Correction Factor for the Deviance Distribution of Proportion Data.

 José Eduardo CORRENTE[1]

Ana Paula Gomes da Silva GIMENES2

 

 

§    ABSTRACT: The analysis of proportion data generally presents certain difficulties since the distribution underlying such data can be considered to be binomial, that is, it does not follow some basic assumptions for the fit of a mathematical model. A few transformations are suggested; however, good results are not always obtained.In the approach given by generalized linear models, the statistic that measures the quality of the model’s fit for such data is called deviance. It so happens that the deviance distribution is generally unknown. However, it can be approximated by a χ2 distribution for data with a binomial distribution. Nevertheless, that is not good for small sample sizes. In order to improve this approximation, some data correction factors are suggested, but the obtained results are still unsatisfactory. Therefore, this work aims at proposing a new correction factor for data following a binomial distribution so as to obtain an improvement in the deviance distribution for any sample size. To that end, a constant is added to the response variable and, through the expected deviance value, such constant is calculated so as to reduce the error made in the approximation. Simulations of the binomial distribution and deviance calculation are made and QQ-plots are used to compare with distribution χ2.

§    KEYWORDS: Binomial distribution, deviance, Taylor series, generalized linear models.

 

 



[1] 1Departamento de Ciˆencias Exatas, Escola Superior de Agricultura Luiz de Queiróz da Universidade de São Paulo, CEP: 13418-900, Piracicaba-SP, Brasil. E-mail: jecorren@carpa.ciagri.usp.br

2Departamento de Ciˆencias Exatas, Escola Superior de Agricultura Luiz de Queiróz da Universidade de São Paulo, CEP: 13418-900, Piracicaba-SP, Brasil. E-mail: anapaula@linksat.com.br