A variable selection procedure based on predictive ability: a preliminary study on logistic regression

The contribution is meant as a pilot exercise on the development of a variable selection technique that combines fitting and prediction performance. The simplest step towards this goal involves a forward selection algorithm for binary classification achieved via logistic regression. At each step, the algorithm selects the predictor, among the covariates that are significantly associated with the outcome, that entails the significantly largest AUC increment with respect to the previous model. For the sake of illustration, we present some examples relative to the search of the most predictive factors of the propensity to pension planning, health insurance subscription, and the use of Financial Technology services like home banking, taken from the Survey on Household Income and Wealth 2020 run by Bank of Italy. Concluding remarks are provided on further developments