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
significant. Your likelihood ratio basically tells you that the inclusion of the lagged values do not improve your model.
Hope this helps!