Dear list,

Hello, I am Dongwoo Kang. I am studying Spatial Econometric modeling.
I've faced one question while using *spdep* package in R.
 I want to ask your help for my qeustion.

While estimating my empirical models,
I want to test whether residuals of my spatial regression models (SEM, SAR,
SARAR, SDM estimated by maximum likelihood) still have spatial
autocorrelation pattern.

I think I have two options,
1) Moran's I test using *"moran.mc"* function in R,
2) Lagrange multiplier diagnostics with LMerr option using
*"lm.LMtests"* function
in R.

But I also find that for SAR, SDM, *"summary.sarlm"* function returns "LM
test for residual autocorrelation" by default.
However, this LM test is not given for SER and SARAR.

At first, I thought that "Lagrange multiplier diagnostics" and "LM test for
residual autocorrelation" in "*summary.sarlm*" function are same tests.
But in my empirical results, they give me different statistics (please see
below example).

-----< example
>---------------------------------------------------------------------------
> summary.sarlm(sar2, Nagelkerke=T)
...
Log likelihood: -3533.378 for lag model
ML residual variance (sigma squared): 224.88, (sigma: 14.996)
Nagelkerke pseudo-R-squared: 0.76166
Number of observations: 853
Number of parameters estimated: 29
AIC: 7124.8, (AIC for lm: 7393.3)
LM test for residual autocorrelation
test value: 6.8391, p-value: 0.0089184

>
> lm.LMtests(sar2$residuals, listw=w100.listw, test=c("LMerr"))

Lagrange multiplier diagnostics for spatial dependence

data:
residuals: sar2$residuals
weights: w100.listw

LMErr = 3.7108, df = 1, p-value = 0.05406
-------------------------------------------------------------------------------------------------------

I try to find formulation of "LM test for residual autocorrelation" given
by *"summary.sarlm"* function but I couldn't.

Would you tell me where I can get some documents or explanations about "LM
test for residual autocorrelation" given by *"summary.sarlm"*?

I also want to know why "LM test for residual autocorrelation" is not
provided in SER and SARAR models.

Thank you very much for your time.

Best regards,

Dongwoo Kang

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