What is the main distinction between stepwise methods and hierarchical methods in regression?

The main distinction between stepwise methods and hierarchical methods in regression lies in the approach taken to select which variables to include in the analysis. Stepwise methods utilize statistical criteria, such as p-values or Akaike information criterion (AIC), to determine the significance of each variable in relation to the dependent variable. This method systematically adds or removes predictors based on their statistical contributions, which can lead to different models depending on the data at hand.

In contrast, hierarchical methods are based on theoretical or substantive reasoning, predefining the order of entry of variables into the model based on research questions or hypotheses. This approach emphasizes the importance of specific variables based on prior knowledge or theory, rather than just statistical measures. The stepwise approach's reliance on statistical criteria allows for a more flexible model-building process, which can sometimes yield insights that purely theoretical models might overlook.

This statistical criterion-driven nature of stepwise methods makes them distinct and highlights their focus on data-driven variable selection, which can help identify the most predictive variables while managing the complexity of the model.