[R-sig-Geo] removing spatial autocorrelation with ME function and subsequently testing with lm.morantest

[Henri Vallès]

Thank you. This helps.


On Tue, Dec 20, 2011 at 4:36 AM, Roger Bivand <Roger.Bivand at nhh.no> wrote:
> On Mon, 19 Dec 2011, Henri Vallès wrote:
>
>> Hi,
>>
>> I am hoping somebody will be able to assist me.
>>
>> I am using the "ME" function of the "spdep" package to select a suite
>> of eigenvectors that successfully removes any significant spatial
>> autocorrelation (at a nominal level of 0.05) from my dependent
>> variable (density, "den") given a spatial weighting matrix
>> (listwdist).
>
>
> The choice of alpha=0.05 is very conservative, and could well be larger.
> Your results are down to your data:
>
> library(spdep)
> example(columbus)
> lagcol <- SpatialFiltering(CRIME ~ 1, data=columbus, nb=col.gal.nb,
>  style="W", alpha=0.05, verbose=TRUE)
> lmlag <- lm(CRIME ~ fitted(lagcol), data=columbus)
> lm.morantest(lmlag, nb2listw(col.gal.nb))
> lagcol1 <- ME(CRIME ~ 1, data=columbus, family="gaussian",
>  listw=nb2listw(col.gal.nb), alpha=0.05, stdev=TRUE, verbose=TRUE)
> lmlag1 <- lm(CRIME ~ fitted(lagcol1), data=columbus)
> lm.morantest(lmlag1, nb2listw(col.gal.nb))
>
> which all show lm.morantest() at approximately the target alpha. Note that
> ME() with the default Gaussian family is the same as SpatialFiltering() but
> using a bootstrap test on the regression residuals (an approximation),
> rather than the analytical test, so SpatialFiltering() would normally be
> preferred. There is something in your data that is driving this. Please try
> to reproduce your problem with a data set shipped with spdep or maptools.
> Your null model is also asking for trouble, as most of the observed
> autocorrelation in dens is caused by missing covariates.
>
> Hope this helps,
>
> Roger
>
>
>>
>> The code and output:
>>
>>> ME_model=ME(den~1,listw=listwdist,verbose=TRUE,nsim=999,alpha=0.05)
>>
>>
>> eV[,1], I: 0.2267349 ZI: NA, pr(ZI): 0.001
>> eV[,8], I: 0.1727207 ZI: NA, pr(ZI): 0.001
>> eV[,3], I: 0.1490887 ZI: NA, pr(ZI): 0.001
>> eV[,5], I: 0.1260945 ZI: NA, pr(ZI): 0.001
>> eV[,2], I: 0.1042690 ZI: NA, pr(ZI): 0.001
>> eV[,15], I: 0.08287102 ZI: NA, pr(ZI): 0.001
>> eV[,10], I: 0.06740037 ZI: NA, pr(ZI): 0.001
>> eV[,7], I: 0.0513471 ZI: NA, pr(ZI): 0.001
>> eV[,21], I: 0.03391224 ZI: NA, pr(ZI): 0.018
>> eV[,13], I: 0.01831637 ZI: NA, pr(ZI): 0.073
>>
>>
>> However, when I use the "lm.morantest" function to double-check
>> whether there is any significant autocorrelation in the residuals,
>> using "den" as the dependent variable and the selected eigenvectors as
>> predictors (ME_model$vectors), the test indicates that there still is
>> considerable autocorrelation left in the residuals:
>>
>> model=lm(den~ME_model$vectors)
>>
>>> lm.morantest(model,listwdist)
>>
>>
>>       Global Moran's I for regression residuals
>>
>> data:
>> model: lm(formula = den ~ ME_model$vectors)
>> weights: listwdist
>>
>> Moran I statistic standard deviate = 5.2239, p-value = 8.761e-08
>> alternative hypothesis: greater
>> sample estimates:
>> Observed Moran's I        Expectation           Variance
>>     1.831637e-02      -2.453698e-02       6.729546e-05
>>
>>
>> In contrast, I get a different result (but one that would be more
>> consistent with the outcome of the ME function) when I extract the
>> residuals from the model above and run a "moran.test" on those
>> residuals, although I have just found out that using the residuals
>> this way appears not to be valid:
>>
>>> moran.test(residuals(model),listwdist)
>>
>>
>> Moran's I test under randomisation, .
>> data:  residuals(model)
>> weights: listwdist
>> Moran I statistic standard deviate = 1.5546, p-value = 0.06002
>> alternative hypothesis: greater
>> sample estimates:
>> Moran I statistic       Expectation          Variance
>>    0.0183163706     -0.0024154589      0.0001778361
>>
>>
>> I would very much appreciate if anyone could help me understand these
>> discrepancies between methods or what is it that I am doing wrong?
>>
>> Regards,
>>
>> Henri Valles
>> Lecturer in Ecology
>> Department of Biological and Chemical Sciences
>> University of the West Indies, Cave Hill Campus, Barbados, BB11000
>> tel (Direct): (246) 417-4328
>> E-mail: hevals at gmail.com
>>
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>>
>
> --
> Roger Bivand
> Department of Economics, NHH Norwegian School of Economics,
> 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