Comparative Analysis of the Modified Spatial Variance Shift Outlier Model

Abstract

Spatial outliers pose substantial challenges in spatial data analysis, often distorting parameter estimates and leading to misleading conclusions. Various accommodation strategies have evolved through variance-shift frameworks and hierarchical robust approaches, but comprehensive evaluations across multiple contamination levels remain limited. While standard frameworks such as Mixed Models (MM), Spatial Autoregressive (SAR) models and Spatial Generalized Linear Mixed Models (SGLMM) address specific data complexities like random effects or spatial dependencies, they generally fail to account for spatial outliers concurrently. This study evaluates the performance of the Modified Spatial Variance Shift Outlier Model (m-SVSOM) in comparison with these earlier methods and the existing Spatial Variance Shift Outlier Model (SVSOM). A simulation study was conducted across various sample sizes (n = 16, 100, 256, 1000) and varying outlier proportions (5%, 10%, 15%, and 20%). The estimation accuracy of the proposed model was assessed using the Mean Squared Error (MSE) and Root Mean Squared Error (RMSE). The results consistently demonstrate that the m-SVSOM outperforms the Mixed Model, SAR, SGLMM, and the SVSOM across all scenarios. Specifically, the Modified SVSOM maintained the lowest error metrics even as contamination levels increased, indicating superior robustness in accommodating outliers and managing spatial dependencies. These findings suggest that the m-SVSOM provides a more robust and efficient framework for accommodating spatial outliers while retaining the information contained in influential observations.