The robustification of distance-based linear models: Some proposals

Abstract

In this work tailor robust metrics are proposed to be used in the predictors’ space of distance-based predictive models. The first proposal is a robust version of Gower’s distance, which takes into account the correlation structure of the data. The second one is a rather complex metric, constructed via Related Metric Scaling, which is able to discard redundant information coming from different sources. Another novelty is the proposal of a distance-based trimming statistic to robustify the metrics. The performance of the models based on new robust metrics is evaluated through a simulation study and compared to those based on Euclidean, Gower’s and generalized Gower’s metrics in the presence of outliers in several datasets of multivariate heterogeneous data. Mean squared error (also median and standard deviation) are used to evaluate the effectiveness in the prediction of responses. Finally, two applications in the areas of sustainable transport and finance and banking are provided in order to illustrate the predictive power of these models. Computations are made using the dbstats package for R.