Download PDF
Methods Inf Med 2009; 48(03): 306-310
DOI: 10.3414/ME0571
Original Articles
Schattauer GmbH

On Graphically Checking Goodness-of-fit of Binary Logistic Regression Models

G. Gillmann
1   Swiss Federal Statistical Office, Neuchâtel, Switzerland
2   Department of Social and Preventive Medicine, University of Bern, Bern, Switzerland
,
C. E. Minder
2   Department of Social and Preventive Medicine, University of Bern, Bern, Switzerland
3   Horten Zentrum, University of Zurich, Zurich, Switzerland
› Author Affiliations
Further Information

Publication History

received: 15 May 2008

accepted: 20 March 2008

Publication Date:
17 January 2018 (online)

    Permissions and Reprints

Summary

Objectives: This paper is concerned with checking goodness-of-fit of binary logistic regression models. For the practitioners of data analysis, the broad classes of procedures for checking goodness-of-fit available in the literature are described. The challenges of model checking in the context of binary logistic regression are reviewed. As a viable solution, a simple graphical procedure for checking goodness-of-fit is proposed.

Methods: The graphical procedure proposed relies on pieces of information available from any logistic analysis; the focus is on combining and presenting these in an informative way.

Results: The information gained using this approach is presented with three examples. In the discussion, the proposed method is put into context and compared with other graphical procedures for checking goodness-of-fit of binary logistic models available in the literature.

Conclusion: A simple graphical method can significantly improve the understanding of any logistic regression analysis and help to prevent faulty conclusions.

Keywords

Nonlinear models - residuals
 

  • References

  • 1 Strasak AM. et al. The Use of Statistics in Medical Research: A Comparison of The New England Journal of Medicine and Nature Medicine. The American Statistician 2007; 61: 47-55.
    CrossrefPubMedSearch in Google Scholar
  • 2 Davison AC. Statistical models. Cambridge: Cambridge University Press; 2003. Section 8.6.
    Search in Google Scholar
  • 3 Draper N, Smith H. Applied Regression Analysis. New York: Wiley & Sons; 1998
    Search in Google Scholar
  • 4 Weisberg S. Applied Linear Regression. New York: Wiley & Sons; 1985
    Search in Google Scholar
  • 5 Daniel C, Wood F, Gorman JW. Fitting Equations to Data: Computer Analysis of Multifactor Data. New York: Wiley & Sons; 1980
    Search in Google Scholar
  • 6 Hosmer J, Lemeshow S. Applied Logistic Regression. New York: Wiley & Sons; 1989
    Search in Google Scholar
  • 7 Brown CC. On a goodness-of-fit test for the logistic model based on score statistics. Communications in Statistics 1982; 11 (10) 1087-1105.
    PubMedSearch in Google Scholar
  • 8 Stukel TA. Generalized logistic models. Journal of the American Statistical Association 1988; 83: 426-431.
    CrossrefPubMedSearch in Google Scholar
  • 9 Le Cessie S, van Houwelingen JC. A Goodness-offit Test for Binary Regression Models Based on Smoothing Methods. Biometrics 1991; 47: 1267-1282.
    CrossrefPubMedSearch in Google Scholar
  • 10 Hosmer D, Hosmer T, le Cessie S, and Lemeshow S. A Comparison of Goodness-of-Fit Tests for the Logistic Regression Model. Statistics in Medicine 1997; 16: 965-980.
    CrossrefPubMedSearch in Google Scholar
  • 11 Fienberg SE, Gong GD. Comment following the paper of Landwehr, Pregibon and Shoemaker. Journal of the American Statistical Association 1984; 79: 72-77.
    CrossrefPubMedSearch in Google Scholar
  • 12 Copas JB. Binary Regression Models for Contaminated Data (with discussion). Journal of the Royal Statistical Society B 1988; 50: 225-265.
    PubMedSearch in Google Scholar
  • 13 Copas JB. Plotting p against x. Journal of the Royal Statistical Society C. (Applied Statistics) 1983; 32: 25-31.
    PubMedSearch in Google Scholar
  • 14 Copas JB, Marshall P. The offender group reconviction scale: A statistical reconviction score for use by probation officers. Journal of the Royal Statistical Society, Series C. (Applied Statistics) 1998; 47: 159-171.
    CrossrefPubMedSearch in Google Scholar
  • 15 Stuck AE, Minder CE, Peter-Wuest I, Gillmann G. et al. A Randomized Trial of In-Home Visits for Disability Prevention in Community-Dwelling Older People at Low and High Risk for Nursing Home Admission. Archives of Internal Medicine 2000; 160: 977-986.
    CrossrefPubMedSearch in Google Scholar
  • 16 Spiegelhalter DJ. Probabilistic prediction in patient management and clinical trials. Statistics in Medicine 1986; 5: 421-433.
    CrossrefPubMedSearch in Google Scholar
  • 17 Harrell FE. et al. Tutorial in Biostatistics Development of a clinical prediction model for an ordinal outcome. Statistics in Medicine 1998; 17: 909-944.
    CrossrefPubMedSearch in Google Scholar
  • 18 Steyerberg EW, Vergouwe Y, Keizer HJ, Habbema JDF. Residual mass histology in testicular cancer: development and validation of a clinical prediction rule. Statistics in Medicine 2001; 20: 3847-3859.
    CrossrefPubMedSearch in Google Scholar
  • 19 Cleveland WS. Robust Locally Weighted Regression and Smoothing Scatterplots. Journal of the American Statistical Association 1979; 74: 829-836.
    CrossrefPubMedSearch in Google Scholar
  • 20 Fowlkes E. Some Diagnostics for Binary Logistic Regression via Smothing Methods. Biometrika 1987; 74: 503-515.
    CrossrefPubMedSearch in Google Scholar
  • 21 Cook RD, Weisberg S. Graphics for Assessing the Adequacy of Regression Models. Journal of the American Statistical Association 1997; 92: 490-499.
    CrossrefPubMedSearch in Google Scholar
  • 22 Pardoe I, Cook RD. A Graphical Method for Assessing the Fit of a Logistic Regression Model. The American Statistician 2002; 56: 263-272.
    CrossrefPubMedSearch in Google Scholar
  • 23 Landwehr JM, Pregibon D, Shoemaker AC. Graphical Methods for Assessing Logistic Regression Models. Journal of the American Statistical Association 1984; 79: 61-71.
    CrossrefPubMedSearch in Google Scholar
  • 24 Cox DR, Snell EJ. A General Definition of Residuals. Journal of the Royal Statistical Society B 1968; 30: 248-275.
    PubMedSearch in Google Scholar
  • 25 Pregibon D. Logistic Regression Diagnostics. The Annals of Statistics 1981; 9 (04) 705-724.
    CrossrefPubMedSearch in Google Scholar