Neural networks and logistic regression: Part I

Computational Statistics and Data Analysis

Volumn 21, Issue 6, 1996, Pages 661-682

  Schumacher, Martin ^a   Roßner, Reinhard ^a   Vach, Werner ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Feed forward neural networks; Logistic regression model; Model selection; Newton Raphson algorithm; Overfitting; Survival data

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; FEEDFORWARD NEURAL NETWORKS; MATHEMATICAL MODELS; REGRESSION ANALYSIS;

LOGISTIC REGRESSION; MODEL SELECTION; NEWTON-RAPHSON ALGORITHM;

STATISTICAL METHODS;

LOGISTIC REGRESSION; NEURAL NETWORK; REGRESSION MODEL;

EID: 0030159465     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-9473(95)00032-1     Document Type: Article

References (71)

1. Akaike, H., Fitting autoregressive models for prediction, Ann. Inst. Statist. Math., 21 (1969) 243-247.
2. Amari, S.J., Mathematical methods in neurocomputing, in: O.E. Barndorff-Nielsen, et al. (Eds.) Chaos and networks-statistical and probabilistic aspects (Chapman and Hall, London; 1993).
3. Anderson, J.A., Regression and ordered categorical variables (with discussion), J. Roy. Statist. Soc. B, 46 (1991) 1-30.
4. Andersen, P.K., O. Borgan, R.D. Gill and N. Keiding, Statistical methods based on counting processes, Springer Series in Statistics (Springer, New York, 1993).
5. Barron, A.R., Complexity regularization with application to artificial neural networks, in: G. Roussas (Ed.), Nonparametric functional estimation and related topics (Kluwer Academic Publishers, Amsterdam, 1991).
6. Barron, A.R. and R.L. Barron, Statistical learning networks: a unifying view, in: E. Wegman (Ed.), Computing science and statistics: Proc. 20th Symp. Interface (American Statistical Association, Washington 1988)192-203.
7. Baxt, W. G., Use of an artificial neural network for the diagnosis of myocardial infarction, Ann. Internal Med., 115 (1991) 843-848.
8. Bock, D.R., Multivariate statistical methods in behavioral research (McGraw-Hill, New York; 1975).
9. Breiman, L., J.H. Friedman, R.A. Olshen and C.J. Stone, Classification and regression trees, (Wadsworth and Brooks/Cole, Monterey; 1984).
10. Chamberlain, G., Asymptotic efficiency in estimation with conditional moment restrictions, J. Econometrics, 34 (1987) 305-324.
11. Cheng, B. and D.M. Titterington, Neural networks: A review from a statistical perspective (with discussion), Statist. Sci., 9 (1994) 2-54.
12. Cherkassky, V. and F. Mulier, Statistical and neural network techniques for nonparametric regression, in: P. Cheeseman and R.W. Oldford (Eds.), Selecting models from data: AI and statistics IV (Springer, New York, 1994) 383-392.
13. Cox, D.R., Analysis of binary data (Methuen, London, 1970).
14. Cox, D.R., Regression models and life tables (with discussion), J. Roy. Statist. Soc. B, 34 (1972) 187-220.
15. Cox, D.R. and E.J. Snell, Analysis of binary data, 2nd ed. (Chapman and Hall, London, 1989).
16. de Jongh, P.J. and T. de Wet, An introduction to neural networks, South African Statist. J., 27 (1993) 103-128.
17. Doksum, K.A. and M. Gasko, On a correspondence between models in binary regression analysis and in survival analysis, Internat. Statist. Rev., 58, (1990) 243-252.
18. Engel, J., Polytomous logistic regression, Statist. Neerlandica 42 (1988) 233-252.
19. Fahrmeir, L. and H. Kaufmann, Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models, Ann. Statist. 13 (1985) 342-368.
20. Fahrmeir, L. and G. Tutz, Multivariate statistical modelling based on generalized linear models (Springer, New York; 1994).
