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Table 5 Diagnostics for Spatial Dependence: Lagrange Multiplier Tests for Error Versus LAG Dependence

From: Spatial analysis of elderly access to primary care services

Symbol Test Degrees of Freedom Test statistic value p-value
RS ρ Lagrange Multiplier (lag) 1 1090.35 0.000
RS ρ * Robust LM (lag) 1 173.32 0.000
RS λ Lagrange Multiplier (error) 1 1002.00 0.000
RS λ * Robust LM (error) 1 84.97 0.000
  1. Methodology for proper diagnosis of error process in cross section: If neither RS ρ nor RS λ are significant, but robust tests (RS ρ * RS λ *) are, then ignore the robust tests. When RS ρ is more significant (lower p-value) than RS λ , and RS ρ * is significant while RS λ * is not, then lag autocorrelation is most likely the correct error structure. When RS λ is more significant (lower p-value) than RS ρ , and RS λ * is significant while RS ρ * is not, then error autocorrelation is most likely the correct error structure. We find that RS ρ is more significant then RS λ , as it has a larger test statistic value (and the same degrees of freedom). The same is also true of the robust tests, so we conclude that a lag process is more likely than an error process in these data.