[R-sig-Geo] How to efficiently generate data of neighboring points
Lom Navanyo
|omn@v@@|@ @end|ng |rom gm@||@com
Tue Jun 9 22:26:10 CEST 2020
Thank you very much. I will try as much as I can to see which model best
fits the data.
I have about 3400 wells and about 1500 irrigators.
--------
Lom
On Tue, Jun 9, 2020 at 5:36 AM Roger Bivand <Roger.Bivand using nhh.no> wrote:
> On Mon, 8 Jun 2020, Lom Navanyo wrote:
>
> > Some farmers own more than one well and thus can extract from their
> > multiple wells. Others are single well owners.
> >
> > The amount of water pumped by the irrigator from their wells is the unit
> of
> > observation. And I do not know how it might sound but
> > I would say "irrigator-well" is the unit of analysis?
> >
> > Both crops and technology have seasonal patterns, though not pronounced
> > probably due to switching costs.
> >
> > I have two segments of the data: A section or a group of neighboring
> > irrigators pay fees for water withdrawal. The second group (of
> > neighbors) does not pay any fee aside their individual lift cost (which
> > is not observed in the data). I do not intend to run a
> > difference-in-difference model with respect to the fee as that's not
> > what I want to study. So I intend to run separate models/specifications
> > for the two groups.
>
> This feels like a linear mixed effects model with an irrigator random
> effect and a temporal random effect. A spatial random effect (ICAR?) might
> be added, but it will be hard to split the identification of the irrigator
> RE from a spatially structured RE for the wells. I think that you should
> be looking at the mgcv package, the second edition of Simon Wood's book,
> and either an MRF or a Gaussian Process ("gp") spatial RE for the wells.
>
> It may very well be that a group RE (fee/no fee) would discriminate
> between the groups statistically, but I'm out of my depth here. Anyway,
> mgcv, using a flexible functional form on water level, and RE's for the
> other components, seems possible. Structural regression using BayesX or
> INLA are also possible. You have 5 years, how many irrigators and how many
> wells?
>
> Roger
>
> >
> > Thanks,
> > -----------------
> > Lom
> >
> > On Sun, Jun 7, 2020 at 5:06 AM Roger Bivand <Roger.Bivand using nhh.no> wrote:
> >
> >> On Fri, 5 Jun 2020, Lom Navanyo wrote:
> >>
> >>> Thank you once again. To clarify, which is more suitable, end of year
> >> water
> >>> levels or yearly average measure of water levels?
> >>>
> >>> Also below are a few more notes to throw more light on my
> variables/data:
> >>>
> >>> These wells are solely for irrigation purposes and are
> >>> irrigator/farmer-owned and operated. No farmer/irrigator moves to
> >>> another well not owned by him. The only reason to suspect any spatial
> >>> externalities is because the wells share a common aquifer. And this is
> >>> essentially what I am testing.
> >>
> >> Is irrigation by fixed pipe, or can the water be moved to the area of
> >> another well? Can irrigators extract water from multiple wells? Is then
> >> the irrigator the unit of observation rather than the well?
> >>
> >>>
> >>> It is also understood that there are not much variation in the
> geography
> >>> and geology of the study region.
> >>>
> >>> I have data a number of well specific features in addition to the water
> >>> level. I also have some farm data including cropping and technology use
> >>> data. No soil data though.
> >>> No recharge data too as well.
> >>
> >> OK, the farming data may reflect the demand for water. Do the different
> >> crops or technologies have different seasonal patterns, leading to
> >> different draw-down patterns in the wells over time?
> >>
> >>>
> >>> In fact, I agree a lot factors can come to play here and I may not have
> >> or
> >>> observe all but I was thinking I could incorporate some fixed effects
> >>> to take care of those, especially for those I suspect (or perhaps by
> >>> theory) are likely to not vary much in terms of their effect on
> >>> irrigation(pumping) decisions across farmers
> >>> or effect on water level.
> >>>
> >>> My panel is rather a short one: I have a five year panel data.
> >>>
> >>> Given the above, is it still not advisable to use any spatial
> econometric
> >>> analysis? Just a simple OLS will suffice?
> >>
> >> OLS probably not, but the decisions are starting to look like farmers'
> >> cropping decisions, leading to varied need for water. Do the farmers pay
> >> for the water or the irrigation technology?
> >>
> >> I'm starting to think that maybe SUR is a possibility, but am unsure how
> >> your short panel would handle that.
> >>
> >> Roger
> >>
> >>>
> >>> Thanks.
