Partial Least Squares Regression for Binary Responses and Its Associated Biplot Representation
Laura Vicente-González, José Luis Vicente Villardón
Abstract
In this paper, we propose a generalization of Partial Least Squares Regression (PLS-R) for a matrix of several binary responses and a a set of numerical predictors. We call the method Partial Least Squares Binary Logistic Regression (PLS-BLR). That is equivalent to a PLS-2 model for binary responses. Biplot and even triplot graphical representations for visualizing PLS-BLR models are described, and an application to real data is presented. Software packages for the calculation of the main results are also provided. We conclude that the proposed method and its visualization using triplots are powerful tools for the interpretation of the relations among predictors and responses.
Topics & Concepts
Partial least squares regressionBiplotGeneralizationBinary numberRepresentation (politics)Logistic regressionComputer scienceSet (abstract data type)StatisticsRegression analysisLeast-squares function approximationInterpretation (philosophy)VisualizationBinary dataMathematicsArtificial intelligencePattern recognition (psychology)ChemistryBiochemistryGeneArithmeticGenotypePolitical scienceProgramming languageMathematical analysisEstimatorLawPoliticsSpectroscopy and Chemometric AnalysesSensory Analysis and Statistical MethodsAdvanced Statistical Methods and Models