Model selection procedures and their error-reduction targets

Doyle, John R. 2011. Model selection procedures and their error-reduction targets. [Working Paper]. Social Science Research Network. Available at: http://dx.doi.org/10.2139/ssrn.1789907

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Abstract

This brief note compares model selection procedures in regression. On the one hand there is an observed error reduction ratio that we calculate from the data: h = SSE2/SSE1, where SSE1 and SSE2 are the sums of squared errors in Models 1 and 2, respectively. On the other hand there is a target ratio, which we call H, which is set by the model selection procedure via an expression involving the numbers of variables and observations. If h < H the procedure accepts Model 2 as superior to Model 1. The aim of this note is to derive expressions for each model selection procedure that have the form H = 1/(1x), where x varies from procedure to procedure. These common-form expressions for H allow us to compare model selection procedures transparently. The procedures we examine are: Akaike’s Information Criterion (AIC), Bayesian Information Criterion (BIC), Amemiya’s Prediction Criterion (PC), change in R2 (ΔR2), adjusted R2, and adjusted Rf2 which we have created as a simple generalization of adjusted R2. We show that it is less liberal than adjusted R2 and relates closely to AIC and PC: in so doing it provides fresh insight into their properties.

Item Type:	Monograph (Working Paper)
Date Type:	Publication
Status:	Published
Schools:	Business (Including Economics)
Subjects:	Q Science > Q Science (General) Q Science > QA Mathematics
Uncontrolled Keywords:	Model Selection ; AIC ; BIC ; Prediction Criterion ; Adjusted R2 ; F-Test ; Error Reduction Ratio
Publisher:	Social Science Research Network
ISSN:	15565068
Last Modified:	05 Nov 2019 03:29
URI:	https://orca.cardiff.ac.uk/id/eprint/27492

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