[R-sig-Geo] Spatial lags using gridded data

[Steve Pickering]

Many thanks for this, Roger.  Answers my question; raises a few more.
Life's like that sometimes!

 - Steve.
Steve Pickering
Assistant Professor
Graduate School of Law
Kobe University
2-1 Rokkodai-cho
Nada-ku, Kobe
657-8501 Japan
pickering at penguin.kobe-u.ac.jp
http://www.stevepickering.net
*** This year's Conflict Research Society Conference is at the
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On 21 August 2014 19:15, Roger Bivand <Roger.Bivand at nhh.no> wrote:
> On Thu, 21 Aug 2014, Steve Pickering wrote:
>
>> Hello, all,
>>
>> Sorry for the silly question.
>>
>> I'm struggling to apply spatial lags to a data grid.  I've been
>> working through the notes on Luc Anselin's spdep, but just can't
>> figure out how to apply it to gridded data.
>>
>> Consider the following very simple 5 x 5 grid:
>>
>> ids <- c(1:25)
>> lats <-
>> c(30,30,30,30,30,31,31,31,31,31,32,32,32,32,32,33,33,33,33,33,34,34,34,34,34)
>> lngs <-
>> c(10,11,12,13,14,10,11,12,13,14,10,11,12,13,14,10,11,12,13,14,10,11,12,13,14)
>> conflict <- c(0,0,0,0,0,0,0,0,1,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,0)
>> conflictLag <-
>> c(0,0,0.125,0.125,0.125,0,0.125,0.375,0.25,0.25,0.125,0.25,0.375,0.25,0.25,0.125,0.125,0.375,0.25,0.125,0.125,0.125,0.125,0,0)
>> pop <- sample(100, 25)
>>
>> newGrid = data.frame(ids, lats, lngs, conflict, conflictLag, pop)
>>
>> Here, I have a conflict dummy, to determine whether there was some
>> sort of conflict or war in that grid cell.  I also have a population
>> variable (for the purposes of this exercise, determined at random).
>>
>> If I wanted to run a regression on this without including spatial
>> lags, I could do something very simple, like this:
>>
>> model1 = lm(newGrid$conflict ~ newGrid$pop)
>> summary(model1)
>
>
> Thanks for the toy example:
>
> set.seed(1)
>
> pop <- sample(100, 25)
> newGrid = data.frame(ids, lats, lngs, conflict, conflictLag, pop)
> model1 = lm(conflict ~ pop, data=newGrid)
> summary(model1)
>
> Then make a spatial object:
>
> library(sp)
> coordinates(newGrid) <- c("lngs", "lats")
> gridded(newGrid) <- TRUE
> image(newGrid, "conflict")
>
> Create a list of neighbours (here ignoring the possibility that the grid is
> in geographical, not projected coordinates:
>
> library(spdep)
> nb <- dnearneigh(newGrid, 0, sqrt(2))
> summary(nb)
> plot(nb, coordinates(newGrid), add=TRUE)
>
> Choose a model and fitting function:
>
> model2 <- spautolm(conflict ~ pop, data=newGrid, listw=nb2listw(nb,
>  style="W"), family="SAR")
> summary(model2)
>
> but note that conflict is not a continuous variable, so:
>
> model1a = glm(conflict ~ pop, data=newGrid, family=binomial(link=probit))
> summary(model1a)
>
> and
>
> library(spatialprobit)
> W <- as(as_dgRMatrix_listw(nb2listw(nb, style="W")), "CsparseMatrix")
> model2a <- semprobit(conflict ~ pop, W=W, data=newGrid)
> summary(model2a)
>
> which uses MCMC, so is slow. Alternatively, but for the spatially lagged
> response, not for the spatially lagged error term:
>
> model2b <- sarprobit(conflict ~ pop, W=W, data=newGrid)
> summary(model2b)
>
> This object includes effects/impacts (see LeSage & Pace 2009, or Ward &
> Gleditsch 2008).
>
> library(McSpatial)
> model2c <- spprobit(conflict ~ pop, wmat=nb2mat(nb), data=newGrid)
> model2d <- spprobitml(conflict ~ pop, wmat=nb2mat(nb), data=newGrid)
>
> use GMM and ML respectively and do not provide impacts. A recent paper in
> Journal of Regional Science compares spatial probit estimation approaches.
> In addition, the tally of 0 conflicts is 4 of 25, so your data may well also
> be zero-inflated.
>
> Spatial misspecification is possibly only a minor problem, really.
>
> Hope this helps,
>
> Roger
>
>
>>
>> However, I know that I am supposed to include a spatial lag.  As you
>> can see in the code, I have also created a spatial lag variable based
>> on whether there was conflict in adjacent cells (Queen's move, hence a
>> fraction of eight).
>>
>> What I'm struggling with is the correct way to include the spatial lag
>> in my model.
>>
>> Thanks, and sorry for the simple question.
>>
>> - Steve.
>>
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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; fax +47 55 95 91 00
> e-mail: Roger.Bivand at nhh.no
>