[R-sig-Geo] bivariate spatial correlation in R

Mon Jul 31 23:52:13 CEST 2017

Rafael,

I'm sorry, but there is no way you can logically "analyze who benefits the 
recent changes in the transport system in terms of access to jobs" from 
the data you have.

Even if you had aggregate household income data for 2014 and 2017 (not for 
2010 only), you would not know whether wealthier families had not dispaced 
poorer families as accessibility improved. You need individual data, 
either survey or register, preferably panel, to show that changes in 
accessibility change the economic welfare of households controlling for 
movement of households. The timestamps on the data make any attempt to do 
this very risky; the real findings from a hypothetical surevey-based panel 
might be completely different, especially if poorer households were 
displaced (also indirectly, through rising house prices driven by improved 
accessibility). Gauging the welfare effects of transport investments is 
very hard to instrument.

The closest I could get was to map deciles of the change in access (more 
negatives than positives) and compare the aspatial income distributions:

library(spdep)
library(rgdal)
map <- readOGR(dsn=".", layer="test_map")
library(classInt)
cI <- classIntervals(map$diffaccess, n=10, style="quantile")
library(RColorBrewer)
ybrpal <- brewer.pal(6, "YlOrBr")
fC <- findColours(cI, ybrpal)
qtm(map, fill="diffaccess", fill.breaks=cI$brks, format="Europe2")
map$faccess <- factor(findInterval(map$diffaccess, cI$brks,
   all.inside=TRUE), labels=names(attr(fC, "table")))
qtm(map, fill="diffaccess", fill.breaks=cI$brks, format="Europe2")
acc_income <- split(map$income, map$faccess)
do.call("rbind", lapply(acc_income, summary))
dens <- lapply(acc_income, density)
plot(1, ylab="", xlab="", type="n", xlim=c(-2000, 11000), ylim=c(0,
   0.002))
for (i in seq(along=dens)) lines(dens[[i]], col=i)
legend("topright", legend=names(dens), col=1:length(dens), lty=1, bty="n")

These density curves really do not suggest any clear relationship, other 
than that some areas with increased accessibility had higher incomes in 
2010.

You can examine the reverse relationship - were aggregate areas that were 
more wealthy in 2010 able to attract more changes to accessibility? The 
answer seems to be yes, they were able to do this:

nb <- poly2nb(map)
lw <- nb2listw(nb, style = "W", zero.policy = T)
lm.morantest(lm(diffaccess ~ I(income/1000), map), lw)
# SLX model
summary(lmSLX(diffaccess ~ I(income/1000), map, lw))
lm.morantest(lmSLX(diffaccess ~ I(income/1000), map, lw), lw)
# Spatial Durbin error model - SDEM
obj <- errorsarlm(diffaccess ~ I(income/1000), map, lw, etype="emixed")
summary(impacts(obj))
summary(impacts(lmSLX(diffaccess ~ I(income/1000), map, lw)))
LR.sarlm(lmSLX(diffaccess ~ I(income/1000), map, lw), obj)

It would be possible to run lm.morantest.sad() on the output of the SDEM 
model taking global spatial autocorrelation into account. If you need 
that, follow up in this thread.

Bivariate Moran's I should not be used in this case, but could be used in 
other cases - use in change over time is troubling because randomisation 
will not be a good guide as t=1 and t=2 are subject to temporal as well as 
spatial autocorrelation, so you cannot use permutation bootstrap to find 
a usable measure of significance.

Hope this clarifies, and thanks for the code.

Roger

On Sun, 30 Jul 2017, Rafael Pereira wrote:

> Roger,
>
> Population and income data are single point in time and come from the 2010
> Census.
>
> Accessibility variables in 2014 and 2017 show the proportion of jobs
> accessible by public transport under 60 minutes. The variable diffaccess
> shows the difference between these two. It's in percentage points
> (access2017 - access2014)
>
> best,
>
> Rafael H M Pereira
> urbandemographics.blogspot.com
>
> On Sun, Jul 30, 2017 at 7:41 AM, Roger Bivand <Roger.Bivand at nhh.no> wrote:
>
>> Thanks, I'll get back when able, offline now. What are the units of
>> observation, and are aggregate household incomes observed only once?
>>
>> Roger
>>
>> Roger Bivand
>> Norwegian School of Economics
>> Bergen, Norway
>>
>>
>>
>> Fra: Rafael Pereira
>> Sendt: søndag 30. juli, 00.39
>> Emne: Re: [R-sig-Geo] bivariate spatial correlation in R
>> Kopi: Rogério Barbosa, r-sig-geo at r-project.org
>>
>>
>> Hi all, here is a reproducible example to calculate in R bivariate Moran's
>> I and LISA clusters. This example is based on a this answer provided in SO*
>> and it uses a toy model of my data. The R script and the shape file with
>> the data are available on this link. https://gist.github.com/
>> rafapereirabr/5348193abf779625f5e8c5090776a228 What this example does is
>> to estimate the spatial association between household income per capita and
>> the gains in accessibility to jobs. The aim is to analyze who benefits the
>> recent changes in the transport system in terms of access to jobs. So the
>> idea is not to find causal relationships, but spatial association between
>> areas of high/low income who had high/low gains in accessibility. The
>> variables in the data show info on the proportion of jobs accessible in
>> both years 2014 and 2017 (access2014, access2017) and the difference
>> between the two years in percentage points (diffaccess). Roger, I know you
>> have shown to be a bit sceptical about this application of bivariate
>> Moran's I. Do you still think a spatial regression would be more
>> appropriate? Also, I would be glad to hear if others have comments on the
>> code. This function is not implemented in any package so it would be great
>> to have some feedback. Rafael H M Pereira urbandemographics.blogspot.com
>> * https://stackoverflow.com/questions/45177590/map-of-
>> bivariate-spatial-correlation-in-r-bivariate-lisa On Wed, Jul 26, 2017 at
>> 11:07 AM, Roger Bivand wrote: > 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 >> 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 >>> Gómez-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 0,] >>> oregon.tract1$rat >> nb >> lw >> >>> which should
>> still be adjusted by weighting: >>> >>> lm0 >> >>> 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 >>>> >>>>
>> [[alternative HTML version deleted]] >>>> >>>>
>> _______________________________________________ >>>> R-sig-Geo mailing
>> list >>>> R-sig-Geo at r-project.org >>>> https://stat.ethz.ch/mailman/
>> listinfo/r-sig-geo >>>> >>>> >>>> -- >>> Roger Bivand >>> Department of
>> Economics, Norwegian School of Economics, >>> Helleveien 30, N-5045 Bergen,
>> Norway. >>> voice: +47 55 95 93 55 <+47%2055%2095%2093%2055>; 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 >>> >> >> [[alternative HTML version
>> deleted]] >> >> _______________________________________________ >>
>> R-sig-Geo mailing list >> R-sig-Geo at r-project.org >>
>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo >> > > -- > Roger Bivand
>>> Department of Economics, Norwegian School of Economics, > Helleveien 30,
>> N-5045 Bergen, Norway. > voice: +47 55 95 93 55 <+47%2055%2095%2093%2055>;
>> 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