Model Averaging Predictions Is Good; Model Averaging Multiple Regression Coefficients Is Bad

• Activity Number: 195
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Philip Dixon*+
• Companies: Iowa State Univ
• Keywords: model selection ; wildlife ; multiple regression

Abstract

Model averaging, or multi-model inference, avoids the false sense of precision arising when inferences are conditional on a model chosen from data. It accounts for the uncertainty due to model choice. It is widely used in mark-recapture studies to estimate a population size, N, while accounting for uncertainty in the capture probability model. It has since been widely used with model selection in multiple regression. Instead of reporting coefficient estimates for the "best" model, estimates are averaged over a collection of models. I argue that there is a fundamental difference between these two uses of model averaging. In mark-recapture, N is consistently defined in all models. In multiple regression, the interpretation of a specific regression parameter changes between models because the suite of "variables held constant" changes. Using a variety of examples, I show that conditioning on the best model leads to better parameter estimates than model averaging in the multiple regression setting. If the focus is on predicted values, which are consistently defined across models, instead of regression coefficients, model averaging does lead to better predictions.