CATANOVA for ordinal variables using orthogonal polynomials with different scoring methods

In the context of categorical data analysis, the CATegorical ANalysis Of Variance (CATANOVA) has been proposed to analyse the scheme variable-factor, both for nominal and ordinal variables. This method is based on the C statistic and allows to test the statistical significance of the tau index using...

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Bibliographic Details
Published in:Journal of applied statistics 2016-10, Vol.43 (13), p.2490-2502
Main Authors: Sarnacchiaro, Pasquale, D'Ambra, Antonello, D'Ambra, Luigi
Format: Article
Language:English
Subjects:
C statistic
CATANOVA
Contingency table
Data processing
doubly ordered non-symmetrical correspondence analysis
Emerson orthogonal polynomials
Goodman-Kruskal τ
Impact analysis
Multidimensional methods
ordinal variable
Polynomials
Scoring
scoring scheme
Similarity
Statistical data
Statistical tests
Statistics
Variables
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Summary:In the context of categorical data analysis, the CATegorical ANalysis Of Variance (CATANOVA) has been proposed to analyse the scheme variable-factor, both for nominal and ordinal variables. This method is based on the C statistic and allows to test the statistical significance of the tau index using its relationship with the C statistic. Through Emerson orthogonal polynomials (EOP) a useful decomposition of C statistic into bivariate moments (location, dispersion and higher order components) has been developed. In the construction of EOP the categories are replaced by scores, typically natural scores. In the paper, we provide an overview of the main scoring schemes focusing on the advantages and the statistical properties; we pay special attention to the impact of the chosen scores on the C statistic of CATANOVA and the graphical representations of doubly ordered non-symmetrical correspondence analysis. Through a real data example, we show the impact of the scoring schemes and we consider the RV and multidimensional scaling as tools to measure similarity among the results achieved with each method.
ISSN:0266-4763
1360-0532
DOI:10.1080/02664763.2016.1184627