Which model selection method combines elements from both forward and backward selection?

The model selection method that combines elements from both forward and backward selection is indeed the stepwise method. This approach begins with either no predictors in the model or a full model. It strategically adds predictors into the model (the forward selection aspect) based on certain criteria, such as significance levels, while also considering the removal of predictors that no longer contribute significantly to the model (the backward selection aspect).

The flexibility of the stepwise method allows for a more refined model building process, as it can continually test the contribution of variables and adjust by adding or removing them in response to their statistical significance. This characteristic makes stepwise selection particularly useful when working with datasets where the relationships between variables are not fully known in advance, as it helps to find a more optimal set of predictors for the model.

This approach is distinct from purely forward selection, which only adds variables, and purely backward selection, which only removes them. Thus, stepwise selection represents a hybrid methodology that utilizes the strengths of both processes to derive a well-fitted model.