Manté, C.; Cornu, S.; Borschneck, D.; Mocuta, C.; van den Bogaert, R. Detecting the Guttman effect with the help of ordinal correspondence analysis in synchrotron X-ray diffraction data analysis. (English) Zbl 07484695 J. Appl. Stat. 49, No. 2, 291-316 (2022). Summary: We propose a method for detecting a Guttman effect in a complete disjunctive table \(\mathbf{U}\) with \(Q\) questions. Since such an investigation is a nonsense when the \(Q\) variables are independent, we reuse a previous unpublished work about the chi-squared independence test for Burt’s tables. Then, we introduce a two-steps method consisting in plugging the first singular vector from a preliminary Correspondence Analysis (CA) of \(\mathbf{U}\) as a score \(x\) into a subsequent singly-ordered Ordinal Correspondence Analysis (OCA) of \(\mathbf{U}\). OCA mainly consists in completing \(x\) by a sequence of orthogonal polynomials superseding the classical factors of CA. As a consequence, in presence of a pure Guttman effect, we should in principle have that the second singular vector coincide with the polynomial of degree 2, etc. The hybrid decomposition of the Pearson chi-squared statistics (resulting from OCA) used in association with permutation tests makes possible to reveal such relationships, i.e. the presence of a Guttman effect in the structure of \(\mathbf{U}\), and to determine its degree – with an accuracy depending on the signal to noise ratio. The proposed method is successively tested on artificial data (more or less noisy), a well-known benchmark, and synchrotron X-ray diffraction data of soil samples. MSC: 62-XX Statistics Keywords:ordinal correspondence analysis; detrended correspondence analysis; randomization; eigenvalues; orthogonal polynomials; synchrotron X-rays diffraction Software:Mathematica; aspect; Canoco PDFBibTeX XMLCite \textit{C. Manté} et al., J. Appl. 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