Abstract

Circumplex models arrange personality or mood variables around a circle such that the relative locations of these variables reflect their correlations. Although circumplex models were originally developed for continuous variables, their applications often involve ordinal variables. To accommodate ordinal variables, we propose estimating Browne’s circumplex correlation structure with polychoric correlations instead of Pearson correlations. We consider ordinary least squares estimation due to its computational robustness with polychoric correlation matrices. We illustrate the newly developed method with an empirical study that involves 18 binary variables and 12,108 participants. We also conduct a simulation study to explore its statistical property and compare it with maximum likelihood estimation with polychoric correlations, ordinary least squares estimation with Pearson correlations, and maximum likelihood estimation with Pearson correlations. The new method provides essentially unbiased point estimates and more satisfactory confidence intervals than other methods.

摘要

Circumplex 模型围绕一个圆圈排列个性或情绪变量，以便这些变量的相对位置反映它们的相关性。尽管环形模型最初是为连续变量开发的，但它们的应用通常涉及序数变量。为了适应序数变量，我们建议使用多元相关而不是 Pearson 相关来估计 Browne 的环状相关结构。我们考虑普通最小二乘法估计，因为它具有多元相关矩阵的计算稳健性。我们通过涉及 18 个二元变量和 12,108 名参与者的实证研究来说明新开发的方法。我们还进行了模拟研究以探索其统计特性，并将其与具有多元相关性的最大似然估计进行比较，具有 Pearson 相关性的普通最小二乘估计，以及具有 Pearson 相关性的最大似然估计。与其他方法相比，新方法提供了基本上无偏的点估计和更令人满意的置信区间。