Standard Article

Reduced Rank Regression

  1. J. Edward Jackson

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a10078

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Jackson, J. E. 2005. Reduced Rank Regression. Encyclopedia of Biostatistics. 7.

Author Information

  1. Rochester, NY, USA

Publication History

  1. Published Online: 15 JUL 2005

Abstract

Problems can arise in multiple regression when the predictor variables are highly correlated. These include inflation of standard errors of the regression coefficients and ill-conditioned covariance matrices of the predictors. Historically, stepwise regression and ridge regression have been employed in these situations. With the advent of more powerful computers, it has become a common practice to obtain the principal components of the predictors variables and use them as predictors. However, there is no guarantee that the largest components will be good predictors. Latent root regression is a possible alternative in which the response variable is included in the principal components solution. Two newer techniques are Partial Least Squares Regression and Maximum Redundancy, both of which use the relationships between the predictors and the responses in obtaining a solution and both can handle the case of multiple responses.

Keywords:

  • multiple regression;
  • principal component analysis;
  • ridge regression;
  • latent root regression;
  • partial least squares regression;
  • maximum redundancy