Abstract

The hierarchical Bayes predictor of small area proportions (HBP) under an area level version of generalized linear mixed model with logit link function is widely used in small area estimation for binary variable. However, this predictor does not account for the presence of spatial nonstationarity in the data, i.e., where the parameters associated with the model covariates vary spatially. This paper develops a spatially nonstationary extension to the hierarchical Bayes predictor of small area proportions that accounts for the presence of spatial nonstationarity in the data. The proposed predictor is referred as the spatial nonstationary hierarchical Bayes predictor (HBNSP). The impact of survey design information is also explored in the proposed predictor. The empirical results from simulation studies using spatially nonstationary data indicate that the HBNSP method performs better, in terms of relative bias and relative mean squared error, than the alternative HBP method that ignore this spatial nonstationarity. The results further show that use of survey-weight to incorporate the sampling design appears to be imperative when sample data is informative. The HBNSP approach is illustrated by applying it to estimation of incidence of indebtedness in farm households across the districts in the state of Bihar in India using debt investment survey data. A map depicting the spatial distribution of incidence of indebtedness in Bihar has also been produced which provides a useful information for the government departments and ministries involved in farm credit distribution related policy planning and monitoring.

摘要

具有logit链接函数的广义线性混合模型的面积级版本下的小面积比例（HBP）的分层贝叶斯预测器广泛用于二元变量的小面积估计。然而，该预测变量并未考虑数据中存在的空间非平稳性，即与模型协变量关联的参数在空间上发生变化。本文对小面积比例的分层贝叶斯预测器进行了空间非平稳扩展，以解释数据中存在的空间非平稳性。所提出的预测器称为空间非平稳分层贝叶斯预测器 (HBNSP)。调查设计信息的影响也在提议的预测变量中进行了探讨。使用空间非平稳数据的模拟研究的经验结果表明，HBNSP 方法在相对偏差和相对均方误差方面比忽略此空间非平稳性的替代 HBP 方法表现更好。结果进一步表明，当样本数据提供信息时，使用调查权重来纳入抽样设计似乎势在必行。HBNSP 方法通过将其应用于使用债务投资调查数据估计印度比哈尔邦各地区农户的债务发生率来说明。