Increasing the power: A practical approach to goodness-of-fit test for logistic regression models with continuous predictors

Computational Statistics and Data Analysis

Volumn 52, Issue 5, 2008, Pages 2703-2713

  Xie, Xian Jin ^a   Pendergast, Jane ^b   Clarke, William ^b  

^a UNIVERSITY OF TEXAS SOUTHWESTERN MEDICAL CENTER   (United States)

^b UNIVERSITY OF IOWA   (United States)

Author keywords

Cluster analysis; Continuous covariates; Generalized linear model; Goodness of fit test; Logistic regression

Indexed keywords

CLUSTER ANALYSIS; INFORMATION ANALYSIS; LOGISTICS; MATHEMATICAL MODELS;

CONTINUOUS COVARIATES; GENERALIZED LINEAR MODEL; GOODNESS-OF-FIT TEST; LOGISTIC REGRESSION;

REGRESSION ANALYSIS;

EID: 38149094864     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2007.09.027     Document Type: Article

References (45)

1. Agresti A. Categorical Data Analysis (1990), Wiley, New York, USA
2. Anderson J.A. Separate sample logistic discrimination. Biometrika 59 1 (1972) 19-35
3. Barnhart H.X., and Williamson J.M. Goodness-of-fit tests for GEE modeling with binary responses. Biometrics 54 (1998) 720-729
4. Chernoff H., and Lehmann E.L. The use of maximum likelihood estimates in chi-square tests for goodness of fit. Ann. Math. Statist. 25 (1954) 579-586
5. Copas J.B. Plotting p against x. Appl. Statist. 32 (1983) 25-31
6. Copas J.B. Unweighted sum of squares test for proportions. Appl. Statist. 38 1 (1989) 71-80
7. Cox D.R., and Snell E.J. The Analysis of Binary Data. second ed (1989), Chapman and Hall, London, UK
8. Cramer H. Mathematical Methods of Statistics (1946), Princeton University Press, NJ, USA
9. Cressie N., and Read T.R.C. Multinomial goodness-of-fit tests. J. Roy. Statist. Soc. 46 (1984) 440-464
10. Farrington C.P. On assessing goodness of fit of generalized linear models to sparse data. J. Roy. Statist. Soc. Ser. B 58 2 (1996) 349-360
11. Gail M.H., Wieand S., and Piantadosi S. Biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates. Biometrika 71 3 (1984) 431-444
12. Gail M.H., Tan W.-Y., and Piantadosi S. Tests for no treatment effect in randomized clinical trials when needed covariates are omitted. Biometrika 75 1 (1988) 57-64
13. Hauck W.W., Neuhaus J.M., Kalbfleisch J.D., and Anderson S. A consequence of omitted covariates when estimating odds ratios. J. Clin. Epidemiol. 44 1 (1991) 77-81
14. Horton N.J., Bebchuk J.D., Jones C.L., Lipsitz S.R., Catalano P.J., Zahner G.E.P., and Fitzmaurice G.M. Goodness-of-fit for GEE: an example with mental health service utilization. Statist. Med. 18 (1999) 213-222
15. Hosmer D.W., and Hjort N.L. Goodness-of-fit processes for logistic regression: simulation results. Statist. Med. 21 (2002) 2723-2738
16. Hosmer D.W., Hosmer T., Le Cessie S., and Lemeshow S. A comparison of goodness-of-fit tests for the logistic regression model. Statist. Med. 16 (1997) 965-980
17. Hosmer D.W., and Lemeshow S. Goodness of fit tests for the multiple logistic regression model. Commun. Statist. Part A-Theory and Methods 9 (1980) 1043-1069
18. Hosmer D.W., and Lemeshow S. Applied Logistic Regression (1989), Wiley, New York, USA
19. IHAST2 web site, 2004. 〈http://ctsdmc.public-health.uiowa.edu/Ihast2/Home.htm〉.
20. Kuss O. Global goodness-of-fit tests in logistic regression with sparse data. Statist. Med. 21 (2002) 3789-3801
21. le Cessie S., and van Houwelingen C. A goodness-of-fit test for binary regression models, based on smoothing methods. Biometrics 47 (1991) 1267-1282
