[R-sig-Geo] How to calculate squared R of spatial autoregressive models

[Roger Bivand]

On Mon, 22 Nov 2010, elaine kuo wrote:

> Dear List,
>
>
>
> I am comparing the squared R values of linear models and its spatial
> autoregressive counterparts. (SARerror)
>
> (1. lm (Y~X1)
>
> 2. lm (Y~ X1+X2)
>
> 3. lm(Y~X1+X2+X3))
>
>
>
> The squared R values of linear models are generated by command summary 
> (lm).
>
>
> Similarly, I tried to produce those of spatial autoregressive models 
> based on the squared Pearson?s correlation of explanatory and response 
> variables. It failed

Don't. There is no direct equivalent to the OLS R-squared, these models 
are fitted by maximum likelihood. You may choose to compare 
likelihood-based measures, so a likelihood ratio test (as reported in the 
output of the summary method for the fitted model) between the fitted 
model and an OLS model with the spatial coefficient fixed at zero is OK. 
If you want something like an R-squared, try the Nagelkerke R-bar-squared, 
based on the likelihood, reported optionally in the summary object - see 
?summary.sarlm. You should then compare this with a Nagelkerke value for 
your OLS model if you feel that this would be helpful.

Roger

>
>
>
> The code is as followed.
>
> Please kindly modify the code and thank you.
>
>
>
> 1. single predictor
>
> sar.x1 <-errorsarlm(Y~X1,data=datam.std,listw=nb8.w, na.action=na.omit,
> method="Matrix", zero.policy=TRUE)
>
> summary(sar.x1)
>
> cor(sar.x1$X1, sar.x1$Y, method = "pearson")
>
>
>
> error message
>
> error in cor(sar.x1$ X1, sar.x1$Y, method = "pearson") :
>
>  supply both 'x' and 'y' or a matrix-like 'x'
>
>
>
> 2. multiple predictors
>
> sar.all <-errorsarlm(Y~X1+X2+X3,data=datam.std,listw=nb8.w,
> na.action=na.omit, method="Matrix", zero.policy=TRUE)
>
> summary(sar.all)
>
> cor(sar.all$X1+ sar.all$X2+ sar.all$X3, sar.x1$Y, method = "pearson")
>
>
>
> error message
>
> error in cor(sar.all$X1+ sar.all$X2+ sar.all$X3, sar.x1$Y, method =
> "pearson") :
>
>  supply both 'x' and 'y' or a matrix-like 'x'
>
>
>
> Elaine
>
> 	[[alternative HTML version deleted]]
>
>

-- 
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Helleveien 30, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no