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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.
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