Prediction by Empirical Similarity via Categorical Regressors

Abstract

A quantifier of similarity is generally a type of score that assigns a numerical value to a pair of sequences based on their proximity. Similarity measures play an important role in prediction problems with many applications, such as statistical learning, data mining, biostatistics, finance and others. Based on observed data, where a response variable of interest is assumed to be associated with some regressors, it is possible to make response predictions using a weighted average of observed response variables, where the weights depend on the similarity of the regressors. In this work, we propose a parametric regression model for continuous response based on empirical similarities for the case where the regressors are represented by categories. We apply the proposed method to predict tooth length growth in guinea pigs based on Vitamin C supplements considering three different dosage levels and two delivery methods. The inferential procedure is performed through maximum likelihood and least squares estimation under two types of similarity functions and two distance metrics. The empirical results show that the method yields accurate models with low dimension facilitating the parameters’ interpretation.