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Richard Hardy
Richard Hardy
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Richard Hardy
Richard Hardy
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Justification for and propertiesoptimality of $R^2_{adj.}$ as a criterion for model selection criterion

In a recent thread, use of adjusted $R^2$ ($R^2_{adj.}$) is mentioned in the context of model selection, e.g.

The adjustment was invented as a solution to problems caused by variable selection

QuestionsQuestion: Is there any justification for using $R^2_{adj.}$ for model selection? That is, does $R^2_{adj.}$ have any optimality properties in the context of model selection?

  1. Is there any justification for using $R^2_{adj.}$ for model selection?
  2. Does it have any optimality properties in the context of model selection?

For example, AIC is an efficient criterion and BIC is a consistent one, but $R^2$ does not coincide with any of them and so makes me wonder if it can be optimal in any other sense.

Justification for and properties of $R^2_{adj.}$ as a criterion for model selection

In a recent thread, use of adjusted $R^2$ ($R^2_{adj.}$) is mentioned in the context of model selection, e.g.

The adjustment was invented as a solution to problems caused by variable selection

Questions:

  1. Is there any justification for using $R^2_{adj.}$ for model selection?
  2. Does it have any optimality properties in the context of model selection?

For example, AIC is an efficient criterion and BIC is a consistent one, but $R^2$ does not coincide with any of them and so makes me wonder if it can be optimal in any other sense.

Justification for and optimality of $R^2_{adj.}$ as a model selection criterion

In a recent thread, use of adjusted $R^2$ ($R^2_{adj.}$) is mentioned in the context of model selection, e.g.

The adjustment was invented as a solution to problems caused by variable selection

Question: Is there any justification for using $R^2_{adj.}$ for model selection? That is, does $R^2_{adj.}$ have any optimality properties in the context of model selection?

For example, AIC is an efficient criterion and BIC is a consistent one, but $R^2$ does not coincide with any of them and so makes me wonder if it can be optimal in any other sense.

Source Link
Richard Hardy
Richard Hardy
  • 69.5k
  • 13
  • 126
  • 278

Justification for and properties of $R^2_{adj.}$ as a criterion for model selection

In a recent thread, use of adjusted $R^2$ ($R^2_{adj.}$) is mentioned in the context of model selection, e.g.

The adjustment was invented as a solution to problems caused by variable selection

Questions:

  1. Is there any justification for using $R^2_{adj.}$ for model selection?
  2. Does it have any optimality properties in the context of model selection?

For example, AIC is an efficient criterion and BIC is a consistent one, but $R^2$ does not coincide with any of them and so makes me wonder if it can be optimal in any other sense.