Adjustments for \(R^{2}\)-measures for Poisson regression models.
type: Item
instance of: scholarly article
title: Adjustments for \(R^{2}\)-measures for Poisson regression models.
zbMATH Open document ID: 1046.62090
DOI: 10.1016/S0167-9473(99)00113-9
author: T. Waldhör
author: Martina Mittlböck
published in: Computational Statistics and Data Analysis
publication date: 2000-10-26T00:00:00Z
review text: In regression models not only the parameter estimates and significance of explanatory variables are of interest, but also the degree to which variation in the dependent variable can be explained by covariates. In recent publications, an \(R^{2}\)-measure based on deviance was recommended for Poisson regression models, one of the most frequently used modelling tools in epidemiological studies. However, when sample size is small relative to the number of covariates in the model, simple \(R^{2}\)-measures may be seriously inflated and may need to be adjusted according to the number of covariates in the model. Two new adjustments for the \(R^{2}\)-measure in Poisson regression models based on deviance residuals are presented and compared by simulation with population values. The proposed measures are also applied to real data sets.
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 65C60
zbMATH DE Number: 1521875
zbMATH Keywords: adjusted Poisson regression
zbMATH Keywords: deviance residuals
zbMATH Keywords: likelihood ratio
zbMATH Keywords: degrees of freedom
MaRDI profile type: Publication
cites work: Statistical models based on counting processes
cites work: Q3709745
cites work: Q3998435
description: scientific article; zbMATH DE number 1521875