Title: Weighted metric scaling in logistic classification
Authors: Eva Boj - University of Barcelona (Spain)
Teresa Costa - Universitat de Barcelona (Spain) [presenting]
Abstract: Weighted distance-based regression was constructed by using the theory and properties of weighted metric scaling. This model is the named distance-based linear model (db-lm). Later in the literature it has been defined the distance-based generalized linear model (db-glm) which allows us to assume error distributions in the exponential family and link functions as in any generalized linear model. Db-glm is fitted using an iterative weighted least squares algorithm where db-lm substitutes ordinary linear model. In linear models, prediction error can be estimated by the squared root of the sum of the process variance and of the estimation variance. The part of the estimation variance can be approximated by applying the delta method and/or by using bootstrap. All these formulations are studied for the generalized linear model with Binomial error distribution and logit link function, the logistic regression. They are illustrated with a real data set with the aim of classifying individuals. Db-lm and db-glm can be fitted with functions dblm and dbglm of the dbstats package for R.