Generalized additive model using marginal integration estimation techniques with interactions

Marginal Integration (MI) is a statistical method that is extensively employed to estimate component functions of the nonparametric additive models. The shortcoming of the purely additive model is that interaction between predictor variables is often ignored, and it may produce poor performance in some real applications. As a result, this research considers the second-order interactions in the regression models. The primary objective is to use marginal integration techniques to estimate the nonparametric additive functions. We compare this model with other models/estimators such as the Generalized Additive Model (GAM), Generalized Additive Model with Selection (GAMSEL), Robust Marginal Integration (RMI), Ordinary Least Squares (OLS), M-estimators based on Tukey and Huber methods, and LASSO. The simulation results indicate that MI has the least root mean prediction error (RMPE) in pure non-linear models with interaction terms. In the presence of outliers, RMI has the least RMPE demonstrating robustness. Finally, an application of the models on Real Estate Price Prediction data obtained from Kaggleshows that the MI method has the least RMPE depicting as the best model.