  Model selection often aims to choose a single model, assuming that the 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 regard for model uncertainty can fail to bring these
patterns to light. We explore multi-model penalized regression (MMPR) to
acknowledge model uncertainty in the context of penalized regression. We
examine how different penalty settings can promote either shrinkage or sparsity
of coefficients in separate models. The method is tuned to explicitly limit
model similarity. A choice of penalty form that enforces variable selection is
applied to predict stacking fault 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.