> >>> ----------------------
> >>> Lom
> >>>
> >>>
> >>>
> >>>
> >>>
> >>> On Fri, Jun 5, 2020 at 3:51 AM Roger Bivand <Roger.Bivand using nhh.no>
> wrote:
> >>>
> >>>> On Fri, 5 Jun 2020, Lom Navanyo wrote:
> >>>>
> >>>>> I fully agree with you and appreciate the listed benefits of not
> taking
> >>>>> things private. I was just trying to be sure the forum here is
> >>>> appropriate
> >>>>> and receptive of a beginner like me.
> >>>>>
> >>>>> To be more explicit with regards to my observations, y is amount of
> >>>>> water withdrawal from wells and an important variable in x is (height
> >>>>> of) water level in the wells. These are end of year figures. I am
> using
> >>>>> the aggregations (sum for y and mean for water level) by band as
> >> spatial
> >>>>> neighborhood variables. There will be one or two indicator variables
> >>>>> also in x. I hope these do not present additional hurdles.
> >>>>
> >>>> There are several further questions. If water level is measured at
> >>>> end-of-year, it is instantaneous at that point, and will depend on
> >> level a
> >>>> year earlier plus inflow from the movements of the water table
> >>>> (precipitation, soils and surface geology, maybe geology if deeper
> >> wells),
> >>>> minus evaporation (if an open well) and extraction. However, your y
> >>>> (extraction) is probably measured over an interval (1 Jan - 31 Dec?).
> It
> >>>> does not depend on level unless level is 0, but depends on the
> closeness
> >>>> of people extracting water for domestic, agricultural or other use.
> >>>>
> >>>> All else equal, you would expect changes in the level in a well to
> >> depend
> >>>> on inputs, evaporation and extraction, and extraction at that well and
> >>>> other nearby wells (which may experience falls in the ground water
> table
> >>>> level not because the water was extracted from those wells, but at
> >>>> neighbouring wells. You may also see users shifting to neerby wells if
> >>>> their closest well runs dry.
> >>>>
> >>>> So you probably need to start with a deterministic hydrological model,
> >> and
> >>>> you need much more information about who extracts and why. Say in
> India,
> >>>> you would also need price data - apparently free water has led to
> >>>> over-extraction.
> >>>>
> >>>> So I would advise against any spatial econometric analysis of the data
> >> you
> >>>> have, because so much is going on in the system as a whole that you
> >> cannot
> >>>> control if all the data you have is as you describe. I also understand
> >>>> better why well water level is endogeneous, but am sure that IV will
> not
> >>>> help, since the level is being driven partly by a deterministic
> >>>> hydrological system which differs from well to well, and extraction
> >> varies
> >>>> by demand.
> >>>>
> >>>> Has anyone worked with this kind of data? Any ideas or contributions
> >> more
> >>>> helpful than the above?
> >>>>
> >>>> Roger
> >>>>
> >>>>>
> >>>>> I am thinking Proximity is relevant in testing spatial
> >>>>> dependency/externality.
> >>>>>
> >>>>> I will consider splm package and the SLX model.
> >>>>>
> >>>>> Thank you.
> >>>>> ---------------
> >>>>> Lom
> >>>>>
> >>>>> On Thu, Jun 4, 2020 at 2:52 PM Roger Bivand <Roger.Bivand using nhh.no>
> >> wrote:
> >>>>>
> >>>>>> On Thu, 4 Jun 2020, Lom Navanyo wrote:
> >>>>>>
> >>>>>>> Thank you. Yes, the OLS is biased and my plan is to use a 2SLS
> >>>> approach.
> >>>>>> I
> >>>>>>> have a variable I intend to use as an IV for y.
> >>>>>>> I have seen a few papers use this approach. Will this approach not
> >>>>>> correct
> >>>>>>> for the endogeneity?
> >>>>>>>
> >>>>>>> Actually, I am not sure if this is a right forum or perhaps if it's
> >>>>>>> appropriate or acceptable to you to take this one-on-one with you
> for
> >>>>>> help:
> >>>>>>
> >>>>>> I do not offer private help. That would presuppose that one person
> has
> >>>> the
> >>>>>> answer. It would also presuppose that all exchanges are only read by
> >> the
> >>>>>> original poster and direct participants, while in fact others may
> join
> >>>> in,
> >>>>>> or follow a thread, or find the thread by searching: google supports
> >> the
> >>>>>> list:r-sig-geo search tag. If the thread goes private, that search
> is
> >>>>>> fruitless.
> >>>>>>
> >>>>>>> My model actually looks like this: y= f(y, x) + e.
