Distance-based beta regression for prediction of mutual funds

Abstract

In the context of regression with a beta-type response variable, we propose a new method that links two methodologies: a distance-based model, and a beta regression with variable dispersion. The proposed model is useful for those situations where the response variable is a rate, a proportion or parts per million, and this variable is related to a mixture of continuous and categorical explanatory variables. We present the main statistical properties and several measures for selection of the most predictive dimensions for the model. In our proposal we only need to choose a suitable distance for both the mean model and the variable dispersion model depending on the type of explanatory variables. The mean and precision predictions for a new individual, and the problem of missing data are also developed. Rather than removing variables or observations with missing data, we use the distance-based method to work with all data without the need to fill in or impute missing values. Finally, an application of mutual funds is presented using the Gower distance for both the mean model and the variable dispersion model. This methodology is applicable to any problem where estimation of distance-based beta regression coefficients for correlated explanatory variables is of interest.