Multivariate Analysis of Mixed Data: The R Package PCAmixdata

TL;DR

This paper introduces the R package PCAmixdata, which extends multivariate analysis techniques to mixed numerical and categorical data, facilitating data exploration, description, and visualization.

Contribution

It provides a unified mathematical framework and detailed algorithms for principal component analysis, varimax rotation, and multiple factor analysis for mixed data types.

Findings

Effective analysis of real-world mixed data sets demonstrated

Enhanced interpretability of multivariate analysis results

User-friendly tools for graphical and numerical data exploration

Abstract

Mixed data arise when observations are described by a mixture of numerical and categorical variables. The R package PCAmixdata extends to this type of data standard multivariate analysis methods which allow description, exploration and visualization of the data. The key techniques/methods included in the package are principal component analysis for mixed data (PCAmix), varimax-like orthogonal rotation for PCAmix, and multiple factor analysis for mixed multi-table data. This paper proposes a unified mathematical presentation of the different methods with common notations, as well as providing a summarised presentation of the three algorithms, with details to help the user understand graphical and numerical outputs of the corresponding R functions. This then allows the user to easily provide relevant interpretations of the results obtained. The three main methods are illustrated on a real dataset composed of four data tables characterizing living conditions in different municipalities in the Gironde region of southwest France.