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首页> 外文期刊>Psychometrika >GOODMAN AND KRUSKAL'S GAMMA COEFFICIENT FOR ORDINALIZED BIVARIATE NORMAL DISTRIBUTIONS
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GOODMAN AND KRUSKAL'S GAMMA COEFFICIENT FOR ORDINALIZED BIVARIATE NORMAL DISTRIBUTIONS

机译：Goodman和Kruskal的伽玛系数用于常见的双核苷酸正常分布

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摘要

We consider a bivariate normal distribution with linear correlation rho whose random components are discretized according to two assigned sets of thresholds. On the resulting bivariate ordinal random variable, one can compute Goodman and Kruskal's gamma coefficient, gamma, which is a common measure of ordinal association. Given the known analytical monotonic relationship between Pearson's rho and Kendall's rank correlation tau for the bivariate normal distribution, and since in the continuous case, Kendall's tau coincides with Goodman and Kruskal's gamma, the hange of this association measure before and after discretization is worth studying. We consider several experimental settings obtained by varying the two sets of thresholds, or, equivalently, the marginal distributions of the final ordinal variables. This study, confirming previous findings, shows how the gamma coefficient is always larger in absolute value than Kendall's rank correlation; this discrepancy lessens when the number of categories increases or, given the same number of categories, when using equally probable categories. Based on these results, a proposal is suggested to build a bivariate ordinal variable with assigned margins and Goodman and Kruskal's gamma by ordinalizing a bivariate normal distribution. Illustrative examples employing artificial and real data are provided.
机译：我们考虑一个具有线性相关rho的二元正态分布，其随机成分根据两组指定的阈值进行离散。在得到的二元有序随机变量上，可以计算Goodman和Kruskal的gamma系数gamma，这是有序关联的常用度量。鉴于二元正态分布的Pearson's rho和Kendall's rank correlation tau之间已知的分析单调关系，并且由于在连续情况下，Kendall's tau与Goodman和Kruskal's gamma一致，这种关联度量在自由裁量前后的变化值得研究。我们考虑了通过改变两组阈值或等效的最终序数变量的边缘分布而获得的几个实验设置。这项研究证实了之前的发现，表明伽马系数的绝对值总是大于肯德尔的秩相关；当类别数量增加时，或者在相同类别数量的情况下，当使用同样可能的类别时，这种差异会减小。基于这些结果，建议通过对二元正态分布进行排序，建立一个具有指定边界和Goodman和Kruskal伽马的二元有序变量。提供了使用人工和真实数据的示例。

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