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Modelling Trends in Ordered Correspondence Analysis Using Orthogonal Polynomials.

Rosaria Lombardo1, Eric J Beh2, Pieter M Kroonenberg3

  • 1Economics Department, Second University of Naples, Corso Gran Priorato di Malta, 81043 , Capua, CE, Italy. rosaria.lombardo@unina2.it.

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Summary
This summary is machine-generated.

This study introduces Emerson polynomials for analyzing ordered contingency tables, enhancing interpretation through moment-based decompositions and a novel polynomial biplot visualization.

Keywords:
bivariate moment decompositiongeneralized singular value decompositionhybrid decompositionpolynomial biplotssymmetric and non-symmetric correspondence analysis

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Area of Science:

  • Statistics
  • Data Analysis

Background:

  • Correspondence analysis is a statistical method for analyzing categorical data.
  • Ordered contingency tables require specialized decomposition techniques.
  • Traditional methods often rely on singular vectors, which may limit interpretability.

Purpose of the Study:

  • To present two novel decomposition methods for correspondence analysis of ordered contingency tables: bivariate moment decomposition and hybrid decomposition.
  • To introduce and explain the properties of Emerson polynomials as bases for these decompositions.
  • To propose a new graphical tool, the polynomial biplot, for enhanced data interpretation.

Main Methods:

  • Utilizing orthogonal polynomials, specifically Emerson polynomials, as bases for row and/or column spaces.
  • Applying bivariate moment and hybrid decomposition techniques to ordered contingency tables.
  • Developing a polynomial biplot for visualizing the results of these decompositions.

Main Results:

  • Emerson polynomials provide a framework for interpreting ordered categorical data through moments (linear, quadratic, higher-order).
  • The proposed decompositions offer an alternative to singular vector-based methods.
  • The polynomial biplot facilitates a more nuanced understanding of the relationships within the data.

Conclusions:

  • The use of Emerson polynomials in correspondence analysis enhances the interpretation of ordered contingency tables.
  • The bivariate moment and hybrid decompositions, coupled with the polynomial biplot, offer valuable insights into categorical data structures.