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Article Dans Une Revue Journal of Applied Statistics Année : 2020

Detecting the Guttman effect with the help of ordinal correspondence analysis in synchrotron X-ray diffraction data analysis

Résumé

We propose a method for detecting a Guttman effect in a complete disjunctive table 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 Since such an investigation is a nonsense when the Q variables are independent, we reuse a previous unpublished work about the chi-squared independence test for Burt's tables.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 U as a score x into a subsequent singly-ordered Ordinal Correspondence Analysis (OCA) of 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 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.
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Dates et versions

hal-02943227 , version 1 (18-09-2020)

Licence

Paternité - Pas de modifications

Identifiants

Citer

Claude Manté, Sophie S. Cornu, D. Borschneck, C. Mocuta, R. van den Bogaert. Detecting the Guttman effect with the help of ordinal correspondence analysis in synchrotron X-ray diffraction data analysis. Journal of Applied Statistics, 2020, pp.1-26. ⟨10.1080/02664763.2020.1810644⟩. ⟨hal-02943227⟩
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