Keywords
partial least squares
dimensionality reduction
análisis de componentes principales
mı́nimos cuadrados parciales
reducción de la dimensionalidad
How to Cite
Abstract
We present and compare principal components regression and partial least squares regression, and their solution to the problem of multicollinearity. We illustrate the use of both techniques, and demonstrate the superiority of partial least squares.
References
Frank, I.E.; Friedman, J.H. (1993) “A statistical view of some chemometrics regression tools”, Technometrics 35:109–148.
Garthwaite, P.H. (1994) “An interpretation of partial least square regression”, Journal of the American Statistical Association 89(425): 122–127.
Helland, I. (1988) “On the structure of partial least squares regression”, Communications in Statistics, Simulation and Computation, 17(2): 581–607.
Hoskulsson, A. (1988) “PLS regression methods”, Chemometrics, 2: 211–228.
Mardia, K.V.; Kent, J.T.; Bibby, J.M. (1997) Multivariate Analysis. Academic Press, London.
Massy, W.F. (1965) “Principal Components Regression in Exploratory Statistical Research”, Journal of the American Statistical Association, 60: 234–246.
Stone, M.; Brooks, R.J. (1990) “Continuum regression: cross-validated sequentially constructed prediction embracing ordinary least squares, partial least squares and principal components regression”, Journal of the Royal Statistical Society 52: 237–269.
Trygg, J. (2001) Parsimonious Multivariate Models. PhD Thesis, Umea University, Research Group for Chemometrics Department of Chemistry.
Wold, H. (1975) “Soft modeling by latent variables; the nonlinear iterative partial least square approach”, Perspectives in Probability and Statistics, Papers in Honour of M.S. Bartlett.