We propose a family of association measures for two-way contingency tables whose latent distribution can be assumed to be bivariate normal. When this assumption holds, the power-divergence measuring departure from independence can be approximated in closed form as a function of the latent correlation coefficient. By inverting this relationship, we obtain a family of measures $ρ_{(λ)}$, indexed by a scalar parameter $-1 \leq λ\leq 1$, that directly approximates the latent correlation. Special cases include the informational measure of correlation proposed by Linfoot (1957) at $λ= 0$ and Pearson's contingency coefficient $C$ at $λ= 1$. Additionally, we derive asymptotic distributions via the delta method and construct two families of confidence intervals. Simulation studies confirm that the proposed measures approximate the true latent correlation more faithfully than conventional divergence-based measures, and that they successfully distinguish between weak and moderate associations where existing measures tend to give indistinguishable values. Compared with the polychoric correlation coefficient, the proposed measures are computed several thousand times faster and remain numerically stable even when the latent correlation is close to one.

翻译：我们提出一类用于二维列联表的关联测度族，其潜在分布可假定为二元正态分布。当该假设成立时，衡量偏离独立性的幂散度可近似表示为潜在相关系数的闭式函数。通过反转这一关系，我们得到由标量参数$-1 \leq λ\leq 1$索引的测度族$ρ_{(λ)}$，该族直接近似潜在相关系数。特例包括Linfoot (1957)在$λ= 0$时提出的信息相关性测度，以及$λ= 1$时的皮尔逊列联系数$C$。此外，我们通过Delta方法推导了渐近分布，并构建了两类置信区间。模拟研究表明，所提出的测度比传统散度基测度更真实地逼近潜在相关系数，并且能成功区分现有方法常给出无差别值的弱关联与中等关联。与多分格相关系数相比，所提测度的计算速度快数千倍，且即便潜在相关系数接近1时仍保持数值稳定性。