A comparison of methods for analysing regression models with both spectral and designed variables

In many situations one performs designed experiments to find the relationship between a set of explanatory variables and one or more responses. Often there are other factors that influence the results in addition to the factors that are included in the design. To obtain information about these so-called nuisance factors, one can sometimes measure them using spectroscopic methods. The question then is how to analyze this kind of data, i.e. a combination of an orthogonal design matrix and a spectroscopic matrix with hundreds of highly collinear variables. In this paper we introduce a method that is an iterative combination of partial least squares (PLS) and ordinary least squares (OLS) and compare its performance with other methods such as direct PLS, OLS and a combination of principal component analysis and least squares. The methods are compared using two real data sets and using simulated data. The results show that the incorporation of external information from spectroscopic measurements gives more information from the experiment and lower variance in the parameter estimates. We also find that the introduced algorithm separates the information from the spectral and design matrices in a nice way. It also has some advantages over PLS in showing lower bias and being less influenced by the relative weighting of the design and spectroscopic variables. Copyright (C) 2005 John Wiley & Sons, Ltd.