Pearson residuals aid the task of identifying model misspecification because they compare the estimated, using data, model with the model assumed under the null hypothesis. We present different formulations of the Pearson residual system that account for the measurement scale of the data and study their properties. We further concentrate on the case of mixed-scale data, that is, data measured in both categorical and interval scale. We study the asymptotic properties and the robustness of minimum disparity estimators obtained in the case of mixed-scale data and exemplify the performance of the methods via simulation.

中文翻译：

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离散和混合尺度数据模型的基于距离的估计方法

Pearson 残差有助于识别模型错误指定的任务，因为它们将使用数据估计的模型与在原假设下假设的模型进行比较。我们提出了 Pearson 残差系统的不同公式，这些公式说明了数据的测量尺度并研究了它们的特性。我们进一步关注混合尺度数据的情况，即以分类和区间尺度测量的数据。我们研究了在混合尺度数据的情况下获得的最小视差估计器的渐近特性和鲁棒性，并通过模拟举例说明了这些方法的性能。