Bounded response variables such as percentages, proportions, or rates are common in applications involving social and educational datasets, including rates of poverty or rates of achievement by municipalities, counties or provinces. New regression models have been proposed in recent years by considering distributions such as the Beta, Simplex and Kumaraswamy models for this type of data. However, to this type of dataset, it is common to observe the spatial dependence of units. For instance, municipalities or counties are organized into states. For this case, the supposition of independence among observations in the same state removes relevant relations between neighboring provinces. In this paper, we present a model of spatially bounded distribution regression with a Bayesian estimation approach where spatial relations are modeled by a spatial random variable with a particular dependence structure, such as the intrinsic conditional autoregressive model or the Leroux definition. Additionally, the Bayesian inferential method and model comparison criteria are discussed. Simulation studies and an application in reading comprehension spatial data are used to illustrate the performance of the proposed model and the estimation method adopted.

中文翻译：

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有限响应变量的空间回归模型以及相关程度的评估

在涉及社会和教育数据集的应用程序中，诸如百分比，比例或比率之类的有界响应变量是常见的，包括贫困率或市，县或省的成就率。近年来，通过考虑此类数据的Beta，Simplex和Kumaraswamy模型的分布，提出了新的回归模型。但是，对于这种类型的数据集，通常要观察单位的空间依赖性。例如，市或县被组织成州。对于这种情况，假设同一州的观测值之间具有独立性，就消除了邻近省份之间的相关关系。在本文中，我们提出了一种使用贝叶斯估计方法的空间有界分布回归模型，其中空间关系是通过具有特定依赖结构的空间随机变量建模的，例如固有条件自回归模型或Leroux定义。此外，讨论了贝叶斯推理方法和模型比较标准。通过仿真研究和在理解空间数据读取中的应用来说明所提出模型的性能和所采用的估计方法。