimated coeffcients was very small. Nevertheless, the Poisson-Tweedie model showed a better performance with smaller values for the mean squared errors, particularly in scenarios with more dispersion. Hence, it would be possible to suggest the data analyst in which situations it would be enough to work with the popular negative binomial model or when it would be best to use the Poisson-Tweedie family. Additionally, the comparison between the fit of the negative binomial mode land that of the Poisson-Tweedie family is illustrated by analysing the number fpediatric consultations of a group of children who receive health care in a public health center in Rosario, Argentina. Although the results obtained in both models were similar, the estimates in the Poisson-Tweedie model were more accurate.
En estudios que involucran el análisis de datos de conteo es común encontrar una gran cantidad de ceros. La sobredispersión que ello provoca ha sido tenida en cuenta en diferentes alternativas de modelización siendo el modelo binomial negativo la más utilizada. En 2018 se suma la propuesta desarrollada por Bonat (2018) ellos consideraron una nueva clase de modelos, basada en los modelos con dispersión Poisson-Tweedie, los cuales se adaptan en forma automática a diferentes grados de sobredispersión en datos de conteo. Este trabajo presenta un estudio por simulación para comparar las estimaciones derivadas del modelo Poisson-Tweedie con las del binomial negativo frente a diferentes niveles de sobredispersión. Se encontraron estimaciones de los coeficientes del modelo con sesgos muy pequeños para ambos modelos y errores cuadráticos medios levemente menores para el modelo Poisson-Tweedie, evidenciando su mejor desempeño en los escenarios de mayor dispersión. Así, sería posible sugerir al analista de datos en qué situaciones es suficiente trabajar con el popular modelo binomial negativo o cuándo es mejor recurrir a la familia Poisson-Tweedie. Además, se ilustra la comparación del ajuste de estos modelos sobre el número de consultas pediátricas en un centro de salud de la ciudad de Rosario, Argentina. Si bien los resultados obtenidos fueron similares, se observó una ganancia en la precisión de las estimaciones del modelo Poisson-Tweedie.
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