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. 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 leverages density power divergence estimation to achieve robustness by implicitly downweighting such observations; the ensuing weights constitute a useful tool for pinpointing potential sources of model misspecification. 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.

翻译：连续变量与有序变量之间的关联通常通过多序列相关模型进行建模。然而，该模型基于部分潜正态性假设，在实践中可能因异常值或随意响应等原因（但不限于此）导致设定错误。通常使用的最大似然估计量对此类设定错误高度敏感：仅需一个非由部分潜正态性生成的观测值就足以产生任意糟糕的估计。作为解决方案，我们提出了一种新颖的多序列相关模型估计量，旨在对偏离该模型的观测值所产生的不利影响保持稳健性。该估计量利用密度功率散度估计，通过隐式降低此类观测值的权重来实现稳健性；由此产生的权重构成了定位模型设定错误潜在来源的有效工具。所提出的估计量推广了最大似然估计，具有一致性且渐近服从高斯分布。作为稳健性的代价，需要牺牲部分效率，但在保持超过98%最大似然效率的同时仍可获得显著的稳健性。我们通过模拟实验和人格心理学实证应用证明了该估计量的稳健性与实用价值，其中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。