Comparative benefits of analyzing spatial aggregate data using Stata’s Sp versus gsem and sem

We demonstrate the powers of the underutilized Stata spatial analytical module Sp, with an eye on the broader and older path analytic modeling framework (gsem and sem, which stands for structural equation modeling [SEM]). Spatial aggregate data have become widely available, yet analysts often ignore their spatial structure (regions have neighbors, and neighboring regions are more similar than by chance). Research often reports artificial naïve/a-spatial associations that ignore this spatial nonindependence. We analyze public data from the CDC, on social vulnerability and life expectancy, at census tract level, using the state of CT in the U.S. as illustration. We compare (1) the spregress modeling options against SEM models that include the outcome’s spatial lag as copredictor; (2) a two-step mediation model with spregress against SEM with indirect effects; (3) the total effects of a spatial predictor on a spatial outcome estimated with spregress by adding up effects from neighbors to each region (and back), against nonrecursive SEM models that use spatial lag versions of each spatial variable as instrumental variables. We point to several extensions of spatial modeling into the SEM approach, like spatial factor analysis and spatial "causal" mediation models, and contrast Stata’s utilities against GeoDa and Mplus comparable models.