Auto-Regressive Latent Variable Modeling: A General Framework for Bayesian Spatial Structural Equation Models

Abstract

Spatial analytic approaches are classical models in econometric literature (LeSage & Pace, 2009). Recently, the behavioral sciences have seen an increase in their application, but spatial effects are generally still ignored (Stakhovych et al., 2012; Musafer et al., 2017; Oud & Folmer, 2008; Hogan& Tchernis, 2004). Spatial analysis models are synonymous with social network auto-regressive models which are also gaining popularity in the behavioral sciences. Structural Equation Models (SEM) are widely used in psychological research for measuring and testing multi-faceted constructs (Bollen, 1989). While SEM 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). Further, recent work has established methods to account for spatial and network effects in SEM (Oud & Folmer, 2008). However, a cohesive framework which can simultaneously estimate latent interaction/polynomial effects and account for spatial effects, has not been established. To accommodate this I provide a novel model, the Bayesian Spatial Auto-Regressive Structural Equation Model (SASEM). In the first chapter of this dissertation I review existing literature relevant to spatial analysis and latent interaction effects in SEM. In the next chapter I present a new modeling framework which can accommodate these effects. In the next chapter I investigate model performance with a series of Monte-Carlo studies. Results are promising particularly for one sub-model of the SASEM. I provide an empirical example using the spatially 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 results, implications, limitations, and recommendations.