On the Cliff-Ord Test for Spatial Correlation

Abstract

It is shown that the test for spatial correlation in regressiondisturbances can be derived by the application of Silvey's (1959) Lagrange Multiplier method.

The political economy of cultural spending: evidence from Italian cities

“…In principle, several alternative models can be estimated to capture spatial interdependence. 36 To identify which spatial interaction model is the most appropriate for the spatial pattern exhibited by our data, one should examine the Lagrange multiplier (LM) test statistics developed by the literature (Burridge 1980;Anselin 1988b;Anselin et al 1996). 37 While the LM-LAG test rejects the null at a marginally significant level (p = 0.0919), the LM-ERR fails to do so, indicating that the mixed regressive-SAR model is the most appropriate model for our data.…”

Population and employment location in Swedish municipalities 1994–2004

“…The remaining specification tests with explicitly stated alternative hypothesis suggested by Burridge (1980) and Anselin (1988), respectively, are based on the LM principle which discriminates between a spatial error or spatial lag alternative. If present, these spatial processes have inevitable but very different consequences for the properties of the estimator.…”

On the bootstrap for Moran’sItest for spatial dependence

“…The test is based on asymptotic normality of a standardized test statistic by deducting the estimated mean and dividing by the standard error. Burridge (1980) shows that for the regressive equation y n = X n β+u n with SAR errors u n = ρM n u n +ϵ n , or with SMA errors u n = ρM n ϵ n + ϵ n , where ϵ n ∼ N(0, σ 2 I n ), X n is an n × k x matrix of exogenous variables and I n is the n × n identity matrix, the LM test statistic for ρ = 0 is proportional to the Moran I statistic, which is…”