A1 Refereed original research article in a scientific journal
Rank-Polyserial Correlation: A Quest for a "Missing" Coefficient of Correlation
Authors: Metsämuuronen Jari
Publisher: FRONTIERS MEDIA SA
Publication year: 2022
Journal: Frontiers in Applied Mathematics and Statistics
Journal name in source: FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS
Journal acronym: FRONT APPL MATH STAT
Article number: 914932
Volume: 8
Number of pages: 20
DOI: https://doi.org/10.3389/fams.2022.914932
Publication's open availability at the time of reporting: Open Access
Publication channel's open availability : Open Access publication channel
Web address : https://www.frontiersin.org/articles/10.3389/fams.2022.914932/full
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/175960544
Self-archived copy's licence: CC BY
Self-archived copy's version: Publisher`s PDF
In the typology of coefficients of correlation, we seem to miss such estimators of correlation as rank-polyserial (RRPS) and rank-polychoric (RRPC) coefficients of correlation. This article discusses a set of options as RRP, including both RRPS and RRPC. A new coefficient JTgX based on Jonckheere-Terpstra test statistic is derived, and it is shown to carry the essence of RRP. Such traditional estimators of correlation as Goodman-Kruskal gamma (G) and Somers delta (D) and dimension-corrected gamma (G2) and delta (D2) are shown to have a strict connection to JTgX, and, hence, they also fulfil the criteria for being relevant options to be taken as RRP. These estimators with a directional nature suit ordinal-scaled variables as well as an ordinal- vs. interval-scaled variable. The behaviour of the estimators of RRP is studied within the measurement modelling settings by using the point-polyserial, coefficient eta, polyserial correlation, and polychoric correlation coefficients as benchmarks. The statistical properties, differences, and limitations of the coefficients are discussed.
Keywords:
dimension-corrected D, dimension-corrected G, Goodman-Kruskal G, point-polyserial correlation, polyserial correlation, rank-biserial correlation, rank-polyserial correlation, Somers D
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