Enhancing Spatial Autoregressive Models with Bootstrap Techniques: A Methodological Investigation into Bias, Precision, and Sample Size Effects
Abstract
This study introduces and evaluates two novel bootstrap-enhanced methods: the Bootstrap Simultaneous Autoregressive Lag Model (BSALM) and the Bootstrap Simultaneous Autoregressive Error Model (BSAEM), within the framework of classical Spatial Simultaneous Autoregressive (SAR) models. Using simulated datasets from normal distributions across varying sample sizes ( 10 to 500) and secondary real-world data, the study examines their effectiveness in addressing spatial dependencies. The study’s objectives include assessing bias, standard errors, variability, and the influence of sample size on model efficiency. Results demonstrate that both methods significantly reduce bias and variability as sample size increases, highlighting the critical role of adequate data dimensions in spatial analysis. BSALM consistently outperformed BSAEM in bias reduction, while BSAEM proved more adept at capturing complex spatial interdependencies despite exhibiting higher variability. Challenges with smaller datasets revealed increased biases and variability, emphasizing the importance of cautious interpretation in such scenarios. Real-world applications underscored dataset-specific performance variations, with BSALM excelling in bias correction and BSAEM managing intricate spatial structures. By integrating bootstrap techniques into SAR modelling, this study provides practical tools for enhancing predictive accuracy and model validation. While computational demands remain a consideration, these findings offer valuable insights into balancing bias, variability, and efficiency, paving the way for future advancements in spatial econometric analysis.
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