¹Universidad Nacional de Colombia, Departamento de Estadística, Bogotá, Colombia. Ph.D. student. Email: jedavilas@unal.edu.co
²Universidad Nacional de Colombia, Departamento de Estadística, Bogotá, Colombia. Professor. Email: lalopezp@unal.edu.co
³Universidad Nacional de Colombia, Departamento de Estadística, Bogotá, Colombia. Professor. Email: lgdiazm@unal.edu.co

We introduce a new approach for modeling multivariate overdispersed binomial data, from a plant pathogen complex. After recalling some theoretical foundations of generalized linear models (GLMs) and Copula functions, we show how the later can be used to model correlated observations and overdispersed data. We illustrate this approach using fungal incidence in vegetables, which we analyzed using Gaussian copula with Beta-binomial margins. Compared to classical and generalized linear models, the model using Gaussian copula function best controls for overdispersion, being less prone to the underestimation of standard errors, the major cause of wrong inference in the statistical analysis of plant pathogen complex.

Key words: Epidemiological methods, Extra-binomial variation, Multivariate data.

Se introduce un nuevo enfoque para modelar datos binomiales multivariados con sobredispersión, obtenidos de complejos de patógenos vegetales. Después de revisar los conceptos básicos de los modelos lineales generalizados (GLMs) y las funciones Cópula, se muestra cómo estas últimas pueden usarse para modelar observaciones correlacionadas y datos con sobredispersión. Se ilustra el método usando la incidencia de hongos en hortalizas, analizando el caso por medio de la función cópula Gaussiana con marginales Beta-binomiales. Comparado con los modelos lineales clásicos y generalizados, el modelo construido con la cópula Gaussiana es el que mejor controla la sobredispersión, siendo menos propenso a la subestimación de los errores estándar, la causa más importante de inferencia inapropiada en el análisis estadístico de complejos de patógenos vegetales.

Palabras clave: métodos epidemiológicos, variación extra-binomial, datos multivariados.

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