A comparison of multiway regression and scaling methods

Recent years have seen an increase in the number of regression problems for which the predictor and/or response arrays have orders higher than two, i.e. multiway data. Examples are found in, e.g. industrial batch process analysis, chemical calibration using second-order instrumentation and quantitative structure–activity relationships (QSAR). As these types of problems increase in complexity in terms of both the dimensions and the underlying structures of the data sets, the number of options with respect to different types of scaling and regression models also increases. In this article, three methods for multiway regression are compared: unfold partial least squares (PLS), multilinear PLS and multiway covariates regression (MCovR). All three methods differ either in the structural model imposed on the data or the way the model components are calculated. Three methods of scaling multiway arrays are also compared, along with the option of applying no scaling. Three data sets drawn from industrial processes are used in the comparison. The general conclusion is that the type of data and scaling used is more important than the type of regression model used in terms of predictive ability. The models do differ, however, in terms of interpretability.