Are ordinal models useful for classification? a revised analysis

References

• Anderson , J. A. 1984 . Regression and ordered categorical variables (with discussion) . Journal of the Royal Statistical Society, Series B , 46 : 1 – 30 .
   Google Scholar
• Anderson , J. A. and Philips , P. R. 1981 . Regression, discrimination and measurement models for ordered categorical variables . Applied Statistics , 30 : 22 – 31 .
   Google Scholar
• Armstrong , B. G. and Sloan , M. 1989 . Ordinal regression models for epidemiologic data . American Journal of Epidemiology , 129 : 191 – 204 .
   PubMed Web of Science ®Google Scholar
• Ashby , D. , Pocock , S. J. and Shaper , A. G. 1986 . Ordered polytomous regression: an example relating serum biochemistry and haematology to alcohol consumption . Applied Statistics , 35 : 289 – 301 .
   Web of Science ®Google Scholar
• Bohrer , R. and Schervish , M. J. 1981 . An error bounded algorithm for multivariate normal probabilities of rectangular regions . Technometrics , 23 : 297 – 300 .
   Web of Science ®Google Scholar
• Campbell , M. K. 1986 . Asymptotic error rates of classification procedures when the response variable is ordinal. , University of Western Ontario . Unpublished Ph.D. thesis
   Google Scholar
• Campbell , M. K. , Donner , A. P. and Webster , K. M. 1991 . Are ordinal models useful for classification? . Statistics in Medicine , 10 : 383 – 394 .
   PubMed Web of Science ®Google Scholar
• Dawid , A. P. 1976 . Properties of diagnostic data distributions . Biometries , 32 : 647 – 658 .
   PubMed Web of Science ®Google Scholar
• Efron , B. 1986 . How biased is the apparent error rate of a prediction rule? . Journal of the American Statistical Association , 81 : 461 – 470 .
   Web of Science ®Google Scholar
• Eisenbeis , A. and Avery , R. B. 1975 . Discriminant Analysis and Classification Procedures , Lexington, MA : D. C. Heath .
   Google Scholar
• Engel , J. and Perlman , M. D. 1988 . Polytomous logistic regression . Statistica Neerlandica , 42 : 233 – 252 .
   Google Scholar
• Finney , D. J. 1947 . The estimation from individual records of the relationship between dose and quanta1 response . Biometrika , 34 : 320 – 334 .
   PubMed Web of Science ®Google Scholar
• Greenwood , C. and Farewell , V. 1989 . A comparison of regression models for ordinal data in an analysis of transplanted kidney function . Canadian Journal of Statistics , 16 : 325 – 335 .
   Google Scholar
• Hand , D. J. 1986 . Recent advances in error rate estimation . Pattern Recognition Letters , 4 : 335 – 346 .
   Web of Science ®Google Scholar
• Harrell , F. E. Jnr. 1987 . The LOGIST Procedure . SAS.SUGI , 12 : 269 – 292 .
   Google Scholar
• Holtbriigge , W. and Schumacher , M. 1991 . A comparison of regression models of ordered categorical data . Applied Statistics , 40 : 249 – 259 .
   Google Scholar
• Lee , E. T. 1974 . A computer program for linear logistic regression analysis . Computer Programs in Biomedicine , 4 : 80 – 92 .
   PubMedGoogle Scholar
• Lesaffre , E. 1986 . Logistic discriminant analysis with applications in electrocardiography , Belgium : University of Leuven . Unpublished Ph.D. thesis
   Google Scholar
• Lesaffre , E. , Willems , J. L. and Albert , A. 1989 . Estimation of error rate in multiple group logistic discrimination. The approximate leaving-one-out method . Communications in Statistics-Theory and Methods , 18 : 2989 – 3007 .
   Web of Science ®Google Scholar
• Lindsey , J. K. 1989 . The analysis of categorical data using GLIM , New York : Springer-Verlag .
   Google Scholar
• McCullagh , P. 1980 . Regression models for ordinal data (with discussion) . Journal of the Royal Statistical Socieq, Series B , 42 : 109 – 142 .
   Google Scholar
• McCullagh , P. and Nelder , J. A. 1989 . Generalized Linear Models , New York : Chapman & Hall . 2nd ed
   Google Scholar
• Numerical Algorithms Group . 1991 . NAG Manual Mark 15 , Oxford : Numerical Algorithms Group .
   Google Scholar
• Press , S. J. and Wilson , S. 1978 . Choosing between logistic regression and discriminant analysis . Journal of the American Statistical Association , 73 : 699 – 705 .
   Web of Science ®Google Scholar
• Rudolfer , S. M. , Watson , P. C. , Abramowitz , M. and Stegun , I. A. 1992 . “ Table Erratum: Formula 26.3.16 ” . In Handbook of mathematical functions with formulas, graphs and mathematical tables , New York : Wiley . 1964. Mathematics of Computation, 59, 727
   Google Scholar
• Rudolfer , S. M. and Watson , P. C. 1993 . Evaluation of orthant probabilities for singular bi- and trivariate normal distributions. . J. Statist. Compur. Simul. , 48 : 219 – 232 .
   Web of Science ®Google Scholar
• Walker , S. H. and Duncan , D. B. 1967 . Estimation of the probability of an event as a function of several independent variables . Biometrika , 54 : 167 – 179 .
   PubMed Web of Science ®Google Scholar
• Watson , P. C. 1992 . Classification properties of ordinal logistic regression , England : University of Manchester . Ph.D. Thesis
   Google Scholar
• Webster , K. M. 1989 . Influence of data generation technique on simulation studies of classification procedures. , Canada : University of Western Ontario . M.Sc. Thesis
   Google Scholar
• Wilde , C. 1989 . Unpublished remarks during invited presentation , Department of Epidemiology and Biostatistics, University of Western Ontario .
   Google Scholar