Modeling with latent variables

There are three common ways of modeling data using the latent variables approach:

• Principal component regression (PCR ) which generates the latent variables from the independent variables X. Selected latent variables are then used to fit the dependent variables by multiple linear regression. PCR calculations can be based on the singular value decomposition (SVD) of the matrix X'X.
• Maximum redundancy analysis (MRA) generates the latent variables from the dependent variables Y. This approach seeks directions in the factor space with the most variation in the dependent (response) variables. Predictive results are often not very accurate. MRA calculations are based on the SVD of the matrix Y'Y.
• Partial least squares regression (PLS) attempts to set up a model using two sets of latent variables, one set is based on the independent variables X, the other is calculated from the dependent variables Y. The PLS approach usually yields the best results of these three methods. PLS calculations can be based on the SVD of the matrix X'Y.