Zachary Roman, University of Zurich

Bayesian spatial and network auto-regressive structural equation modeling: A novel approach

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Zachary Roman

Spatial analytic approaches are classic models in econometric literature (LeSage & Pace, 2009), but relatively new in social sciences. Spatial analysis models are synonymous with social network autoregressive models which are also gaining popularity. These models have two major benefits. First, dependent data, either socially or spatially, must be accounted for to acquire unbiased results. Second, analysis of the dependence provides rich additional information such as spillover effects (Valente et al.,1997; LeSage & Pace, 2009). Structural equation models (SEM) are widely used in psychological research for measuring and testing multi-faceted constructs (Bollen, 1989). While SEM models are widely used, limitations remain, in particular latent interaction/polynomial effects are troublesome (Brandt et al., 2014). Recent work has produced methods to account for these issues (Brandt et al., 2018) as well as integrating spatial and network effects in SEM (Oud & Folmer, 2008) to a limited extent. However, a cohesive framework which can simultaneously estimate latent interaction/polynomial effects and account for spatial effects with both exogenous and endogenous latent variables has not been established. To accommodate this, I provide a novel model, the Bayesian spatial auto-regressive structural equation model (SASEM). First I briefly outline classic auto-regressive models. Next I present the SASEM and introduce simulation results to exemplify its performance. Finally, I provide an empirical example using the dependent extended US southern homicide data (Messner et al., 1999; Land et al., 1990) to show the rich interpretations made possible by the SASEM. Finally, I discuss implications, limitations, recommendations, and future research.

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