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Confidence regions for simple correspondence analysis using the Cressie-Read family of divergence statistics


 
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1. Title Title of document Confidence regions for simple correspondence analysis using the Cressie-Read family of divergence statistics
 
2. Creator Author's name, affiliation, country Eric Beh; University of Wollongong, Australia and Stellenbosch University, South Africa; Australia
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Confidence circle; confidence ellipse; correspondence analysis; log-ratio analysis; eccentricity; semi-major axes
 
4. Description Abstract

When examining the association between symmetrically associated categorical variables, correspondence analysis provides a visual means of identifying the structure of this association. An important and sometimes overlooked feature that can help the analyst determine whether those categories that provide a statistically significant contribution to the association is the confidence region. When constructing these regions, correspondence analysis traditionally (but not always) considers Pearson’s chi-squared statistic as the core measure of association between the variables. Such a statistic is a special case of the Cressie-Read family of divergence statistics as is the log-likelihood ratio statistic, Freedman-Tukey statistic, and other such measures. Therefore, this paper will consider the construction of confidence regions in correspondence analysis where this family of divergence statistics is used as the measure of association. Doing so provides a means of simply constructing confidence regions for each category of a contingency table and allows for such regions to be constructed when log-ratio analysis (LRA) or the Hellinger distance decomposition (HDD) method is applied to the contingency table.
 
5. Publisher Organizing agency, location Coordinamento SIBA - Università del Salento
 
6. Contributor Sponsor(s) NA
 
7. Date (YYYY-MM-DD) 2023-10-18
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format pdf
 
10. Identifier Uniform Resource Identifier http://siba-ese.unisalento.it/index.php/ejasa/article/view/25964
 
10. Identifier Digital Object Identifier 10.1285/i20705948v16n2p423
 
11. Source Publication/conference title; vol., no. (year) Electronic Journal of Applied Statistical Analysis; Vol 16, No 2 (2023): Electronic Journal of Applied Statistical Analysis
 
12. Language English=en en
 
13. Relation Supp. Files
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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