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Theory and Methods

A Lack-of-Fit Test for the Mean Function in a Generalized Linear Model

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Pages 420-426 | Received 01 Dec 1989, Published online: 27 Feb 2012

References

  • Baker , R. J. and Nelder , J. A. 1978 . The GUM System Release 3 Manual , Oxford , , UK : Numerical Algorithms Group .
  • Bickel , P. J. and Wichura , M. J. 1971 . Convergence Criteria for Multiparameter Stochastic Processes and Some Applications . The Annals of Mathematical Statistics , 42 : 1656 – 1670 .
  • Billingsley , P. 1968 . Convergence of Probability Measures , New York : John Wiley .
  • Brillinger , D. R. 1977 . The Identification of a Particular Nonlinear Time Series System . Biometrika , 64 : 509 – 515 .
  • Brillinger , D. R. 1983 . “ A Generalized Linear Model With Gaussian Regressor Variables ” . In A Festschrift for Erich L. Lehmann Edited by: Bickel , P. , Doksum , K. and Hodges , J. L. 97 – 114 .
  • Carroll , R. J. and Ruppert , D. 1988 . Transformations and Weighting in Regression , New York : Chapman & Hall .
  • Christensen , R. 1989 . Lack-of-fit Tests Based on Near or Exact Replication . The Annals of Statistics , 17 : 673 – 683 .
  • Christensen , R. Small Sample Characterizations of Near Replicate Lack of Fit Tests . Journal of the American Statistical Association , (in press)
  • Cox , D. and Koh , E. 1986 . A Smoothing Spline Based Test of Model Adequacy in Polynomial Regression , Madison, Dept. of Statistics . Technical Report 787, University of Wisconsin
  • Cox , D. , Koh , E. , Wahba , G. and Yandell , B. S. 1988 . Testing the (Parametric) Null Model Hypothesis in (Semiparametric) Partial and Generalized Spline Models . The Annals of Statistics , 16 : 113 – 119 .
  • Dempster , A. P. and Ryan , L. M. 1985 . Weighted Normal Plots . Journal of the American Statistical Association , 80 : 845 – 850 .
  • Draper , N. R. and Smith , H. 1981 . Applied Regression Analysis, , 2nd ed. , New York : John Wiley .
  • Efron , B. 1982 . The Jackknife, the Bootstrap and Other Resampling Plans , Philadelphia : SIAM .
  • Fahrmeir , L. and Kaufmann , H. 1986 . correction to “Consistency and Asymptotic Normality of the Maximum Likelihood Estimator in Generalized Linear Models,” . The Annals of Statistics , 14 : 1643
  • Fahrmeir , L. and Kaufmann , H. 1985 . Consistency and Asymptotic Normality of the Maximum Likelihood Estimator in Generalized Linear Models . The Annals of Statistics , 13 : 342 – 368 .
  • Fienberg , S. E. and Gong , G. D. 1984 . Comment on “Graphical Methods for Assessing Logistic Regression Models,” . Journal of the American Statistical Association , 79 : 72 – 77 . by J. M. Landwehr, D. Pregibon, and A. C. Shoemaker
  • Finney , D. J. 1947 . The Estimation From Individual Records of the Relationship Between Dose and Quantal Response . Biometrika , 34 : 320 – 334 .
  • Hastie , T. and Tibshirani , R. 1986 . Generalized Additive Models . Statistical Sciences , 1 : 297 – 318 .
  • Hastie , T. and Tibshirani , R. 1990 . Generalized Additive Models , London : Chapman & Hall .
  • Huber , P. J. 1981 . Robust Statistics , New York : John Wiley .
  • Joglekar , G. , Schuenemeyer , J. H. and LaRiccia , V. 1989 . Lack of fit Testing When Replicates Are Not Available . The American Statistician , 43 : 135 – 143 .
  • Lange , N. and Ryan , L. 1989 . Assessing Normality in Random Effects Models . The Annals of Statistics , 17 : 624 – 642 .
  • Li , K. and Duan , N. 1989 . Regression Analysis Under Link Violation . The Annals of Statistics , 17 : 1009 – 1052 .
  • McCullagh , P. and Nelder , J. A. 1989 . Generalized Linear Models, , 2nd ed. , London : Chapman & Hall .
  • Neill , J. W. and Johnson , D. E. 1985 . Testing Linear Regression Function Adequacy Without Replication . The Annals of Statistics , 13 : 1482 – 1489 .
  • Neill , J. W. and Johnson , D. E. 1989 . A Comparison of Some Lack of Fit Tests Based on Near Replicates . Communications in Statistics, Part A–Theory and Methods , 18 : 3533 – 3570 .
  • Pierce , D. A. and Kopecky , K. J. 1979 . Testing Goodness of Fit for the Distribution of Errors in Regression Models . Biometrika , 66 : 1 – 5 .
  • Pregibon , D. 1980 . Goodness of Link Test for Generalized Linear Models . Applied Statistics , 29 : 15 – 23 .
  • Pregibon , D. 1981 . Logistic Regression Diagnostics . The Annals of Statistics , 9 : 705 – 724 .
  • Pregibon , D. 1985 . “ Link tests ” . In Encyclopedia of Statistical Sciences , Edited by: Kotz , S. , Johnson , N. L. and Read , C. B. Vol. 5 , 82 – 85 . New York : Wiley .
  • Press , W. H. , Flannery , B. P. , Teukolsky , S. A. and Vetterling , W. T. 1986 . Numerical Recipes: The Art of Scientific Computing , Cambridge , , UK : Cambridge University Press .
  • Randles , R. H. 1984 . On Tests Applied to Residuals . Journal of the American Statistical Association , 79 : 349 – 354 .
  • Shillington , E. R. 1979 . Testing Lack of Fit in Regression Without Replication . The Canadian Journal of Statistics , 7 : 137 – 146 .
  • Tsiatis , A. A. 1980 . A Note on a Goodness-of-Fit Test for the Logistic Regression Without Replication . Biometrika , 67 : 250 – 251 .
  • Utts , J. M. 1982 . The Rainbow Test for Lack of Fit in Regression . Communications in Statistics, Part A–Theory and Methods , 11 : 2801 – 2815 .

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