The infamous Måge plot

Some multiblock regression Methods (such as SO-PLS and PO-PLS) allow for different numbers of components in each block. There are two strategies for selecting the numbers of components for these models: sequential and global. With the sequential strategy, the number of components to use for the first block is determined before the second block is introduced, and so on. With the global strategy, all blocks are taken into account from the beginning. Models With all combinations of components from each block are tested, and the combination giving the minimum prediction error is selected. Often, several combinations have approximately equally good prediction ability, and in such cases it is important to also take the total number of components into account. The Måge plot is a valuable tool for evaluating the models and selecting the optimal numbers of components.

The Måge plot shows the prediction error for each combination of components, as a function of the total number of components. From this perspective, it is possible to decide the total dimensionality of the system and the individual dimensionalities of each block at the same time. It is also easy to identify models that are indistinguishable from a prediction point of view. In the figure below, it is obvious that the total complexity is three. The two most predictive components are found in the first block,  and the predictive ability is almost equal whether the third component is taken from the second or third block (combination “210” and “201” are almost equal).

Matlab code for making the plot can be found here: MagePlot




Måge, I., Mevik, B. H., & Næs, T. (2008). Regression models with process variables and parallel blocks of raw material measurements. Journal of Chemometrics, 22(8), 443–456.

Næs, T., Tomic, O., Afseth, N. K., Segtnan, V., & Måge, I. (2013). Multi-block regression based on combinations of orthogonalisation, PLS-regression and canonical correlation analysis. Chemometrics and Intelligent Laboratory Systems, 124, 32–42.

Biancolillo, A., Måge, I., & Næs, T. (2015). Combining SO-PLS and linear discriminant analysis for multi-block classification. Chemometrics and Intelligent Laboratory Systems, 141, 58–67.


14th AgroStat symposium

The 2016 AgroStat symposium was held at Nestlé Research Center in Lausanne, Switzerland on March 21-24. It was professionally organized and had a lot of high quality scientific contributions in chemometrics, sensometrics, big data and risk & process. Most of the presentations and all posters were in English, while a few exceptions were French. The first day was reserved for a variety of workshops. There were around 120 participants, mostly French and Swiss, but also from Canada, Great Britain, Scandinavia, Portugal, Italy, USA, Germany and some other countries.

From Nofima Kristian Hovde Liland contributed with a poster describing the R package MatrixCorrelation and the newly developed Similarity of Matrices Index.


Presentations, posters and short papers are available from:

Multiblock classification: SO-PLS and LDA

Combining SO-PLS and linear discriminant analysis for multi-block classification

allessandraThe “Combining SO-PLS and linear discriminant analysis for multi-block classification”, written by Alessandra Biancolillo, Ingrid Måge and Tormod Næs was recently published in Chemometrics and Intelligent Laboratory systems. This is the first paper by Ph.D student Alessandra. Congratulations!


The aim of the present work is to extend the Sequentially Orthogonalized-Partial Least Squares (SO-PLS) regression method, usually used for continuous output, to situations where classification is the main purpose. For this reason SO-PLS discriminant analysis will be compared with other commonly used techniques such as Partial Least Squares-Discriminant Analysis (PLS-DA) and Multiblock-Partial Least Squares Discriminant Analysis (MB-PLS-DA). In particular we will focus on how multiblock strategies can give better discrimination than by analyzing the individual blocks. We will also show that SO-PLS discriminant analysis yields some valuable interpretation tools that give additional insight into the data. We will introduce some new ways to represent the information, taking into account both interpretation and predictive aspects.

More details

Full reference:

Biancolillo, A., Måge, I., & Næs, T. (2015). Combining SO-PLS and linear discriminant analysis for multi-block classification. Chemometrics and Intelligent Laboratory Systems, 141(0), 58-67.

Available software

The software used in this paper, can be downloaded from software&downloads