Essential Statistical Concepts, Definitions, and Terminology - Sampling Spatial Units for Agricultural Surveys - page 27

this issue, which is known as the spatial common factor problem, see Anselin
( 1988 , p. 227).
The R code for the ML estimate of the SDM, using the data set LasRosas,isas
follows.

> library(spdep)
> SDM < - lagsarlm((YIELD~N+N2), type ¼ "mixed", data ¼ LasRosas@data,
+ LasRosas_listw,tol.solve ¼ 1.0e-18)

> summary(SDM)
Call:lagsarlm(formula ¼ (YIELD ~ N + N2), data ¼ LasRosas@data, listw ¼
LasRosas_listw, type ¼ "mixed", tol.solve ¼ 1e-18)

Residuals:
Min 1Q Median 3Q Max

-21.075223 -2.227662 -0.023912 2.196076 26.976214

Type: mixed
Coefficients: (asymptotic standard errors)
Estimate Std. Error z value Pr( > |z|)
(Intercept) 3.42742215

1.07518811 3.1877 0.001434

N 0.12614687 0.00808258 15.6073 < 2.2e-16

N2 0.00036035 0.00005823 -6.1885 6.074e-10

lag.N 0.03947487 0.03685194 1.0712 0.284091

lag.N2 -0.00085500 0.00027295 -3.1325 0.001733

Rho: 0.89577, LR test value: 2461.1, p-value: < 2.22e-16

Asymptotic standard error: 0.01256
z-value: 71.321, p-value: < 2.22e-16

Wald statistic: 5086.7, p-value: < 2.22e-16
Log likelihood: -4900.657 for mixed model
ML residual variance (sigma squared): 13.715, (sigma: 3.7034)
Number of observations: 1738
Number of parameters estimated: 7
AIC: 9815.3, (AIC for lm: 12274)
LM test for residual autocorrelation
test value: 334.71, p-value: < 2.22e-16

Another alternative to the previously mentioned models is the spatial lag model
(SLM, Anselin 1988 ). It is very popular in spatial econometrics, and is obtained by
simply adding a spatially lagged dependent variable to the classical linear model

2 I

y ¼ ˁ 1 Wy þ X

ʲ þ ε ε / N 0, ˃ : ð 1 :

54 Þ

The model in Eq. ( 1.54 ) does not appear to have a direct link with spatial random
field theory as outlined in this paragraph (Arbia 2006 ). There are some different