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10 - Model Selection

Published online by Cambridge University Press:  03 February 2022

Timothy DelSole
Affiliation:
George Mason University, Virginia
Michael Tippett
Affiliation:
Columbia University, New York
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Summary

This chapter discusses the problem of selecting predictors in a linear regression model, which is a special case of model selection. One might think that the best model is the one with the most predictors. However, each predictor is associated with a parameter that must be estimated, and errors in the estimation add uncertainty to the final prediction. Thus, when deciding whether to include certain predictors or not, the associated gain in prediction skill should exceed the loss due to estimation error. Model selection is not easily addressed using a hypothesis testing framework because multiple testing is involved. Instead, the standard approach is to define a criterion for preferring one model over another. One criterion is to select the model that gives the best predictions of independent data. By independent data, we mean data that is generated independently of the sample that was used to inform the model building process. Criteria for identifying the model that gives the best predictions in independent data include Mallows’ Cp, Akaike’s Information Criterion, Bayesian Information Criterion, and cross-validated error.

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Publisher: Cambridge University Press
Print publication year: 2022

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  • Model Selection
  • Timothy DelSole, George Mason University, Virginia, Michael Tippett, Columbia University, New York
  • Book: Statistical Methods for Climate Scientists
  • Online publication: 03 February 2022
  • Chapter DOI: https://doi.org/10.1017/9781108659055.011
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  • Model Selection
  • Timothy DelSole, George Mason University, Virginia, Michael Tippett, Columbia University, New York
  • Book: Statistical Methods for Climate Scientists
  • Online publication: 03 February 2022
  • Chapter DOI: https://doi.org/10.1017/9781108659055.011
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Model Selection
  • Timothy DelSole, George Mason University, Virginia, Michael Tippett, Columbia University, New York
  • Book: Statistical Methods for Climate Scientists
  • Online publication: 03 February 2022
  • Chapter DOI: https://doi.org/10.1017/9781108659055.011
Available formats
×