Polychoric correlation is often an important building block in the analysis of rating data, particularly for structural equation models. However, the commonly employed maximum likelihood (ML) estimator is highly susceptible to misspecification of the polychoric correlation model, for instance through violations of latent normality assumptions. We propose a novel estimator that is designed to be robust to partial misspecification of the polychoric model, that is, the model is only misspecified for an unknown fraction of observations, for instance (but not limited to) careless respondents. In contrast to existing literature, our estimator makes no assumption on the type or degree of model misspecification. It furthermore generalizes ML estimation and is consistent as well as asymptotically normally distributed. We demonstrate the robustness and practical usefulness of our estimator in simulation studies and an empirical application on a Big Five administration. In the latter, the polychoric correlation estimates of our estimator and ML differ substantially, which, after further inspection, is likely due to the presence of careless respondents that the estimator helps identify.

翻译：多分格相关系数在评分数据分析中常作为重要基础构件，尤其对于结构方程模型而言。然而，常用的最大似然估计量对多分格相关模型的设定误差极为敏感，例如当潜在正态性假设被违反时。我们提出一种新型估计量，专门针对多分格模型的部分设定误差具有稳健性——即模型仅对未知比例的观测值存在设定误差，例如（但不限于）随意作答的受访者。与现有文献不同，我们的估计量对模型设定误差的类型或程度不作任何假设。该估计量进一步推广了最大似然估计，且具有一致性及渐近正态分布特性。我们通过模拟研究和一项大五人格测评的实证应用，证明了该估计量的稳健性与实际效用。在实证应用中，我们的估计量与最大似然估计得出的多分格相关系数存在显著差异，经进一步检验发现，这种差异很可能源于估计量所识别的随意作答受访者的存在。