Comparing confidence intervals for Goodman and Kruskal’s gamma coefficient

L.A. van der Ark, R.C.M. van Aert

Research output: Contribution to journalArticleScientificpeer-review

Abstract

This study was motivated by the question which type of confidence interval (CI) one should use to summarize sample variance of Goodman and Kruskal's coefficient gamma. In a Monte-Carlo study, we investigated the coverage and computation time of the Goodman–Kruskal CI, the Cliff-consistent CI, the profile likelihood CI, and the score CI for Goodman and Kruskal's gamma, under several conditions. The choice for Goodman and Kruskal's gamma was based on results of Woods [Consistent small-sample variances for six gamma-family measures of ordinal association. Multivar Behav Res. 2009;44:525–551], who found relatively poor coverage for gamma for very small samples compared to other ordinal association measures. The profile likelihood CI and the score CI had the best coverage, close to the nominal value, but those CIs could often not be computed for sparse tables. The coverage of the Goodman–Kruskal CI and the Cliff-consistent CI was often poor. Computation time was fast to reasonably fast for all types of CI.
Keywords: categorical marginal models, confidence intervals, Goodman and Kruskal's gamma, sampling variance
Original languageEnglish
Pages (from-to)2491-2505
JournalJournal of Statistical Computation and Simulation
Volume85
Issue number12
DOIs
Publication statusPublished - 2015

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Confidence interval
Coefficient
Wood
Sampling
Coverage
Sample variance
Profile Likelihood
Small Sample
Coefficients
Association Measure
Marginal Model
Monte Carlo Study
Categorical
Categorical or nominal
Tables

Cite this

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title = "Comparing confidence intervals for Goodman and Kruskal’s gamma coefficient",
abstract = "This study was motivated by the question which type of confidence interval (CI) one should use to summarize sample variance of Goodman and Kruskal's coefficient gamma. In a Monte-Carlo study, we investigated the coverage and computation time of the Goodman–Kruskal CI, the Cliff-consistent CI, the profile likelihood CI, and the score CI for Goodman and Kruskal's gamma, under several conditions. The choice for Goodman and Kruskal's gamma was based on results of Woods [Consistent small-sample variances for six gamma-family measures of ordinal association. Multivar Behav Res. 2009;44:525–551], who found relatively poor coverage for gamma for very small samples compared to other ordinal association measures. The profile likelihood CI and the score CI had the best coverage, close to the nominal value, but those CIs could often not be computed for sparse tables. The coverage of the Goodman–Kruskal CI and the Cliff-consistent CI was often poor. Computation time was fast to reasonably fast for all types of CI.Keywords: categorical marginal models, confidence intervals, Goodman and Kruskal's gamma, sampling variance",
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Comparing confidence intervals for Goodman and Kruskal’s gamma coefficient. / van der Ark, L.A.; van Aert, R.C.M.

In: Journal of Statistical Computation and Simulation, Vol. 85, No. 12, 2015, p. 2491-2505.

Research output: Contribution to journalArticleScientificpeer-review

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AB - This study was motivated by the question which type of confidence interval (CI) one should use to summarize sample variance of Goodman and Kruskal's coefficient gamma. In a Monte-Carlo study, we investigated the coverage and computation time of the Goodman–Kruskal CI, the Cliff-consistent CI, the profile likelihood CI, and the score CI for Goodman and Kruskal's gamma, under several conditions. The choice for Goodman and Kruskal's gamma was based on results of Woods [Consistent small-sample variances for six gamma-family measures of ordinal association. Multivar Behav Res. 2009;44:525–551], who found relatively poor coverage for gamma for very small samples compared to other ordinal association measures. The profile likelihood CI and the score CI had the best coverage, close to the nominal value, but those CIs could often not be computed for sparse tables. The coverage of the Goodman–Kruskal CI and the Cliff-consistent CI was often poor. Computation time was fast to reasonably fast for all types of CI.Keywords: categorical marginal models, confidence intervals, Goodman and Kruskal's gamma, sampling variance

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