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

[Danlin Yu]

Hi, Philine:

I always use AIC for not just goodness of fit, but a base to compare 
which model might tells a better story. In addition, I think the 
log-likelihood value is a good candidate, too. It is, after all, a 
"likelihood" measure, so a larger likelihood value, a better model.

Hope this helps.

Danlin


On 7/24/2016 10:01 AM, Philine Gaffron wrote:
> 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)


-- 
___________________________________________
Danlin Yu, Ph.D.
Professor of GIS and Urban Geography
Associate Editor of ASCE Journal of Urban Planning & Development
Department of Earth & Environmental Studies
Montclair State University
Montclair, NJ, 07043
Tel: 973-655-4313
Fax: 973-655-4072
email: yud at mail.montclair.edu
webpage: csam.montclair.edu/~yu