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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.44 no.2 Bogotá July/Dec. 2021 Epub Aug 27, 2021
https://doi.org/10.15446/rce.v44n2.85606
Original articles of research
Influence Diagnostics for Correlated Binomial Regression Models: An Application to a Data Set on High-Cost Health Services Occurrence
Diagnósticos de influencia para modelos de regresión binomial correlacionada: una aplicación a un conjunto de datos sobre la ocurrencia de servicios de salud de alto costo
1 Department of Statistics, Federal University of São Carlos, São Carlos, Brazil
2 Department of Statistics, Federal University of Bahia, Salvador, Brazil
This paper considers a frequentist perspective to deal with the class of correlated binomial regression models (Pires & Diniz, 2012), thus providing a new approach to analyze correlated binary response variables. Model parameters are estimated by direct maximization of the log-likelihood function. We also consider a diagnostic analysis under the correlated binomial regression model setup, which is performed considering residuals based on predictive values and deviance residuals (Cook & Weisberg, 1982) to check for model assumptions, and global influence measure based on case-deletion (Cook, 1977) to detect influential observations. Moreover, a sensitivity analysis is carried out to detect possible influential observations that could affect the inferential results. This is done using local influence metrics (Cook, 1986) with case-weight, response, and covariate perturbation schemes. A simulation study is conducted to assess the frequentist properties of model parameter estimates and check the performance of the considered diagnostic metrics under the correlated binomial regression model. A data set on high-cost claims made to a private health care provider in Brazil is analyzed to illustrate the proposed methodology.
Key words: Generalized binomial distribution; Health care provider; Influence; Overdispersion; Regression; Residuals
Este artículo considera una perspectiva frecuentista para tratar con la clase de modelos de regresión binomial correlacionada (Pires & Diniz, 2012), proporcionando así un nuevo enfoque para analizar variables de respuesta binaria correlacionadas. Los parámetros del modelo se estiman mediante la maximización directa de la función de log-verosimilitud. También consideramos un análisis de diagnóstico bajo la configuración del modelo de regresión binomial correlacionada, que se realiza considerando los residuos basados en valores predictivos y los residuos de desviación (Cook & Weisberg, 1982) para verificar los supuestos del modelo y la medida de influencia global basada en la eliminación de casos (Cook, 1977) para detectar observaciones influyentes. Además, se realiza un análisis de sensibilidad para detectar posibles observaciones influyentes que podrían afectar los resultados inferenciales. Esto se hace utilizando métricas de influencia local (Cook, 1986) con esquemas de perturbación de covariable, variable respuesta y ponderación de casos. Se realiza un estudio de simulación para evaluar las propiedades frecuentistas de los estimadores de parámetros del modelo y verificar el rendimiento de las métricas de diagnóstico consideradas bajo el modelo de regresión binomial correlacionada. Se analiza un conjunto de datos sobre un plan de salud de un operador brasileño para ilustrar la metodología propuesta.
Palabras clave: Distribución binomial generalizada; Plan de salud; Influencia; Sobredispersión; Regresión; Residuos
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Received: March 2020; Accepted: March 2021
This is an open-access article distributed under the terms of the Creative Commons Attribution License
