2013/09/21 by Julio César Hernández Sánchez, Sánchez, Julio César Hernández, José Luis Vicente Villardón +2 · 1 citation
Agricultural and Biological Sciences · Chemistry · Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #Sensory Analysis and Statistical Methods #Spectroscopy and Chemometric Analyses #Statistical Methods and Applications #stat.ME
paper · pdf · doi:10.48550/arxiv.1309.5486
22 pages, 8 figures
arxiv created 2013/09/21 · openalex publication_date 2013/09/21 · arxiv updated 2013/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, linear or even binary logistic biplots are not adequate and techniques as Multiple Correspondence Analysis (MCA), Latent Trait Analysis (LTA) or Item Response Theory 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, 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 gives a graphical representation for LTA similar to the one obtained in MCA.