W-based versus latent variables spatial autoregressive models: evidence from Monte Carlo simulations
Liu, A. ; Folmer, H. ; Oud, J.H.L. - \ 2011
Annals of Regional Science 47 (2011)3. - ISSN 0570-1864 - p. 619 - 639.
regression-models - weights matrix - specification - econometrics
In this paper, we compare by means of Monte Carlo simulations two approaches to take spatial autocorrelation into account: the classical spatial autoregressive model and the structural equations model with latent variables. The former accounts for spatial dependence and spillover effects in georeferenced data by means of a spatial weights matrix W. The latter represents spatial dependence and spillover effects by means of a latent variable in the structural (regression) model while the observed spatially lagged variables are related to the latent spatial dependence variable in the measurement model. The simulation results based on Anselin's Columbus, Ohio, crime data set show that the misspecified latent variables approach slightly trails the correctly specified classical approach in terms of bias and root mean squared error of the coefficient estimators.
How to get rid of W: a latent variables approach to modelling spatially lagged variables
Folmer, H. ; Oud, J. - \ 2008
Environment and Planning A 40 (2008)10. - ISSN 0308-518X - p. 2526 - 2538.
regression-analysis - weights matrix - econometrics
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.