Logistic biplot for nominal data

Julio César Hernández-Sánchez () and José Luis Vicente-Villardón
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Julio César Hernández-Sánchez: Spanish Statistical Office
José Luis Vicente-Villardón: University of Salamanca

Advances in Data Analysis and Classification, 2017, vol. 11, issue 2, No 5, 307-326

Abstract: Abstract Classical biplot methods allow for the simultaneous representation of individuals (rows) and variables (columns) of a data matrix. For binary data, logistic biplots have been recently developed. When data are nominal, both classical and binary logistic biplots are not adequate and techniques such as multiple correspondence analysis (MCA), latent trait analysis (LTA) or item response theory (IRT) for nominal items should be used instead. In this paper we extend the binary logistic biplot to nominal data. The resulting method is termed “nominal logistic biplot”(NLB), although the variables are represented as convex prediction regions rather than vectors. Using the methods from computational geometry, the set of prediction regions is converted to a set of points in such a way that the prediction for each individual is established by its closest “category point”. Then interpretation is based on distances rather than on projections. We study the geometry of such a representation and construct computational algorithms for the estimation of parameters and the calculation of prediction regions. Nominal logistic biplots extend both MCA and LTA in the sense that they give a graphical representation for LTA similar to the one obtained in MCA.

Keywords: Biplot; Categorical variables; Logistic responses; Latent traits; Computational geometry; Inverse Voronoi problem; 62H25 Factor analysis and principal components; correspondence analysis; 62H30 Classification and discrimination; cluster analysis; 62H99 None of the above; but in this section (multivariate analysis); 68U05 computer graphics; computational geometry (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s11634-016-0249-7

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