Followup on my questions concerning R + spdep:

I used dnearneigh() instead of knearneigh() to get the point point

relationships I wanted.

The old version looked like this:

http://users.pandora.be/requested/thesis/oldconnections.png

notice the sparse connection pattern between the points, certainly in the

centre.

I used dnearneight() to change this into this:

http://users.pandora.be/requested/thesis/connections.png

so the center points get more connections/interactions.

all ok, for the weights... but as before the weights are relative to the

connection and not to the distance and the connection. A consequence from

a binary spatial connectivity matrix I presume. nbdists() gives me a matix

of all the distances in the neighbourhood directions but I can't use them

to be a relative measure to convert the old weights into distance weighted

ones.

Question is, what's the influence of this on the final result?

Old results:

Moran's I test under normality

Moran I statistic standard deviate = 0.2911, p-value = 0.771

alternative hypothesis: two.sided

sample estimates:

Moran I statistic Expectation Variance

-0.03762590 -0.08333333 0.02464896

New results with the same data and a new weights matrix:

data: a1$data

weights: a1.listw

Moran's I test under normality

Moran I statistic standard deviate = 0.3303, p-value = 0.7412

alternative hypothesis: two.sided

sample estimates:

Moran I statistic Expectation Variance

-0.03703572 -0.08333333 0.01964896

Moran's I test under randomisation

Moran I statistic standard deviate = 0.3305, p-value = 0.741

alternative hypothesis: two.sided

sample estimates:

Moran I statistic Expectation Variance

-0.03703572 -0.08333333 0.01962520

Monte-Carlo simulation of Moran's I

number of simulations + 1: 1000

statistic = -0.037, observed rank = 673, p-value = 0.327

alternative hypothesis: greater

You can see that the p-value drops over normal, random to the MC

simulation.

But I don't come to a significant difference between the statistic and the

expected value. I think I can conclude that in this case there is a slight

to zero spatial autocorrelation between samples and this could as well

been a set of data sampled at random in this particular plot.

Just for the record: I don't see the difference between what is done in

the test under randomisation and the test using MC simulation.

As I may quote:

"With a Monte Carlo test the significance of an observed test statistic is

assessed by comparing it with as a sample of test statistics obtained by

generating random samples using some assumed model. If the assumed model

implies that all data orderings are equally likely then this amounts to a

randomisation test with random sampling of the randomisation distribution"

- "Brian F. J. Manly - Randomization, bootstrap and monte carlo methods in

biology"

But this last one is something for the people who wrote the code I think.

Any comments, would be appreciated... It's uncharted territory for me so..

Best regards,

Koen.

------- Forwarded message -------

From: Roger Bivand <Roger.Bivand@...>

To: Koen Hufkens <koen.hufkens@...>

Subject: Re: AI-GEOSTATS: Moran's I

Date: Sun, 14 Mar 2004 17:43:53 +0100 (CET)

> On Sun, 14 Mar 2004, Koen Hufkens wrote:

--

>

>> Hi list,

>>

>> I have some coding and theoretical questions regarding the Moran's I

>> index

>> and the R + spdep packages.

>>

>> - To illustrate the situation of the sampling plot:

>>

>> http://users.pandora.be/requested/thesis/a1grid.gif

>> (coordinates in lat lon projection, point size representative for sample

>> value)

>>

>> - The data distribution:

>>

>> http://users.pandora.be/requested/thesis/hista1.gif

>> (haven't tested for normality yet)

>

> First, thanks for including links to your figures, makes helping easier.

>>

>>

>> => My method to get my Moran's I index in R + spdep:

>>

>> a1.knn <- knearneigh(a1$coords, k=4, lonlat=TRUE)

>> #with a1$coords the latlon coords out of a geoR geodata file

>>

>> a1.nb <- knn2nb(a1.knn)

>> # conversion to nb object

>>

>> a1.listw <- nb2listw(a1.nb)

>> # conversion to listw object, requested for moran.test()

>

> Note that you have called nb2listw() with the default style, which is

> row-standardised ("W") - so with 4 neighbours for each object, all thw

> weights will be 1/4. With style="B", the weights would all be 1. This

> isn't a full analogy of a rook pattern, because those around the edges

> will already be queen style or more. Look at plot(a1.nb, a1$coords) to

> see

> this.

>

>>

>> results <- moran.test(a1$data, a1.listw, randomization=FALSE,

>> alternative="two.sided")

>>

>> The results show the following statistics:

>>

>> > moran.test(a1$data, a1.listw, randomisation=FALSE,

>> > alternative="two.sided")

>>

>> Moran's I test under normality

>>

>> data: a1$data

>> weights: a1.listw

>>

>> Moran I statistic standard deviate = 0.2911, p-value = 0.771

>> alternative hypothesis: two.sided

>> sample estimates:

>> Moran I statistic Expectation Variance

>> -0.03762590 -0.08333333 0.02464896

>>

>> With a Moran's I of -0.04 and a p-value of 0.771 I would say this isn't

>> much of a statistic or not exactly what I expected.

>>

> Well, looking at your figure (just eyeballing), there are quite a lot of

> big/small neighbours as well as small/small and big/big. Did you try

> looking at a Moran scatterplot to get a feel for what is going on?

> moran.plot() is the function to try. I think you'll see that all four

> quadrants of the plot have observations, leading to a very flat and

> non-significant relationships. Maybe this is because the k-nearest

> neighbours weights are not reflecting what you want - could you try using

> dnearneigh() for the appropriate number of km instead, or use edit.nb()

> to

> cut out the possibly disturbing long links?

>

>> I would think that since I evaluate ecological/biophysical paramters it

>> wouldn't be possible to get negative correlations since in vegetations

>> there is always some kind of autocorrelation involved. It could be just

>> a

>> little but certainly not negative.

>

> Note that it is still greater than its expectation (which shows that you

> only have the 13 observations shown on the figure), but with the variance

> you have is not significantly different from its expectation. Why did you

> use normality rather than randomisation (or Monte Carlo)? With so few

> observations, this may be an issue.

>

>>

>> Strange thing is that I get the same weights in my weights class of my

>> a1.listw file

>>

> Explained above - this was what you asked for. For distance weighted see

> nbdists(), though your points are regularly spaced.

>

>> > a1.listw$weights

>> [[1]]

>> [1] 0.25 0.25 0.25 0.25

>>

>> [[2]]

>> [1] 0.25 0.25 0.25 0.25

>>

>> [[3]]

>> [1] 0.25 0.25 0.25 0.25

>> ...

>>

>> I think it has something to do with the k-value in knearneigh(), but

>> even

>> if I change it to 8 (changing from bishops/rooks to queens case?) they

>> stay the same. Any idea why this is the case?

>>

>> So maybe the strange statistics could be a problem of a faulty weights

>> matrix. So if you have any comments on the code/method used it would be

>> appreciated.

>>

>> Best regards,

>> Koen.

>>

>> --

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