9 Model Selection

# 9 Model Selection - Statistics 191 Introduction to Applied...

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Unformatted text preview: Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Statistics 191: Introduction to Applied Statistics Model Selection Jonathan Taylor Department of Statistics Stanford University March 1, 2010 1 / 1 Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Topics Outline Goals of model selection. Criteria to compare models. (Some) model selection. Bias- variance trade-off. 2 / 1 Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Election data Description Variable Description V votes for a presidential candidate I are they incumbent? D Democrat or Republican incumbent? W wartime election? G GDP growth rate in election year P (absolute) GDP deflator growth rate N number of quarters in which GDP growth rate > 3 . 2% 3 / 1 Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Model selection Problem & Goals When we have many predictors (with many possible interactions), it can be difficult to find a good model. Which main effects do we include? Which interactions do we include? Model selection procedures try to simplify / automate this task. Election data has 2 6 = 64 different models with just main effects! 4 / 1 Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Model selection General comments This is an “unsolved” problem in statistics: there are no magic procedures to get you the “best model.” In some sense, model selection is “data mining.” Data miners / machine learners often work with very many predictors. Our model selection problem is generally at a much smaller scale than “data mining” problems. 5 / 1 Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Model selection Hypothetical example Suppose we fit a a model F : Y n × 1 = X n × ( p +1) β ( p +1) × 1 + ε n × 1 with predictors X 1 ,..., X p ....
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9 Model Selection - Statistics 191 Introduction to Applied...

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