A Latent Auto-Regressive Approach for Bayesian Structural Equation Modeling of Spatially or Socially Dependent Data

Area of Science:

• Social Sciences
• Econometrics
• Behavioral Sciences
• Psychological Research

Background:

• Spatial analytic approaches, while classic in econometrics, are emerging in social sciences.
• Spatial analysis models, also known as social network auto-regressive models, are gaining traction in behavioral sciences.
• Structural Equation Models (SEM) are prevalent in psychology for construct measurement but lack flexibility for spatial/social dependency, especially with nonlinear effects.

Purpose of the Study:

• To present a cohesive framework, the Bayesian Spatial Auto-Regressive Structural Equation Model (BARDSEM), for estimating latent interaction/polynomial effects.
• To simultaneously account for spatial effects with both exogenous and endogenous latent variables.
• To demonstrate the performance and interpretability of BARDSEM using simulation and empirical data.

Main Methods:

• Developed the Bayesian Spatial Auto-Regressive Structural Equation Model (BARDSEM).
• Estimated latent interaction/polynomial effects alongside spatial dependencies.
• Utilized simulation studies and an empirical example with spatially dependent US southern homicide data.

Main Results:

• The BARDSEM framework successfully estimates nonlinear effects and accounts for spatial dependencies.
• Simulation results exemplify the model's performance in handling dependent data.
• Empirical application on homicide data reveals rich interpretations of spillover effects.

Conclusions:

• BARDSEM offers a flexible and powerful approach for analyzing complex social and spatial dependencies within structural equation modeling.
• The model provides unbiased results by accounting for data dependence and offers insights into spillover effects.
• BARDSEM has significant implications for psychological research and other social sciences dealing with interdependent data.