> >>>>>>> Aside the endogeneity of y (which I intend to instrument by another
> >>>>>>> variable z), there is simultaneity between y and x.
> >>>>>>> I intend to use the lag of x as instrument for x. Given that I am
> >>>>>> seeking
> >>>>>>> to test spatial dependency, do you see some fatal flaws with my
> >>>> approach?
> >>>>>>>
> >>>>>>
> >>>>>> What is the support of your observations, point, or are they
> >>>> aggregations?
> >>>>>> Why may proximity make a difference - often, apparent spatial
> >>>>>> autocorrelation is caused by observing inappropriate entities, or by
> >>>>>> omitting covariates, or by using the wrong functional form.
> >>>>>>
> >>>>>>
> >>>>>>> I have also seen other empirical approaches like static and dynamic
> >>>>>> spatial
> >>>>>>> panel data modelling. I will be reviewing them also to see
> >> suitability
> >>>>>> for
> >>>>>>> my objective.
> >>>>>>> But, any further directions or suggestions are highly appreciated.
> >>>>>>
> >>>>>> If the data are spatial panel, you can look at the splm package.
> >>>>>> Personally, I have never found instruments any use at all, because
> the
> >>>>>> instruments are typically at best weak because of shared spatial
> >>>> processes
> >>>>>> with the response, unless the model is really well specified from
> >> known
> >>>>>> theory. In space, almost everything is close to endogeneous unless
> the
> >>>>>> opposite is demonstrated. So causal relationships are less
> worthwhile,
> >>>>>> because they are at best conditional on omitted variables and
> >>>>>> autocorrelation engendered by the choice of observational entities.
> >>>>>>
> >>>>>> Further, because spatial processes are driven by the inverse matrix
> of
> >>>> the
> >>>>>> input graph of proximate neighbours (the covariance matrix of the
> >>>> spatial
> >>>>>> process), you don't need to start from more than the first order
> >>>>>> neighbours. Maybe your x has the same spatial pattern as y, so that
> >> the
> >>>>>> residuals are white noise with no spatial structure.
> >>>>>>
> >>>>>> Recently, analysts prefer to start with the SLX model (Halleck Vega
> &
> >>>>>> Elhorst 2015 and others), so that might be worth exploring. If only
> >> the
> >>>>>> direct impacts seem important, OLS may be enough.
> >>>>>>
> >>>>>> Hope this helps,
> >>>>>>
> >>>>>> Roger
> >>>>>>
> >>>>>>>
> >>>>>>> Thanks,
> >>>>>>> -------------------
> >>>>>>> Lom
> >>>>>>>
> >>>>>>>
> >>>>>>>
> >>>>>>> On Thu, Jun 4, 2020 at 3:48 AM Roger Bivand <Roger.Bivand using nhh.no>
> >>>> wrote:
> >>>>>>>
> >>>>>>>> On Thu, 4 Jun 2020, Lom Navanyo wrote:
> >>>>>>>>
> >>>>>>>>> Thank you very much for your support. This gives me what I need
> >> and I
> >>>>>>>> must
> >>>>>>>>> say listw2sn() is really great.
> >>>>>>>>>
> >>>>>>>>> Why do I need the data in the format as in dataout? I am trying
> to
> >>>> test
> >>>>>>>>> spatial dependence (or neighborhood effect) by running a
> regression
> >>>>>>>>> model that entails pop_size_it = beta_1*sum of pop_size of point
> >> i's
> >>>>>>>>> neighbors within a specified radius. So my plan is to get the
> >>>> neighbors
> >>>>>>>>> for each focal point as per the specified bands and their
> >> attributes
> >>>>>> (eg
> >>>>>>>>> pop_size) so I can can add them (attribute) by the bands.
> >>>>>>>>
> >>>>>>>> Thanks, clarifies a good deal. Maybe look at the original localG
> >>>>>> articles
> >>>>>>>> for exploring distance relationships (Getis and Ord looked at
> >>>> HIV/AIDS);
> >>>>>>>> ?spdep::localG or
> >>>>>> https://r-spatial.github.io/spdep/reference/localG.html.
> >>>>>>>>
> >>>>>>>> Further note at OLS is biased as you have y = f(y) + e, so y on
> both
> >>>>>>>> sides. The nearest equivalent for a single band is
> >>>>>> spatialreg::lagsarlm()
> >>>>>>>> with listw=nb2listw(wd1, style="B") to get the neighbour sums
> >> through
> >>>>>> the
> >>>>>>>> weights matrix. So both your betas and their standard errors are
> >>>>>> unusable,
> >>>>>>>> I'm afraid. You are actually very much closer to ordinary kriging,
> >>>>>> looking
> >>>>>>>> at the way in which distance attenuates the correlation in value
> of
> >>>>>>>> proximate observations.
