A comparison of the Hosmer–Lemeshow, Pigeon–Heyse, and Tsiatis goodness-of-fit tests for binary logistic regression under two grouping methods

References

• Bertolini, G., Damico, R., Nardi, D., Tinazzi, A., Apolone, G. ( 2000). One model, several results: The paradox of the Hosmer–Lemeshow goodness-of-fit test for the logistic regression model. Journal of Epidemiology and Biostatistics 5(4):251–253.
   PubMedGoogle Scholar
• Canary, J. D. ( 2013). Grouped Goodness-of-Fit Tests for Binary Regression Models. PhD dissertation, University of Tasmania, Tasmania, Australia.
   Google Scholar
• Chernoff, H., Lehmann, E. L. ( 1954). The use of maximum likelihood estimates in χ2 tests for goodnessof-fit. The Annals of Mathematical Statistics 25(3):579–586.
   Google Scholar
• Cook, N. R., Paynter, N. P. ( 2011). Performance of reclassification statistics in comparing risk prediction models. Biometrical Journal 53(2):237–258.
   PubMed Web of Science ®Google Scholar
• Dreiseitl, S., Osl, M. ( 2012). Effects of data grouping on calibration measures of classifiers. Computer-Aided Systems Theory – EUROCAST 2011:359–366.
   Google Scholar
• Etterson, M. A. ( 2011). User's Guide for MCestimate. Washington, DC: Smithsonian Migratory Bird Center.
   Google Scholar
• Fisher, R. A. (1922). On the interpretation of X2 from contingency tables, and the calculation of P. Journal of the Royal Statistical Society 85(1): 87–94.
   Google Scholar
• Halteman, W. A. ( 1980). A Goodness-of-Fit Statistic for Binary Logistic Regression. Doctor of Philosophy dissertation, Seattle, WA: University of Washington.
   Google Scholar
• Henderson, H. V., Searle, S. R. ( 1981). On deriving the inverse of a sum of matrices. SIAM Review 23(1):53–60.
   Web of Science ®Google Scholar
• Horton, N. J., Bebchuk, J. D., Jones, C. L., Lipsitz, S. R., Catalano, P. J., Zahner, G. E. P., Fitzmaurice, G. M. ( 1999). Goodness-of-fit for G.E.E.: An example with mental health service utilization. Statistics in Medicine 18(2):213–222.
   PubMed Web of Science ®Google Scholar
• Hosmer, D. W., Hosmer, T., le Cessie, S., Lemeshow, S. ( 1997). A comparison of goodness-of-fit tests for the logistic regression model. Statistics in Medicine 16(9):965–980.
   PubMed Web of Science ®Google Scholar
• Hosmer, D. W., Lemeshow, S. ( 1980). Goodness-of-fit tests for the multiple logistic regression model. Communications in Statistics – Theory and Methods 9(10):1043–1069.
   Web of Science ®Google Scholar
• Hosmer, D. W., Lemeshow, S., Sturdivant, R. X. ( 2013). Applied Logistic Regression. New York, NY: John Wiley.
   Google Scholar
• Johnson, T. N., Kennedy, P. L., Etterson, M. A. ( 2012). Nest success and cause specific nest failure of grassland passerines breeding in prairie grazed by livestock. Journal of Wildlife Management 76(8):1607–1616.
   Web of Science ®Google Scholar
• Kendall, M. G., Stuart, A., Ord, J. K. ( 1994). Kendall's Advanced Theory of Statistics, 6th ed., Vol. 1. Distributional Theory. London: Edward Arnold.
   Google Scholar
• Kendall, M. G., Stuart, A., Ord, K., Arnold, S. ( 1999). Kendall's Advanced Theory of Statistics, 6th ed., Vol. 2A Classical Inference and the Linear Model. London: Wiley.
   Google Scholar
• Lawrence, I., Lin, K. ( 1989). A concordance correlation coefficient to evaluate reproducibility. Biometrics 45(1):255–268.
   Web of Science ®Google Scholar
• Le Cessie, S., van Houwelingen, J. C. ( 1991). A goodness-of-fit test for binary regression models based on smoothing methods. Biometrics 47(4):1267–1282.
   Web of Science ®Google Scholar
• Lemeshow, S., Hosmer, D. W. ( 1982). A review of goodness-of-fit statistics for use in the development of logistic regression models. American Journal of Epidemiology 115(1):92–106.
   PubMed Web of Science ®Google Scholar
• Liu, Y., Nelson, P. I., Yang, S. ( 2012). An omnibus lack of fit test in logistic regression with sparse data. Statistical Methods & Applications 21(4):437–452.
   Web of Science ®Google Scholar
• Milligan, G. W. ( 1980). An examination of the effect of six types of error perturbation on fifteen clustering algorithms. Psychometrika 45(3):325–342.
   Web of Science ®Google Scholar
• Milligan, G. W. ( 1981). A Monte Carlo Study of thirty internal criterion measures for cluster analysis. Psychometrika 46(2):187–199.
   Web of Science ®Google Scholar
• Moore, D. S. ( 1971). A Chi-square statistic with random cell boundaries. The Annals of Mathematical Statistics 42(1):147–156.
   Google Scholar
• Moore, D. S., Spruill, M. C. ( 1975). Unified large-sample theory of general chi-squared statistics for tests of fit. The Annals of Statistics 3(3):599–616.
   Web of Science ®Google Scholar
• Pearson, K. ( 1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 50(302):157–175.
   Google Scholar
• Pigeon, J. G., Heyse, J. F. ( 1999a). A cautionary note about assessing the fit of logistic regression models. Journal of Applied Statistics 26(7):847.
   Web of Science ®Google Scholar
• Pigeon, J. G., Heyse, J. F. ( 1999b). An improved goodness of fit statistic for probability prediction models. Biometrical Journal 41(1):71–82.
   Web of Science ®Google Scholar
• Pulkstenis, E., Robinson, T. J. ( 2002). Two goodness-of-fit tests for logistic regression models with continuous covariates. Statistics in Medicine 21(1):79–93.
   PubMed Web of Science ®Google Scholar
• Rao, C. R. (1948). Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. In Mathematical Proceedings of the Cambridge Philosophical Society 44(1):50–57.
   Google Scholar
• Rao, C. R. ( 1973). Linear Statistical Inference and Its Applications, 2nd ed. New York, NY: John Wiley & Sons, Inc.
   Google Scholar
• Rector, T. S., Anand, I. S. ( 2010). Research Needed to Support Clinical Use of Biomarkers as Prognostic Indicators for Patients with Heart Failure. Cardiology Research and Practice. http://doi.org/10.4061/2010/453851
   Google Scholar
• StataCorp. ( 2007). Stata Statistical Software: Release 10. College Station, TX: StataCorp LP.
   Google Scholar
• Stukel, T. A. ( 1988). Generalized logistic models. Journal of the American Statistical Association 83(402):426–431.
   Web of Science ®Google Scholar
• Su, J. Q., Wei, L. J. ( 1991). A lack-of-fit test for the mean function in a generalized linear model. Journal of the American Statistical Association 86(414):420–426.
   Web of Science ®Google Scholar
• Tsiatis, A. A. ( 1980). A note on a goodness-of-fit test for the logistic regression model. Biometrika 67(1):250–251.
   Web of Science ®Google Scholar
• Xie, X., Pendergast, J., Clarke, W. ( 2008). Increasing the power: A practical approach to goodness-of-fit test for logistic regression models with continuous predictors. Computational Statistics & Data Analysis 52(5):2703–2713.
   Web of Science ®Google Scholar