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A Skew-Normal Mixture Regression Model

机译：斜偏正态混合回归模型

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摘要

A challenge associated with traditional mixture regression models (MRMs), which rest on the assumption of normally distributed errors, is determining the number of unobserved groups. Specifically, even slight deviations from normality can lead to the detection of spurious classes. The current work aims to (a) examine how sensitive the commonly used model selection indices are in class enumeration of MRMs with nonnormal errors, (b) investigate whether a skew-normal MRM can accommodate nonnormality, and (c) illustrate the potential of this model with a real data analysis. Simulation results indicate that model information criteria are not useful for class determination in MRMs unless errors follow a perfect normal distribution. The skewnormal MRM can accurately identify the number of latent classes in the presence of normal or mildly skewed errors, but fails to do so in severely skewed conditions. Furthermore, across the experimental conditions it is seen that some parameter estimates provided by the skew-normal MRM become more biased as skewness increases whereas others remain unbiased. Discussion of these results in the context of the applicability of skew-normal MRMs is provided.
机译：与传统的混合回归模型（MRM）相关的挑战在于确定未观察到的组数，该模型基于正态分布误差的假设。具体而言，即使是与正常性的微小偏差也可能导致伪造类别的检测。当前的工作旨在（a）研究常用模型选择指标在具有非正态误差的MRM的类枚举中的敏感度;（b）研究偏态正态MRM是否可以适应非正态性;以及（c）说明这种可能性具有真实数据分析的模型。仿真结果表明，除非错误遵循理想的正态分布，否则模型信息标准对于MRM中的类别确定没有用。正常偏态MRM在存在正常或轻度偏斜错误的情况下可以准确地识别潜在类别的数量，但是在严重偏斜的情况下则无法这样做。此外，在整个实验条件下，可以看到随着偏斜度的增加，由偏斜正常MRM提供的某些参数估计会变得更加有偏差，而其他参数估计则保持不变。提供了在偏态正态MRM适用性的背景下对这些结果的讨论。

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