22. McCullagh P. On the asymptotic distribution of Pearson's statistic in linear exponential-family models. Internat. Statist. Rev. 53 1 (1985) 61-67
23. McCullagh P. The conditional distribution of goodness-of-fit statistics for discrete data. J. Amer. Statist. Assoc. 81 393 (1986) 104-107
24. Milligan G. An examination of the effect of six types of error perturbation on fifteen clustering algorithms. Psychometrika 45 (1980) 325-342
25. Milligan G. A Monte Carlo study of thirty internal criterion measures for cluster analysis. Psychometrika 46 (1981) 187-199
26. Molinari L. Distribution of the chi-squared test in nonstandard situations. Biometrika 64 1 (1977) 115-121
27. Nagelkerke N., Moses S., Plummer F.A., Brunham R.C., and Fish D. Logistic regression in case-control studies: the effect of using independent as dependent variables. Statist. Med. 14 (1995) 769-775
28. Nagelkerke N., Smits J., le Cessie S., and van Houwelingen H. Testing goodness-of-fit of the logistic regression model in case-control studies using sample reweighting. Statist. Med. 24 (2005) 121-130
29. Nelder J.A., and Wedderburn R.W.M. Generalized linear models. J. Roy. Statist. Soc. A 135 (1972) 370-384
30. Orme C. The calculation of the information matrix test for binary data models. The Manchester School 54 4 (1988) 370-376
31. Osius G., and Rojek D. Normal goodness-of-fit tests for multinomial models with large degrees of freedom. J. Amer. Statist. Assoc. 87 420 (1992) 1145-1152
32. Pigeon J.G., and Heyse J.F. A cautionary note about assessing the fit of logistic regression models. J. Appl. Statist. 26 7 (1999) 847-853
33. Pulkstenis E., and Robinson T.J. Two goodness-of-fit tests for logistic regression models with continuous covariates. Statist. Med. 21 (2002) 79-93
34. Rao C.R. Linear Statistical Inference and Its Applications. second ed (1973), Wiley, New York
35. Read T.R.C., and Cressie N.A.C. Goodness-of-Fit Statistics for Discrete Multivariate Data (1988), Springer, New York, USA
36. Robinson L.D., and Jewell N.P. Some surprising results about covariate adjustment in logistic regression models. Internat. Statist. Rev. 59 (1991) 227-240
37. Todd, M.M., Hindman, B.J., Clarke, W.R., Torner, J.C., for the Intraoperative Hypothermia for Aneurysm Surgery Trial (IHAST) Investigators. 2005. Mild intraoperative hypothermia during surgery for intracranial aneurysm. New England J. Med. 352, 135-145.
38. Tsiatis A.A. A note on a goodness-of-fit test for the logistic regression model. Biometrika 67 1 (1980) 250-251
39. Watson G.S. On chi-square goodness-of-fit tests for continuous distributions. J. Roy. Statist. Soc. B 20 (1958) 44-61
40. Watson G.S. Some recent results in the chi square goodness of fit tests. Biometrics 15 (1959) 440-468
41. White H. Maximum likelihood estimation of misspecified models. Econometrica 50 1 (1982) 1-25
42. Williams D.A. Generalized linear models diagnostics using the deviance and single case deletions. Appl. Statist. 36 2 (1987) 181-191
43. Xie, X.-J., 2005. A goodness-of-fit test for logistic regression models with continuous predictors. Ph.D. Thesis, the University of Iowa.
44. Xie Y., and Manski C.F. The logit model and response-based samples. Sociol. Methods Res. 17 (1988) 283-302
45. Zheng B. An information matrix test for logistic regression models based on case-control data. Biometrika 88 4 (2001) 921-932