Distance-based regression for non-normal data

Distance-based regression (DBR) is a good alternative method for estimating the unknown parameters in regression modeling when dealing with mixed-type of exploratory variables. The concept of DBR is similar to classical linear regression (LR), but the explanatory variables are measured based on distance instead of raw values. This study extends the early study by Cuadras that investigated DBR on normal data, to consider the data that are non-normal. At the same time, we propose a new approach of DBR. The new DBR is focused on the categorical explanatory variables where it investigated the binomial, nominal and ordinal data separately. The investigation was set up in a Monte Carlo study, aiming to compare the performance of DBR over bootstrapping regression (nonparametric) based on R square (R²), mean square error (MSE) and Bayesian information criterion (BIC). The findings indicate that both DBR and new DBR outperformed LR in both numerical exploratory variables and mixed-type of exploratory variables.