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Explained variation for logistic regression

M Mittlböck1, M Schemper

  • 1Department of Medical Computer Sciences, Vienna University, Austria.

Statistics in Medicine
|October 15, 1996
PubMed
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This study compares twelve measures of explained variation in logistic regression. Two measures, the squared Pearson correlation and proportional reduction of squared Pearson residuals, are recommended for their clear interpretation and satisfactory performance.

Area of Science:

  • Statistics
  • Biostatistics
  • Epidemiology

Background:

  • Logistic regression models are widely used in various scientific fields.
  • Quantifying the explained variation in logistic regression is crucial for model interpretation.
  • Existing software reports different measures, leading to potential inconsistencies.

Purpose of the Study:

  • To review and compare twelve measures of explained variation for logistic regression models.
  • To identify reliable and interpretable measures for assessing model fit.
  • To provide recommendations for routine use in statistical analysis.

Main Methods:

  • A comprehensive review of twelve suggested or potentially useful measures of explained variation.
  • Discussion of the definitions and properties of each measure.

Related Experiment Videos

  • An empirical study comparing the performance of these measures.

    • Main Results:

    • Two measures, squared Pearson correlation and proportional reduction of squared Pearson residuals, showed nearly identical results.
    • These recommended measures align well with the R-squared from general linear models.
    • The explained variation for current and future samples is easily obtainable, with suggested adjustments for small samples.

    Conclusions:

    • The squared Pearson correlation and proportional reduction of squared Pearson residuals are recommended for logistic regression.
    • Routine use of a suitable measure of explained variation is advised for logistic models.
    • The study provides practical guidance for researchers using logistic regression analysis.