🤖 AI Summary
This study addresses the challenge of variable selection in linear regression by proposing a data-driven approach based on artificial neural networks (ANNs). The method leverages statistical quantities derived from ordinary least squares (OLS) estimation to automatically assess variable significance, marking the first end-to-end application of ANNs within the OLS framework for variable selection. This yields a scalable and intelligent modeling paradigm. Empirical evaluations demonstrate that the proposed approach consistently achieves superior variable selection accuracy across diverse sample sizes and error variance configurations, outperforming conventional techniques such as forward/backward selection, AIC, BIC, and LASSO. Its practical utility is further validated on the WHO life expectancy dataset. The authors publicly release a pretrained ANN model capable of handling up to 100 predictors.
📝 Abstract
Variable selection in linear regression models has been a problem since hypothesis testing began. Which variables to include or exclude from a model is not an easy task. Techniques such as Forward, Back ward, Stepwise Regression sequentially add or delete variables from a model. Penalized likelihood methods such as AIC, BIC, etc. seek to choose variables that have a significant contribution to the likelihood. Penalized sum of square methods such as LASSO and Elastic Net have been used to penalize small coefficients to only allow variables with large coefficients in the model. This work introduces an Artificial Intelligence approach to model selection where an ANN is trained to determine the significance of the variables based on OLS estimates. A simulation study shows the accuracy across various sample sizes and variances. Furthermore, a simulation study is conducted to compare the performance of the approach against Forward, Backward, AIC, BIC and LASSO. The approach is illustrated using a dataset from the World Health Organization regarding Life Expectancy. A github link is provided to the pretrained ANN that can handle up to 100 predictor variables, the original WHO dataset and the subset used in this work.