Evaluating Local Parameter Reliability in Hierarchical Geographically Weighted Regression: A Bootstrap and Sign Consistency Approach

Abstract

The Hierarchical Geographically Weighted Regression (HGWR) model is widely used to capture spatial heterogeneity and hierarchical data structures simultaneously. However, the reliability of its local parameter estimates remains a critical issue due to potential variability across locations. This study aims to evaluate the reliability of local parameters in the HGWR model using a bootstrap-based approach combined with sign consistency analysis, using an empirical stunting prevalence dataset in Indonesia. A cluster bootstrap procedure at the provincial level was implemented with 500 replications to generate empirical distributions of parameter estimates, enabling the assessment of statistical significance through confidence intervals. In addition, sign consistency was employed to examine the stability of the direction of local effects across bootstrap replications. The results show that while some local parameters are statistically significant, they do not always exhibit consistent directional effects, indicating potential instability. Conversely, several parameters demonstrate both statistical significance and high sign consistency, suggesting robust local relationships. These findings highlight that relying solely on statistical significance may lead to misleading interpretations of local effects in HGWR models. The combination of bootstrap and sign consistency provides a more comprehensive framework for assessing parameter reliability. This approach contributes to improving the interpretability and robustness of spatial multilevel modeling, particularly in applications involving complex hierarchical and spatial data.