Features of the Polynomial Biplot for Ordered Contingency Tables

For more than 20 years, variants of correspondence analysis have arisen that accommodate for the structure ordered categorical variables using orthogonal polynomials. When visual display from this is biplot, projections linking origin to standard coordinate each category a common feature. In case when column variable, say, consists categories, biplot can be constructed so their determined polynomials which require set priori scores reflect categories. first two are used construct they produce configuration coordinates appear parabolic in shape. This article verifies exact nature relationship and examines various features points. Particular emphasis given focus, vertex, intercepts directrix we also briefly examine impact choosing different on these features. The R function, parabola.exe(), perform calculates included as supplementary material article. Supplementary files available online.