标题： 稳健的多序列相关系数估计 显示英文标题

标题： Robust Estimation of Polyserial Correlation

摘要： 连续变量和有序变量之间的关联通常通过多相关模型进行建模。 然而，由于例如（但不限于）异常值或随意的回答，该基于部分潜在正态性假设的模型在实践中可能会被错误指定。 我们证明了通常使用的最大似然（ML）估计量对这种错误指定非常敏感：一个由部分潜在正态性生成的观测值就足以产生任意差的估计值。 作为补救措施，我们提出了一种新的多相关模型估计量，旨在对与该模型不一致的观测值的不利影响具有鲁棒性。 该估计量通过隐式地降低这些观测值的权重来实现鲁棒性；由此产生的权重构成了一个有用的工具，用于精确定位模型错误指定的潜在来源。 我们证明了所提出的估计量推广了ML，并且也是相合的以及渐近高斯的。 为了获得鲁棒性，必须牺牲一些效率，但在保持超过98%的ML效率的同时，可以获得显著的鲁棒性。 我们在模拟实验和人格心理学中的一个实证应用中展示了我们估计量的鲁棒性和实际有用性，在那里我们的估计量有助于识别异常值。 最后，所提出的方法已在免费开源软件中实现。 显示英文摘要

摘要： The association between a continuous and an ordinal variable is commonly modeled through the polyserial correlation model. However, this model, which is based on a partially-latent normality assumption, may be misspecified in practice, due to, for example (but not limited to), outliers or careless responses. We demonstrate that the typically used maximum likelihood (ML) estimator is highly susceptible to such misspecification: One single observation not generated by partially-latent normality can suffice to produce arbitrarily poor estimates. As a remedy, we propose a novel estimator of the polyserial correlation model designed to be robust against the adverse effects of observations discrepant to that model. The estimator achieves robustness by implicitly downweighting such observations; the ensuing weights constitute a useful tool for pinpointing potential sources of model misspecification. We show that the proposed estimator generalizes ML and is consistent as well as asymptotically Gaussian. As price for robustness, some efficiency must be sacrificed, but substantial robustness can be gained while maintaining more than 98% of ML efficiency. We demonstrate our estimator's robustness and practical usefulness in simulation experiments and an empirical application in personality psychology where our estimator helps identify outliers. Finally, the proposed methodology is implemented in free open-source software.