Running a Best-Subsets Logistic Regression: An Alternative to Stepwise Methods

Abstract

Although the algorithm for generating a best-subsets variable-selection routine in logistic regression was presented more than a decade ago, a search of the literature reveals that the technique is seldom applied. A possible explanation is its omission from popular statistical computing packages. Newer versions of the Statistical Analysis System (SAS) provide limited capabilities, and the Statistical Package for the Social Sciences (SPSS) does not allow for its calculation. Using a sample data set, this article briefly describes in nonmathematical terms how to implement and interpret results from a best-subsets logistic regression using SAS.The purpose of this article is to briefly describe a best-subsets approach to selecting optimal predictor variables in logistic regression. After laying the theoretical framework, the first section of the article suggests possible reasons for the absence of published empirical studies employing best-subsets logistic regression. Next, the procedural steps are described along with computer syntax. Finally, a sample data set is used to demonstrate application and interpretation of the variable-selection technique.Correspondence concerning this article should be sent to Jason E. King,

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“…He further argued that the larger the value, the greater the importance. Further, King J. E. (2003) suggests that stepwise methods produce outcome in the same faulty df and values of the probability, while the majority researchers act like if their anticipated probabilities were perfect. He further noted that "this dynamic should especially be considered" when taking to mean significance tests for precise model stricture, for instance the Wald's test (King J. E. (2003).…”

“…Further, King J. E. (2003) suggests that stepwise methods produce outcome in the same faulty df and values of the probability, while the majority researchers act like if their anticipated probabilities were perfect. He further noted that "this dynamic should especially be considered" when taking to mean significance tests for precise model stricture, for instance the Wald's test (King J. E. (2003). Among other tests in this model, Hosmer and Lemeshow (H & L) Test shows a Chi-Square value of 11.327 at 0.184 significance level, and we know a tested result of non-significance in the H & L Test predicts an appropriate goodness-of-fit, although we may not have been able to conclude from this test that our model explains much of the variance in the outcome.…”

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“…A best-subsets modeling procedure was followed (Hosmer, Borko, & Lemeshow, 1989;King, 2003). The best-subsets modeling approach is a method of selecting optimal predictor variables for a dependent variable, typically a binary one (Hosmer et al, 1989), but the procedure can be used in linear regression with a continuous dependent variable (King, 2003).…”

“…The best-subsets modeling approach is a method of selecting optimal predictor variables for a dependent variable, typically a binary one (Hosmer et al, 1989), but the procedure can be used in linear regression with a continuous dependent variable (King, 2003). The purpose of applying the best-subsets approach in this study was to use a data-driven rather than intuitive method of selecting an optimal set of predictor variables for the final model.…”

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“…Further, King J. E. (2003) suggests that stepwise methods produce outcome in the same faulty df and values of the probability, while the majority researchers act like if their anticipated probabilities were perfect. He further noted that "this dynamic should especially be considered" when taking to mean significance tests for precise model stricture, for instance the Wald's test (King J. E. (2003). Among other tests in this model, Hosmer and Lemeshow (H & L) Test shows a Chi-Square value of 11.327 at 0.184 significance level, and we know a tested result of non-significance in the H & L Test predicts an appropriate goodness-of-fit, although we may not have been able to conclude from this test that our model explains much of the variance in the outcome.…”