W-based versus latent variables spatial autoregressive models: evidence from Monte Carlo simulations

Abstract

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. JEL Classification

Estimating regression coefficients by W-based and latent variables spatial autoregressive models in the presence of spillovers from hotspots: evidence from Monte Carlo simulations

“…Given these specifications as well as (6), (7) and (10), estimation of SEM is standard and can be done by means of the software package Mx (Neale et al 2003). 4 As in Liu et al (2010), the performances of the approaches will be compared in terms of bias and RMSE for various sample sizes, specifications of weights matrices and values of the spatial autoregressive coefficient. The bias of an estimatorθ with respect to the true value of the parameter θ is defined to be:…”

“…Anselin's (1988) Columbus, Ohio, crime data set, that SEM produces estimates of the regression coefficients of the explanatory variables that are virtually identical to those obtained by the W-based approach, while the autoregression coefficients slightly differ. To gain further insight into the properties of the W-based approach and SEM, Liu et al (2010) carried out a series of Monte Carlo simulations on the basis of the spatial structure in Anselin (1988). The latent spatially lagged variable in the SEM model was measured by a number of nearest neighbors.…”

Estimation of Autoregressive Models with Two Types of Weak Spatial Dependence by Means of the W-Based and the Latent Variables Approach: Evidence from Monte Carlo Simulations

“…Spatial dependence is often multidimensional in that it comes from different sources: for instance, from locations that do and that do not have common borders or vertexes (first-order and higher order spatial dependence, respectively), or from both neighbours and hotspots. For instance, innovation in a spatial system may come from spillovers from neighbouring regions and from diffusion from a hotspot: that is, a geographical area that exhibits a high volume or intensity of a certain phenomenon or activity, in the present example, one or more regions with high innovativeness (Liu et al, 2011a;2011b). [See Griffith and Arbia (2010) for a discussion of several types of spatial dependence that are simultaneously present.]…”

“…The second problem concerns the definitions of the parameter space of the spatial lag parameters and how this can affect model specification, estimation, and inference. Folmer and Oud (2008) and Liu et al (2011a;2011b) show that the SEM approach allows for straightforward inclusion of various kinds of spatial dependence in the model: for example, spatial dependence due to spillover from the nearest neighbours or from distanceweighted hotspots. It can also capture different types of contiguity, including nonspatial contiguity such as dependence between regions due to economic, social, or demographic similarity (see Case et al, 1993).…”

“…To gain insight into the performance of the W-based approach and SEM in the case of models with one type of spatial dependence only, Liu et al (2011a) carried out a series of Monte Carlo simulations based on Anselin's (1988) Columbus, Ohio, crime dataset [which was also used by Folmer and Oud (2008) for illustrative purposes]. The latent spatial lag variable in the SEM model was measured by varying numbers of nearest neighbours.…”