Influence Measures for Cumulative Multinomial ModelsA point of view based on Divergence measures
Editorial: Comité organizador del XXX Congreso Nacional de Estadística e Investigación Operativa y IV Jornadas de Estadística Pública
ISBN: 978-84-690-7249-3
Año de publicación: 2007
Congreso: Congreso Nacional de Estadística e Investigación Operativa (30. 2007. Valladolid)
Tipo: Aportación congreso
Resumen
The most widely used model in multinomial ordinal regression is the socalled cumulative multinomial model. In this work, we extend the tools for detecting influential observations given by Cook (1977) and Johnson (1985) to the cumulative multinomial model. Cook´s statistic is commonly used for the detection of influential observations in regression analysis. It is an overall measure of the change in the parameter estimates when one or more observations are deleted from the data set. Originally, it was developed for normal linear regression models. However, it has been extended to generalized linear models as well. We give a further generalization based on divergence measures. On the other hand, Johnson proposed measures for detecting influence relative to the determination of probabilities for logistic regression. We extend these here to the cumulative multinomial model. Finally, the relationships among measures are indicated.