Detection of Influential Observations in Spatial Regression Model Based on Outliers and Bad Leverage Classification

Influential observations (IOs), which are outliers in the x direction, y direction or both, remain a problem in the classical regression model fitting. Spatial regression models have a peculiar kind of outliers because they are local in nature. Spatial regression models are also not free from the effect of influential observations. Researchers have adapted some classical regression techniques to spatial models and obtained satisfactory results. However, masking or/and swamping remains a stumbling block for such methods. In this article, we obtain a measure of spatial Studentized prediction residuals that incorporate spatial information on the dependent variable and the residuals. We propose a robust spatial diagnostic plot to classify observations into regular observations, vertical outliers, good and bad leverage points using a classification based on spatial Studentized prediction residuals and spatial diagnostic potentials, which we refer to as and . Observations that fall into the vertical outliers and bad leverage points categories are referred to as IOs. Representations of some classical regression measures of diagnostic in general spatial models are presented. The commonly used diagnostic measure in spatial diagnostics, the Cook’s distance, is compared to some robust methods, (using robust and non-robust measures), and our proposed and plots. Results of our simulation study and applications to real data showed that the Cook’s distance, non-robust and robust were not very successful in detecting IOs. The suffered from the masking effect, and the robust suffered from swamping in general spatial models. Interestingly, the results showed that the proposed plot, followed by the plot, was very successful in classifying observations into the correct groups, hence correctly detecting the real IOs.

The Effect of Socioeconomic and Environmental Factors on Obesity

This paper examined the effect of socio-economic and environmental factors on obesity in Cleveland (Ohio) using an OLS model and three spatial regression models: spatial error model, spatial lag model, and a spatial error model with a spatially lagged response (SEMSLR). Comparative assessment of the models showed that the SEMSLR and the spatial error models were the best models. The spatial effect from the various spatial regression models was statistically significant, indicating an essential spatial interaction among neighboring geographic units and the need to account for spatial dependency in obesity research. The authors also found a statistically significant positive association between the percentage of families below poverty, Black population, and SNAP recipient with obesity rate. The percentage of college-educated had a statistically significant negative association with the obesity rate. The study shows that health outcomes such as obesity are not randomly distributed but are more clustered in deprived and marginalized neighborhoods.

An ecological study of chronic kidney disease in five Mesoamerican countries: associations with crop and heat

Background Mesoamerica is severely affected by an epidemic of Chronic Kidney Disease of non-traditional origin (CKDnt), an epidemic with a marked variation within countries. We sought to describe the spatial distribution of CKDnt in Mesoamerica and examine area-level crop and climate risk factors. Methods CKD mortality or hospital admissions data was available for five countries: Mexico, Guatemala, El Salvador, Nicaragua and Costa Rica and linked to demographic, crop and climate data. Maps were developed using Bayesian spatial regression models. Regression models were used to analyze the association between area-level CKD burden and heat and cultivation of four crops: sugarcane, banana, rice and coffee. Results There are regions within each of the five countries with elevated CKD burden. Municipalities in hot areas and much sugarcane cultivation had higher CKD burden, both compared to equally hot municipalities with lower intensity of sugarcane cultivation and to less hot areas with equally intense sugarcane cultivation, but associations with other crops at different intensity and heat levels were not consistent across countries. Conclusion Mapping routinely collected, already available data could be a first step to identify areas with high CKD burden. The finding of higher CKD burden in hot regions with intense sugarcane cultivation which was repeated in all five countries agree with individual-level studies identifying heavy physical labor in heat as a key CKDnt risk factor. In contrast, no associations between CKD burden and other crops were observed.