Reduced-rank vector generalized linear models

Statistical Modeling

Volumn 3, Issue 1, 2003, Pages 15-41

  Yee, Thomas ^a   Hastie, Trevor ^b  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b STANFORD UNIVERSITY   (United States)

Author keywords

categorical data analysis; iteratively reweighted least squares; linear predictors; multinomial logit model; reduced rank regression; stereotype model; vector generalized linear models

Indexed keywords

EID: 84993729357     PISSN: 1471082X     EISSN: None     Source Type: Journal    
DOI: 10.1191/1471082X03st045oa     Document Type: Article

References (38)

1. Ahn S., Reinsel G.C. (1988) Nested reduced-rank autoregressive models for multiple time series. Journal of the American Statistical Association, 83, 849-856.
2. Aitkin M., Anderson D., Francis B., Hinde J. (1989) Statistical Modelling in GLIM. Oxford: Clarendon Press.
3. Akaike H. (1974) A new look at the statistical model identification. IEEE Transactions on Automatic Control, AC-19, 716-723.
4. Anderson J.A. (1984) Regression and ordered categorical variables. Journal of the Royal Statistical Society B, 46, 1-30 (With discussion.)
5. Anderson T.W. (1951) Estimating linear restrictions on regression coefficients for multivariate normal distributions. Annals of Mathematical Statistics, 22, 327-351. [Correction (1980) Annals of Mathematical Statistics, 8, 1400-1400].
6. Benjamin M.A., Rigby R.A., Stasinopoulos M.D. (1998) Fitting non-Gaussian time series models. In Payne R., Green P.J. eds. Proceedings in Computational Statistics COMPSTAT 1998. Heidelberg: Physica, 191-196.
7. Denis J-B, Gower J.C. (1996) Asymptotic confidence regions for biadditive models: interpreting genotype-environment interactions. Applied Statistics, 45, 479-493.
8. Eckart C., Young G. (1936) The approximation of one matrix by one of lower rank. Psychometrika, 1, 211-218.
9. de Falguerolles A., Francis B. (1995) Fitting bilinear models in GLIM. GLIM Newsletter, 25, 9-20.
10. Friedman J.H., Stuetzle W. (1981) Projection pursuit regression. Journal of the American Statistical Association, 76, 817-823.
11. Gabriel, K.R. (1998) Generalised bilinear regression. Biometrika, 85, 689-700.
12. Gabriel K.R., Zamir S. (1979) Lower rank approximation of matrices by least squares with any choice of weights. Technometrics, 21, 489-498.
13. Goodman L.A. (1981) Association models and canonical correlation in the analysis of cross-classifications having ordered categories. Journal of the American Statistical Association, 76, 320-334.
14. Gower J.C., Hand D.J. (1996) Biplots. London: Chapman & Hall.
15. Green P.J. (1984) Iteratively reweighted least squares for maximum likelihood estimation, and some robust and resistant alternative. Journal of the Royal Statistical Society B, 46, 149-192 (With discussion.)
16. Greenland S. (1994) Alternative models for ordinal logistic regression. Statistics in Medicine, 13, 1665-1677.
17. Guisan A., Harrell F.E. (2000) Ordinal response regression models in ecology. Journal of Vegetation Science, 11, 617-626.
18. Haberman S.J. (1981) Tests for independence in two-way contingency tables based on canonical correlation and on linear-by-linear interactions. Annals of Statistics, 9, 1178-1186.
19. Hastie T.J., Tibshirani R.J. (1990) Generalized Additive Model. London: Chapman and Hall.
20. Hastie T., Tibshirani R., Buja A. (1994) Flexible discriminant analysis by optimal scoring. Journal of the American Statistical Association, 89, 1255-1270.
21. Hastie T.J., Tibshirani R.J., Friedman J.H. (2001) Elements of Statistical Learning: Determining, Inference and Prediction. New York: Springer.
22. Izenman A.J. (1975) Reduced-rank regression for the multivariate linear model. Journal of Multivariate Analysis, 5, 248-264.
23. Jørgensen B. (1997) The Theory of Dispersion Models. London: Chapman & Hall.
24. Li W.K. (1994) Time series models based on generalized linear models: some further results. Biometrics, 50, 506-511.
25. McCullagh P. (1980) Regression models for ordinal data. Journal of the Royal Statistical Society B, 42, 109-142.
26. McCullagh P., Nelder J.A. (1989) Generalized Linear Models, 2nd edn. London: Chapman & Hall.
27. Pearson E.S., Hartley H.O. (1972) Biometrika Tables for Statisticians, Vol. II. Cambridge: Cambridge University Press.
28. Reinsel G.C., Velu R.P. (1998) Multivariate Reduced-Rank Regression: Theory and Applications. New York: Springer.
29. Richards F.S.G. (1961) A method of maximum-likelihood estimation. Journal of the Royal Statistical Society B, 23, 469-475.
30. Schmidli H. (1995) Reduced Rank Regression: With Applications to Quantitative Structure-Activity Relationships. Heidelberg: Physica.
31. Seber G.A.F., Wild C.J. (1989) Nonlinear Regression. New York: Wiley.
32. Smyth G.K. (1996) Partitioned algorithms for maximum likelihood and other nonlinear estimation. Statistics and Computing, 6, 201-216.
33. ter Braak C.J.F., Looman C.W.N. (1994) Biplots in reduced-rank regression. Biometrical Journal, 36, 983-1003.
34. ter Braak C.J.F., Prentice I.C. (1988) A theory of gradient analysis. Advances in Ecological Research, 18, 271-317.
35. Thompson R., Baker R.J. (1981) Composite link functions in generalized linear models. Applied Statistics, 30, 125-131.
36. Weisberg S. (2002) Dimension reduction regression in R. Journal of Statistical Software, 7.
37. Wold H., Lyttkens E. (1969) Nonlinear iterative partial least squares (NIPALS) estimation procedures. Bulletin of the International Statistics Institute, 43, 29-51.
38. Yee T.W., Wild C.J. (1996) Vector generalized additive models. Journal of the Royal Statistical Society B, 58, 481-493.