Abstract
In this article, we present PCovR, an R package for performing principal covariates regression (PCovR; De Jong and Kiers 1992). PCovR was developed for analyzing regression data with many and/or highly collinear predictor variables. The method simultaneously reduces the predictor variables to a limited number of components and regresses the criterion variables on these components. The flexibility, interpretational advantages, and computational simplicity of PCovR make the method stand out between many other regression methods. The PCovR package offers data preprocessing options, new model selection procedures, and several component rotation strategies, some of which were not available in R up till now. The use and usefulness of the package is illustrated with a real dataset, called psychiatrists.
Highlights
Principal covariates regression (PCovR) was proposed by De Jong and Kiers (1992) to deal with the interpretational and technical problems that are often encountered when applying linear regression analysis using a relatively high number of predictor variables – say, higher than 10
In PCovR, the predictor variables are reduced to a limited number of components and the criterion variables are regressed on these components
The components are linear combinations of the predictor variables that are constructed in such a way that they summarize the predictor variables as good as possible, but at the same time allow for an optimal prediction of the criterion variables
Summary
Principal covariates regression (PCovR) was proposed by De Jong and Kiers (1992) to deal with the interpretational and technical problems that are often encountered when applying linear regression analysis using a relatively high number of predictor variables – say, higher than 10. As the user may choose the extent to which both aspects (good summary of predictors, optimal prediction of criteria) play a role when constructing the components, PCovR is a flexible approach that subsumes principal components regression (Jolliffe 1982) and reduced-rank regression (Izenman 1975) as special cases. As is often the case with component techniques, the components have rotational freedom (including reflectional and permutational freedom) which can be exploited to enhance the interpretability of the PCovR parameters. Another attractive feature of PCovR is that a closed form solution exists, as optimal model estimates can be obtained by conducting one single eigenvalue decomposition. We will describe the usage of the PCovR package, by giving a step-by-step overview of the available options
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