Rank-Polyserial Correlation: A Quest for a "Missing" Coefficient of Correlation
: Metsämuuronen Jari
Publisher: FRONTIERS MEDIA SA
: 2022
: Frontiers in Applied Mathematics and Statistics
: FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS
: FRONT APPL MATH STAT
: 914932
: 8
: 20
DOI: https://doi.org/10.3389/fams.2022.914932(external)
: https://www.frontiersin.org/articles/10.3389/fams.2022.914932/full(external)
: https://research.utu.fi/converis/portal/detail/Publication/175960544(external)
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.