[R-sig-Geo] Comparing strength of correlation in spatial regression models

[Philine Gaffron]

Dear all,

I am using a spatial regression model (errorsarlm from package spdep) to 
find out about correlation between different metrics for emission loads 
from road traffic received at residential receptor points. The emissions 
metrics have been generated with different methods (like 'sum of vehicle 
kilometres travelled within a buffer' or 'Gaussian plume dispersion 
models') that have very different resource requirements. I would like to 
ascertain which of the three less resource intensive methods I have used 
yields results that correlate most strongly with the results from the 
dispersion model (which is the most involved method).

Is it appropriate in this to compare the Nagelkerke pseudo R^2 values 
for the different spatial models or would another parameter be more 
appropriate (I am using the Akaike Information Criterion to ascertain 
goodness of fit of the spatial over the linear model).

Any hints are greatly appreciated.

Philine

Here is an example of the code I am using with the corresponding output 
(with model, variable and data names simplified for easier reading):

model_1<- errorsarlm(PM_exh ~ VKT, data = PM25, listw=PM25_listw)
summary(model_1, Nagelkerke = TRUE, digits = 4, signif.stars = TRUE)

# Call:errorsarlm(formula = PM_exh ~ VKT, data = PM25, listw=PM25_listw)
#
# Residuals:
#   Min       1Q   Median       3Q      Max
# -4.06775 -0.57955 -0.19595  0.41926  9.87816
#
# Type: error
# Coefficients: (asymptotic standard errors)
# Estimate Std. Error z value  Pr(>|z|)
# (Intercept)  1.35249    0.27593  4.9017 9.503e-07
# VKT  11.71968    0.20272 57.8128 < 2.2e-16
#
# Lambda: 0.95187, LR test value: 4168.2, p-value: < 2.22e-16
# Asymptotic standard error: 0.0064455
# z-value: 147.68, p-value: < 2.22e-16
# Wald statistic: 21809, p-value: < 2.22e-16
#
# Log likelihood: -9130.636 for error model
# ML residual variance (sigma squared): 1.0538, (sigma: 1.0266)
# Nagelkerke pseudo-R-squared: 0.73261
# Number of observations: 6251
# Number of parameters estimated: 4
# AIC: 18269, (AIC for lm: 22435)
-- 

Philine Gaffron
/Institute for Transport Planning and Logistics/
Hamburg University of Technology
/Germany/