## The 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.

A matlab function for creating the plot can be found here: MagePlot