National Center for Geographic Information and Analysis

Based on a large number of Monte Carlo simulation experiments on a regular lattice, we compare the properties of Moran's I and Lagrange multiplier tests for spatial dependence, i.e., for both spatial error autocorrelation and for a spatially lagged dependent variable. We consider both bias and power of the tests for 6 sample sizes, ranging from 25 to 225 observations, for different structures of the spatial weights matrix, for several underlying error distributions, for misspecified weights matrices and for the situation where boundary effects are present. The results provide an indication of the sample sizes for which the asymptotic properties of the tests can be considered to hold. They also illustrate the power of the Lagrange multiplier tests to distinguish between substantive spatial dependence (spatial lag) and spatial dependence as a nuisance (error autocorrelation).