We present a proposal to deal with the non-normality issue in the context of regression models with measurement errors when both the response and the explanatory variable are observed with error. We extend the normal model by jointly modelling the unobserved covariate and the random errors by a finite mixture of scale mixture of skew-normal distributions. This approach allows us to model data with great flexibility, accommodating skewness, heavy tails, and multi-modality. The main virtue of considering measurement error models under the class of scale mixtures of skew-normal distributions is that they have a nice hierarchical representation which allows easy implementation of inference. In order to illustrate the usefulness of the proposed method some simulation studies are presented and a real dataset (Systemic lupus erythematosus) is analyzed.

当响应和解释变量都观察到错误时，我们提出了一个建议，以在具有测量误差的回归模型的背景下处理非正态性问题。我们通过倾斜正态分布的尺度混合的有限混合来联合建模未观察到的协变量和随机误差来扩展正态模型。这种方法使我们能够以极大的灵活性对数据进行建模，适应偏度、重尾和多模态。在倾斜正态分布的尺度混合类下考虑测量误差模型的主要优点是它们具有很好的层次表示，可以轻松实现推理。为了说明所提出方法的有用性，提出了一些模拟研究，并分析了一个真实的数据集（系统性红斑狼疮）。