Spatial nonstationary hierarchical Bayes estimation of small area proportions

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.

Keywords:

• Spatial nonstationarity
• hierarchical Bayes
• binary data
• indebtedness
• spatial mapping

MATHEMATICAL SUBJECT CLASSIFICATION:

• 62D05

Acknowledgments

The authors would like to acknowledge the valuable comments and suggestions of the Editor and an anonymous referee. These led to a considerable improvement in the paper. I also would like to deeply acknowledge the efforts made by Late Dr. Hukum Chandra in finalizing the article. He has left for heavenly abode before the final acceptance of this article.