Comparison of Stopping Rules in Forward “Stepwise” Regression
Abstract
This paper uses the unconditional mean square error of prediction as a criterion for comparing stopping rules used with the forward “stepwise” selection procedure in multivariate normal samples, based on simulations of 48 population correlation matrices. The CP statistic, “F to enter” (.15 < α < .25), a rule which minimizes the sample criterion, and one which sequentially tests the equality of the population criterion (.25 < α < .35) are superior. For these rules, the criterion seldom differs by more than three percent, although there are considerable differences between these and some of the other rules.
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Using a p-value threshold of 0.25 to select variables for multivariable models allows weakly associated variables that may be important collective predictors to be included.
“Using a more conservative p value of < 0.25 to inform which variables should be included in the multivariable predictor models enables variables that could be important collective predictors of an outcome to be simultaneously included in the model even though they are only weakly associated with the outcome in and of themselves (Bendel & Afifi, 1977).”
From Cognitive-behavioral therapy for late-life anxiety: Similarities and differences between Veteran and community participants (2015) · cites this paper as Bendel & Afifi, 1977
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References 32 · Cited by 885
- Authors
- Bendel, R. B., & Afifi, A. A.
- Affiliations
- Washington State University (US)
- University of California, Los Angeles (US)
- ORCID
- Afifi, A. A.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1977-03
- Volume
- 72
- Issue
- 357
- Pages
- 46-53
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2067970576
- Cited by
- 885
- References
- 32
- Citations by year
- 2026: 10 · 2025: 33 · 2024: 58 · 2023: 33 · 2022: 54 · 2021: 75 · 2020: 75 · 2019: 54 · 2018: 37 · 2017: 32 · 2016: 31 · 2015: 38 · 2014: 31 · 2013: 30 · 2012: 24
- FWCI
- 5.74
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- stopping rules, forward selection, feature selection, mean square prediction error, cross-validation, sequential hypothesis testing
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