Solved – How to interpret lagsarlm output from R’s spdep

autoregressiverspatial

I've run lagsarlm on my dataset, using a mixed model and using a row-standardized adjacency matrix. I have results that I think are good, but would am not sure how to interpret them.

  • Does the p-value of 0.12 on rho mean I cannot count on spatial autocorrelation of the response?
  • Does the low p-value for the LM test mean that the error term is not spatially correlated to the response?
  • What about the various p-values of the coefficients: Should I remove predictors that have high p-values and run it again?

.

> summary(lm.lag)

Call:lagsarlm(formula = Y.scaled ~ Narcotics.Crime.Rate + Assault..Homicide. + 
    Infant.Mortality.Rate + Below.Poverty.Level + Per.Capita.Income, 
    data = X.scaled, listw = W.mat, type = "mixed")

Residuals:
     Min       1Q   Median       3Q      Max 
-0.96641 -0.33183 -0.13579  0.15113  3.00270 

Type: mixed 
Coefficients: (asymptotic standard errors) 
                           Estimate Std. Error z value  Pr(>|z|)
(Intercept)                0.007063   0.069365  0.1018 0.9188960
Narcotics.Crime.Rate       0.465759   0.176160  2.6439 0.0081945
Assault..Homicide.         0.202034   0.156141  1.2939 0.1956925
Infant.Mortality.Rate      0.121582   0.130806  0.9295 0.3526420
Below.Poverty.Level        0.051494   0.129330  0.3982 0.6905098
Per.Capita.Income         -0.119833   0.171509 -0.6987 0.4847382
lag.Narcotics.Crime.Rate  -0.673492   0.284876 -2.3642 0.0180710
lag.Assault..Homicide.     0.366021   0.295266  1.2396 0.2151117
lag.Infant.Mortality.Rate  0.010755   0.240319  0.0448 0.9643038
lag.Below.Poverty.Level    0.232895   0.202924  1.1477 0.2510930
lag.Per.Capita.Income      0.885463   0.256441  3.4529 0.0005546

Rho: 0.26724, LR test value: 2.3413, p-value: 0.12598
Asymptotic standard error: 0.14187
    z-value: 1.8838, p-value: 0.059597
Wald statistic: 3.5486, p-value: 0.059597

Log likelihood: -70.92512 for mixed model
ML residual variance (sigma squared): 0.36337, (sigma: 0.6028)
Number of observations: 77 
Number of parameters estimated: 13 
AIC: 167.85, (AIC for lm: 168.19)
LM test for residual autocorrelation
test value: 14.516, p-value: 0.00013896

Best Answer

  • Your Rho is your spatial autoregressive parameter, and it is not
    significant. Your likelihood ratio basically tells you that the inclusion of the lagged values do not improve your model.
  • You LM test, a.k.a Lagrange Multiplier test for the absence of spatial autocorrelation in the lag model residuals, is small so you reject the Hypothesis Null of No Spatial Autocorrelation.
  • The simpler the model, the better.

Hope this helps!