# 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

References:

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.