Spatial Analysis Using Big Data

5.4. Testing spatial autocorrelation based on the spatial econometric models

As discussed in Chapter 4, because it is difficult to specify the correct model from Global Moran's I alone, it is common to concurrently use test statistics based on a maximum-likelihood method that assumes a certain spatial autocorrelation structure as an alternative hypothesis. This section describes the Wald test, LR test, and Lagrangean multiplier (LM) test when an SLM or SAR error model is alternative hypothesis H₁ and a CLR model is the null hypothesis H_0., ¹² based on Anselin (1988).

First, in the discussion of spatial autocorrelation in error terms, we focus on the SAR error model u   =   λ Wu + ε. Null and alternative hypothesis are given by: