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PLS beta regression. (Régression bêta PLS.) (French. English summary) Zbl 1316.62179

Summary: Many responses, for instance experimental results, yields or economic indices, can be naturally expressed as rates or proportions whose values must lie between zero and one or between any two given values. The Beta regression often allows to model these data accurately since the shapes of the densities of Beta laws are very versatile. Yet, as any of the usual regression model, it cannot be applied safely in case of multicollinearity and not at all when the model matrix is rectangular. These situations are frequently found from chemistry to medicine through economics or marketing. To circumvent this difficulty, we derived an extension of PLS regression to Beta regression models. It, as well as several other tools, such as cross validation or bootstrap techniques, is available for the R language in the plsRbeta package.

MSC:

62P30 Applications of statistics in engineering and industry; control charts
62F40 Bootstrap, jackknife and other resampling methods

Software:

R; plsRbeta
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