A statistical framework for multivariate latent variable regression methods based on maximum likelihood

Journal of Chemometrics

Volumn 13, Issue 1, 1999, Pages 49-65

  Burnham, Alison J ^a   Macgregor, John F ^a   Viveros, Roman ^b  

^a MCMASTER UNIVERSITY   (Canada)

^b MCMASTER UNIVERSITY   (Canada)

Author keywords

Canonical co ordinate regression; Continuum regression; Latent variable models; Maximum likelihood; Multivariate regression; Partial least squares; Principal component regression; Reduced rank regression; SIMPLS

Indexed keywords

LEAST SQUARES APPROXIMATIONS; MAXIMUM LIKELIHOOD ESTIMATION; PRINCIPAL COMPONENT ANALYSIS; REGRESSION ANALYSIS;

CANONICAL CO-ORDINATE REGRESSION; CONTINUUM REGRESSION; LATENT VARIABLE MODELING; MA XIMUM LIKELIHOODS; MAXIMUM-LIKELIHOOD; MULTIVARIATE REGRESSION; PARTIAL LEAST-SQUARES; PRINCIPAL COMPONENT REGRESSION; PRINCIPAL COMPONENTS; REDUCED RANK REGRESSION; SIMPLS;

RANDOM ERRORS;

EID: 0002557296     PISSN: 08869383     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-128X(199901/02)13:1<49::AID-CEM531>3.0.CO;2-K     Document Type: Article

References (21)

1. A. J. Burnham, J. F. MacGregor and R. Viveros, Chemometrics Intell. Lab. Syst. submitted.
2. P. Geladi and B. R. Kowalski, Anal. Chim. Acta, 185, 1-17 (1986).
3. P. Nomikos and J. F. MacGregor, Chemometrics Intell. Lab. Syst. 30, 97-108 (1995).
4. S. de Jong and A. Phatak, in Recent Advances in Total Least Squares Techniques and Errors-in-Variables Modelling, ed. by S. Van Huffel, pp. 25-36, SIAM, New York (1997).
5. K. V. Mardia, J. T. Kent and J. M. Bibby, Multivariate Analysis, Academic Press, London (1979).
6. L. J. Gleser, Chemometrics Intell. Lab. Syst. 10, 45-57 (1991).
7. L. J. Gleser, Ann. Statist. 9, 24-44 (1981).
8. L. Breiman and J. H. Friedman, J. R. Statist. Soc. B, 59, 3-54 (1997).
9. I. E. Frank and J. H. Friedman, Technometrics, 35, 109-148 (1993).
10. H. Schmidli, Chemometrics Intell. Lab. Syst. 37, 125-134 (1997).
11. A. Höskuldsson, J. Chemometrics, 2, 211-228 (1988).
12. P. H. Garthwaite, J. Am. Statist. Assoc. 89, 122-127 (1994).
13. R. Manne, Chemometrics Intell. Lab. Syst. 2, 187-197 (1987).
14. A. Phatak and S. de Jong, J. Chemometrics, 11, 311-338 (1997).
15. S. de Jong, Chemometrics Intell. Lab. Syst. 18, 251-263 (1993).
16. R. Brooks and M. Stone, J. Am. Statist. Assoc. 89, 1374-1377 (1994).
17. A. J. Burnham, R. Viveros and J. F. MacGregor, J. Chemometrics, 10, 31-45 (1996).
18. S. de Jong and H. A. L. Kiers, Chemometrics Intell. Lab. Syst. 14, 155-164 (1992).
19. P. D. Wentzell, D. T. Andrews and B. R. Kowalski, Anal. Chem. 69, 2299-2311 (1997).
20. P. McCullough and J. A. Nelder, Generalized Linear Models, 2nd edn, pp. 254-255, Chapman and Hall, London (1989).
21. J. R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, Wiley, Chichester (1988).