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：我们提出了一类适用于潜在分布可假设为二元正态的二维列联表的关联度量。当该假设成立时，用于度量偏离独立性的幂散度可以近似表示为潜在相关系数的闭式函数。通过反演这一关系，我们得到了一族由标量参数 $-1 \leq λ\leq 1$ 索引的度量 $ρ_{(λ)}$，其直接近似于潜在相关系数。特例包括 $λ= 0$ 时 Linfoot (1957) 提出的信息相关度量，以及 $λ= 1$ 时的 Pearson 列联系数 $C$。此外，我们通过 delta 方法推导了渐近分布，并构建了两族置信区间。模拟研究证实，所提出的度量比传统的基于散度的度量更能忠实逼近真实的潜在相关性，并且能成功区分现有度量往往给出难以区分数值的弱关联与中等关联。与多分格相关系数相比，所提出的度量计算速度快数千倍，且在潜在相关性接近 1 时仍能保持数值稳定性。