How to get rid of W: a latent variables approach to modelling spatially lagged variables

In this paper we propose a structural equation model (SEM) with latent variables to model spatial dependence. Rather than using the spatial weights matrix W, we propose to use latent variables to represent spatial dependence and spillover effects, of which the observed spatially lagged variables are indicators. This approach allows us to incorporate and test more information on spatial dependence and offers more flexibility than the representation in terms of Wy or Wx. Furthermore, we adapt the ML estimator included in the software package Mx to estimate SEMs with spatial dependence. We present illustrations based on Anselin¿s Columbus, Ohio, crime dataset.