Multi-Model Penalized Regression

Model fitting often aims to fit a single model, assuming that the imposed form of the model is correct. However, there may be multiple possible underlying explanatory patterns in a set of predictors that could explain a response. Model selection without regarding model uncertainty can fail to bring these patterns to light. We present multi-model penalized regression (MMPR) to acknowledge model uncertainty in the context of penalized regression. In the penalty form introduced here, we explore how different settings can promote either shrinkage or sparsity of coefficients in separate models. A choice of penalty form that enforces variable selection is applied to predict stacking force energy (SFE) from steel alloy composition. The aim is to identify multiple models with different subsets of covariates that explain a single type of response.