Residuals for polytomous logistic regression models based on φ-divergences test statistics

Abstract

When a polytomous logistic regression model fits poorly according to an overall goodness-of-fit test, an examination of residuals highlights where the fit is poor. In this paper we present new families of residuals for politomous logistic regression models based on the φ-divergence test statistic introduced and studied by Gupta et al. [A. Gupta, T. Nguyen and L. Pardo, Some inference procedures in polytomous logistic regression models based on φ-divergences measures, Math. Methods Stat. 3 (2006b), 269–288].

Keywords:

• multinomial sampling
• minimum φ-divergence estimator
• Pearson's residuals
• φ-divergence test statistic
• φ₂-residual based on minimum φ-divergence estimator
• influential observations
• Cook's distance

AMS 2001 Subject Classifications :

• Primary 62H15
• Secondary 62H17

Acknowledgements

This work was supported partially (L. Pardo) by Grant MTM2006-06872. We would like to thank the referees and editor for their helpful comments.