bivariate spatial correlation in R

On Wed, 26 Jul 2017, Rafael Pereira wrote:

Roger,

This example was provided only for the sake or making the code easily
reproducible for others and I'm more interested in how the bi-variate
Moran
could be implemented in R, but your comments are very much welcomed and
I've made changes to the question.

My actual case study looks at bi-variate spatial correlation between (a)
average household income per capita and (b) proportion of jobs in the city
that are accessible under 60 minutes by transit. I don't think I could use
rates in this case but I will normalize the variables using
scale(data$variable).

Please provide a reproducible example, either with a link to a data
subset, or using a builtin data set. My guess is that you do not need
bi-variate spatial correlation at all, but rather a spatial regression.

The "causal" variable would then the the proportion of jobs accessible
within 60 minutes by transit, though this is extremely blunt, and lots of
other covariates (demography, etc.) impact average household income per
capita (per block/tract?). Since there are many missing variables in your
specification, any spatial correlation would be most closely associated
with them (demography, housing costs, education, etc.), and the choice of
units of measurement would dominate the outcome.

This is also why bi-variate spatial correlation is seldom a good idea, I
believe. It can be done, but most likely shouldn't, unless it can be
motivated properly.

By the way, the weighted and FDR-corrected SAD local Moran's I p-values of
the black/white ratio for Oregon (your toy example) did deliver the goods -
if you zoom in in mapview::mapview, you can see that it detects a rate
hotspot between the rivers.

Roger

best,

Rafael H M Pereira

On Mon, Jul 24, 2017 at 7:56 PM, Roger Bivand <Roger.Bivand at nhh.no>
wrote:

On Mon, 24 Jul 2017, Rafael Pereira wrote:

Hi all,

I would like to ask whether some you conducted bi-variate spatial
correlation in R.

I know the bi-variate Moran's I is not implemented in the spdep library.
I left a question on SO but also wanted to hear if anyone if the
mainlist
have come across this.
https://stackoverflow.com/questions/45177590/map-of-bivariat
e-spatial-correlation-in-r-bivariate-lisa

I also know Roger Bivand has implemented the L index proposed by Lee
(2001)
in spdep, but I'm not I'm not sure whether the L local correlation
coefficients can be interpreted the same way as the local Moran's I
coefficients. I couldn't find any reference commenting on this issue. I
would very much appreciate your thoughts this.

In the SO question, and in the follow-up, your presumably throw-away
example makes fundamental mistakes. The code in spdep by Virgilio
G?mez-Rubio is for uni- and bivariate L, and produces point values of
local
L. This isn't the main problem, which is rather that you are not taking
account of the underlying population counts, nor shrinking any estimates
of
significance to accommodate population sizes. Population sizes vary from
0
to 11858, with the lower quartile at 3164 and upper 5698:
plot(ecdf(oregon.tract$pop2000)). Should you be comparing rates in
stead?
These are also compositional variables (sum to pop2000, or 1 if rates)
with
the other missing components. You would probably be better served by
tools
examining spatial segregation, such as for example the seg package.

The 0 count populations cause problems for an unofficial alternative, the
black/white ratio:

oregon.tract1 <- oregon.tract[oregon.tract$white > 0,]
oregon.tract1$rat <- oregon.tract1$black/oregon.tract1$white
nb <- poly2nb(oregon.tract1)
lw <- nb2listw(nb)

which should still be adjusted by weighting:

lm0 <- lm(rat ~ 1, weights=pop2000, data=oregon.tract1)

I'm not advising this, but running localmoran.sad on this model output
yields SAD p-values < 0.05 after FDR correction only in contiguous tracts
on the Washington state line in Portland between the Columbia and
Williamette rivers. So do look at the variables you are using before
rushing into things.

Hope this clarifies,

Roger


best,

Rafael HM Pereira
http://urbandemographics.blogspot.com

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Roger Bivand
Department of Economics, Norwegian School of Economics,
Helleveien 30, N-5045 Bergen, Norway.
voice: +47 55 95 93 55; e-mail: Roger.Bivand at nhh.no
Editor-in-Chief of The R Journal, https://journal.r-project.org/
index.html
http://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en

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--
Roger Bivand
Department of Economics, Norwegian School of Economics,
Helleveien 30, N-5045 Bergen, Norway.
voice: +47 55 95 93 55; e-mail: Roger.Bivand at nhh.no
Editor-in-Chief of The R Journal, https://journal.r-project.org/index.html
http://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en