Application of ridge regression when the model is inherently imperfect: a case study of phase equilibrium
A group contribution equation of state model (a complex nonlinear model) was used to describe and predict phase equilibrium data of n-alkanes. The model used is inherently imperfect, as all molecular thermodynamic models. Ridge regression was used to estimate model parameters from experimental data, and the results are compared with those achieved by ordinary least squares. Three examples are discussed. The first one demonstrates that the prediction based on ridge estimated parameters is much better than that by the OLS estimated parameters, and even slightly better than the prediction through OLS parameters estimated from a larger data base. The second example illustrates that the ridge-based parameters surpass OLS estimators in predicting other thermodynamic properties than those used in estimating parameters. The third example is a simulation showing that the mean square relative error (MSRE) function has a distinct change in the function of the k ridge parameter. The examples show that the method may be fruitfully applied to very complex nonlinear models as well. (C) 2004 Elsevier B.V. All rights reserved.
ridge regression phase equilibrium nonlinear models parameter estimation imperfect model