Pseudo-degrees of freedom for complex predictive models: The example of partial least squares
This paper considers models that are relatively complex considering the extent of the calibration data. Such data frequently arise in chemometric applications, near-infrared spectroscopy (NIRS) being a well-known example. Commonly used models are multiple linear regression (MLR) with variable selection or partial least squares (PLS) regression. The concept of degrees of freedom is undefined for such models; this paper proposes a definition for pseudo-degrees of freedom (PDF) based on predictive performance and an analogy with the standard linear model. The generalization is intended for all models which assume independent and identically distributed errors. Pseudo-degrees of freedom are very easily calculated from ordinary and cross-validation residuals. An example from a real-life NIRS application is given to illustrate the new concept. Copyright (C) 1999 John Wiley & Sons, Ltd.
degrees of freedom pls nirs cross-validation mean squared error of prediction non-linear models model selection