[R-sig-Geo] Heteroskedasticity and different Spatial Weigth Matrices

[caspar hallmann]

Hi Angela,

an idea might be to use gls with some proper variance function (say
varPower). Then take the pearson residuals for you Morans tests.

my 2 cents

Caspar





On Fri, Sep 24, 2010 at 4:23 PM, Angela Parenti <aparenti at ec.unipi.it> wrote:
> Hey everyone,
>
> I'm puzzled about a recent result, and I'm wondering if anyone can help explain it.
>
> I am currently estimating a growth model with many controls by OLS. Looking at the residual tests I find that the Breusch-Pagan test points the presence of heteroskedasticity.
> Moreover, looking for spatial dependence in the residuals using the Moran's I test I find that with 3 definitions of spatial weight matrix I cannot reject
> the null hp of no spatial dependence while with 3 different spatial weight matrices I can.
>
> Here the results in details:
>
> Breush-Pagan Test:
> BP=66.3478, p-value=0
>
> Moran'I test on regression residuals:
>
> 1) W1 is binary matrix with a cut-off=660.8 km (row-standardized):
>     Observed Moran's I=-0.02938, p-value=/0.57547/
>
> 2) W2 is the first-order contiguity matrix(row-standardized):
>     Observed Moran's I=0.1389, p-value=_0.00021_
>
> 3)  W3 is the second-order contiguity matrix(row-standardized):
>     Observed Moran's I=0.0694 , p-value=_0.00724_
>
> 4)  W4 is the matrix s.t each region has at least one neighbour- max distance 1124.710 km -(row-standardized):
>     Observed Moran's I=-0.01286, p-value=/0.91883/
>
> 5)  W5 is the matrix where weights are 1/d_ij^2  with no cut-off(row-standardized):
>     Observed Moran's I=0.03239, p-value=_0.00350_
>
> 6)  W6 is the matrix where weights are 1/exp(2*d_ij)  with no cut-off(row-standardized):
>     Observed Moran's I=0.06847, p-value=/0.15462/
>
>
> Therefore, my questions are:
> - since I find evidence of heteroskedasticity shouldn't I look for aheteroskedasticity-robust version of the Moran's I? If yes, is there the possibility
>   to implement it with the function "lm.morantest"?
> - what should I conclude from such different results using different spatial weight matrices? It seems that the lower the number of neighbours is the higher is the
>   probability of finding spatial effects. In this latter case how can I decide the "right" matrix? By looking at the AIC in the maximum likelihood?
>
> Thank you very much!
>
> Angela Parenti
>
>
>
>
>
>
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>
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