Multivariate Regression

Large set of diagnostics available, including Studentized residuals, COVRATIO, DFFITS, DFBETAS, Cook's distance, leverage, component + residual plots

  • Ridge Regression
  • Principal Components Regression (PCR)
  • Partial Least Squares Regression (PLSR)

PLSR and PCR are the two most widely used regression methods in Chemometrics.  Each can handle datasets with high amounts of collinearity among the variables, and can handle the case in multivariate calibration where there are more variables than
observations. PCR is perhaps the better understood technique from a statistical view, but PLSR is probably used more as it tends to produce a good model using fewer factors than PCR. Its statistical properties are not currently well understood, so there
are very few ways of testing how good a model is, or confidence limits for regression parameters. Practical model testing involves either internal cross-validation, or testing the model with a separate validation set. Chemetrica supports both options for PCR
and PLSR.