21. Faraggi, D. and R. Simon, A neural network for survival data, Statist. Med., 14 (1995) 73-82.
22. Finney, D.J., The estimation from individual records of the relationship between dose and quantal response, Biometrika 34 (1947) 320-334.
23. Finney, D.J., Probit analysis, 3rd edn. Cambridge Univ. Press, Cambridge, 1971.
24. Fogel, D.B., An information criterion for optimal neural network selection, IEEE Trans. Neural Networks, 2 (1991) 490-497.
25. Friedman, J.H., Multivariate adaptive regression splines (with discussion), Ann. Statist. 19 (1991) 1-141.
26. Gallinari, P., S. Thiria, F. Badran and F. Fogelman-Soulie, On the relations between discriminant analysis and multilayer perceptrons, Neural Networks 4 (1991) 349-360.
27. Geman, S., E. Bienenstock, R. Doursat, Neural networks and the bias/variance dilemma, Neural Comput., 4 (1992) 1-58.
28. Hastie, T.J. and R.J. Tibshirani, Generalized additive models, (Chapman and Hall, London, 1990).
29. Hecht-Nielsen, R., Neurocomputing, (Addison-Wesley, Reading, MA, 1990).
30. Hertz, J.A., A. Krogh and R.G. Palmer, Introduction to the theory of neural computation (Addison Wesley Redwood City, U.S.A. 1991).
31. Hinton, G.E., Connectionist learning procedures, Artif. Intelligence, 40 (1989) 185-234.
32. Hosmer, D.W. and S. Lemeshow, Applied logistic regression, (Wiley New York, 1989).
33. Kalbfleisch, J.D. and R. Prentice, The statistical analysis of failure time data (Wiley, New York, 1980).
34. Kappen, H.J. and J.P. Neijt, Neural network analysis to predict treatment outcome, Ann. Oncology, 4, (Suppl). (1993) 31-34.
35. Kippenhan, J.S., W.W. Barker, S. Pascal, J. Nagel and R. Duara, Evaluation of a neural-network classifier for PET scans of normal and Alzheimer disease subjects, J. Nuclear Med., 33 (1992) 1459-1467.
36. Kree, R., Neural networks: architectures, learning and performance, in: H.H. Bock, W. Lenski and M. Richter (Eds.), Information systems and data analysis (Springer, Berlin, 1994).
37. Kullback, S. and R.A. Leibler, On information and sufficiency, Ann. Math. Statist. 22 (1951) 79-86.
38. Liestøl, K., P.K. Andersen and U. Andersen, Survival analysis and neural nets, Statist. Med., 13 (1994) 1189-1200.
39. McCullagh, P., Regression models for ordinal data (with discussion), J. Roy. Statist. Soc. B, 42 (1980) 109-142.
40. McCullagh, P. and J.A. Nelder, Generalized linear models, 2nd edn. (Chapman and Hall, New York, 1989).
41. McLachlan, G.J., Discriminant analysis and statistical pattern recognition, (Wiley, New York, 1992).
42. Michie, D., D.J. Spiegelhalter and C.C. Taylor, Machine learning, neural and statistical classification (Ellis Horwood, New York, 1994).
43. Miller, A.J., Subset selection in regression (Chapman and Hall, London, 1990).
44. Morgenthaler, S., Least-absolute-deviations fits for generalized linear models, Biometrika, 79 (1992) 767-754.
45. Murtagh, F., Neural networks and related 'massively parallel' methods for statistics: a short overview, Internat. Statist. Rev., 62 (1994) 275-288.
46. Pazos, A., V. Maojo, F. Martin and N. Ezquerra, A neural network approach to assess myocardial infarction, in: Lun et al. (Eds.), Medinfo: 92 (Elsevier, Amsterdam, 1992) 659-663.
47. Pregibon, D., Resistant fits for some commonly used logistic models with medical applications, Biometrics, 38 (1982) 485-498.
48. Prentice, R.L. and L.A. Gloeckler, Regression analysis of grouped survival data with application to breast cancer data, Biometrics, 34 (1978) 57-67.
49. Ravdin, P.M., G.M. Clark, A practical application of neural network analysis for predicting outcome of individual breast cancer patients, Breast Cancer Res. Treatment, 22 (1992) 285-293.
50. Ravdin, P.M., G.M. Clark, S.G. Hilsenbeck, M.A. Owens, P. Vendely and M.R. Pandian, A demonstration that breast cancer recurrence can be predicted by neural network analysis, Breast Cancer Res. Treatment 21 (1992) 47-53.
51. Reddy D.C. and D.R. Korrai, Neural networks for classification of EEG signals, in: Lun et al. (Eds.), Medinfo: 92 (Elsevier Amsterdam, 1992) 653-658.
52. Ripley, B.D., Software for neural networks, Techn. Report (University of Oxford, Oxford, 1993a).
53. Ripley, B.D., Statistical aspects of neural networks, in: O.E. Barndorff-Nielsen et al. (Eds.), Chaos and networks - statistical and probabilistic aspects (Chapman and Hall, London 1993b).
54. Ripley, B.D., Neural networks and flexible regression and discrimination, in: K.V. Mardia (ed.), Statistics and images (Carfax, Abingdon, 1994a).
55. Ripley, B.D., Neural networks and related methods for classification (with discussion), J. Roy. Statist. Soc. B, 56 (1994b) 409-456.
56. Rumelhart, D.E., G.E. Hinton and R.J. Williams, Learning representations by back-propagation errors, Nature, 323 (1986) 533-536.
57. SAS-Institute Inc., SAS/STAT user's guide, Version 6, 4th edn. (SAS-Institute. Inc., Cary, NC, 1989).
58. SAS-Institute Inc., Information on neural network macros (1994).
59. Sauerbrei, W., H. Madjar and H.J. Prömpeler, Development of diagnostic rules based on color Doppler flow signals for differentiation of benign and malignant breast tumors, preprint (1994).
60. Schumacher, M., Point estimation in quantal response models, Biomet. J., 22 (1980) 315-334.
61. Somoza, E. and J.R. Somoza, A neural-network approach to predicting admission in a psychiatric emergency room, Med. Decision Making, 13 (1993) 273-280.
62. Spackman, K.A., Maximum likelihood training of connectionist models: comparison with least squares back-propagation and logistic regression, Proc. 15th Ann. Symp. on Computer Applications in Medical Care, 1991.
63. Statistical Sciences Inc., S-Plus data analysis software, Version 3.x (Statistical Sciences Inc., Seattle, 1991).
64. Thisted, R.A., Elements of statistical computing: numerical computation (Chapman and Hall, New York, 1988).
65. Tu, J.V. and M.R.J. Guerriere, Use of a neural network as a predictive instrument for length of stay in the intensive care unit following cardiac surgery, Comput. Biomed. Res. 26 (1993) 220-229.
66. Vach, W., R. Roßner and M. Schumacher, Neural networks and logistic regression, Part II, Comput. Statist. Data Anal., 21 (1996) 631-649.
67. Weigend, A., D. Rumelhart and B. Huberman, Generalization by weight elimination with application to forecasting, in: Advances in neural information processing III (Morgan Kaufman, Los Altos, CA, 1991).
68. Weinstein, J.N., K.W. Kohn, M.R. Greuer, V.N. Viswanadhan, L.V. Rubinstein, et al., Neural computing in cancer drug development: Predicting mechanism of action. Science, 258 (1992) 447-451.
69. White, H., Artificial neural networks: Approximation and learning theory (Basil Blackwell, Oxford, 1992).
70. Wu, Y., M.L. Giger, K. Doi, C.J. Vyborny, R.A. Schmidt and C.E. Metz, Artificial neural networks in mammography: application to decision making in the diagnosis of breast cancer, Radiology 187 (1993) 81-87.
71. Zell, A., N. Mache, R. Hübner, G. Mamier, M. Vogt et al., Stuttgart neural network simulator; user manual, Version 3.2, Report No. 3/93 (Institute for Parallel and Distributed High Performance Systems, University of Stuttgart, 1993).