> >>>>>>>>
> >>>>>>>> Hope this clarifies,
> >>>>>>>>
> >>>>>>>> Roger
> >>>>>>>>
> >>>>>>>>>
> >>>>>>>>> I am totally new to the area of spatial econometrics, so I am
> >> taking
> >>>>>>>> things
> >>>>>>>>> one step at a time. Some readings suggest I may need distance
> >> matrix
> >>>> or
> >>>>>>>>> weight matrix but for now I think I should try the current
> >> approach.
> >>>>>>>>>
> >>>>>>>>> Thank you.
> >>>>>>>>>
> >>>>>>>>> -------------
> >>>>>>>>> Lom
> >>>>>>>>>
> >>>>>>>>> On Wed, Jun 3, 2020 at 8:18 AM Roger Bivand <Roger.Bivand using nhh.no
> >
> >>>>>> wrote:
> >>>>>>>>>
> >>>>>>>>>> On Wed, 3 Jun 2020, Lom Navanyo wrote:
> >>>>>>>>>>
> >>>>>>>>>>> I had the errors with rtree using R 3.6.3. I have since changed
> >> to
> >>>> R
> >>>>>>>>>> 4.0.0
> >>>>>>>>>>> but I got the same error.
> >>>>>>>>>>>
> >>>>>>>>>>> And yes, for Roger's example, I have the objects wd1, ... wd4,
> >> all
> >>>>>>>> with
> >>>>>>>>>>> length 101. I think my difficulty is my inability to output the
> >>>> list
> >>>>>>>>>>> detailing the point IDs t50_fid.
> >>>>>>>>>>
> >>>>>>>>>> library(spData)
> >>>>>>>>>> library(sf)
> >>>>>>>>>> projdata<-st_transform(nz_height, 32759)
> >>>>>>>>>> pts <- st_coordinates(projdata)
> >>>>>>>>>> library(spdep)
> >>>>>>>>>> bufferR <- c(402.336, 1609.34, 3218.69, 4828.03, 6437.38)
> >>>>>>>>>> bds <- c(0, bufferR)
> >>>>>>>>>> wd1 <- dnearneigh(pts, bds[1], bds[2])
> >>>>>>>>>> wd2 <- dnearneigh(pts, bds[2], bds[3])
> >>>>>>>>>> wd3 <- dnearneigh(pts, bds[3], bds[4])
> >>>>>>>>>> wd4 <- dnearneigh(pts, bds[4], bds[5])
> >>>>>>>>>> sn_band1 <- listw2sn(nb2listw(wd1, style="B", zero.policy=TRUE))
> >>>>>>>>>> sn_band1$band <- paste(attr(wd1, "distances"), collapse="-")
> >>>>>>>>>> sn_band2 <- listw2sn(nb2listw(wd2, style="B", zero.policy=TRUE))
> >>>>>>>>>> sn_band2$band <- paste(attr(wd2, "distances"), collapse="-")
> >>>>>>>>>> sn_band3 <- listw2sn(nb2listw(wd3, style="B", zero.policy=TRUE))
> >>>>>>>>>> sn_band3$band <- paste(attr(wd3, "distances"), collapse="-")
> >>>>>>>>>> sn_band4 <- listw2sn(nb2listw(wd4, style="B", zero.policy=TRUE))
> >>>>>>>>>> sn_band4$band <- paste(attr(wd4, "distances"), collapse="-")
> >>>>>>>>>> data_out <- do.call("rbind", list(sn_band1, sn_band2, sn_band3,
> >>>>>>>> sn_band4))
> >>>>>>>>>> class(data_out) <- "data.frame"
> >>>>>>>>>> table(data_out$band)
> >>>>>>>>>> data_out$ID_from <- projdata$t50_fid[data_out$from]
> >>>>>>>>>> data_out$ID_to <- projdata$t50_fid[data_out$to]
> >>>>>>>>>> data_out$elev_from <- projdata$elevation[data_out$from]
> >>>>>>>>>> data_out$elev_to <- projdata$elevation[data_out$to]
> >>>>>>>>>> str(data_out)
> >>>>>>>>>>
> >>>>>>>>>> The "spatial.neighbour" representation was that used in the
> S-Plus
> >>>>>>>>>> SpatialStats module, with "from" and "to" columns, and here
> drops
> >>>>>>>>>> no-neighbour cases gracefully. So listw2sn() comes in useful
> >>>>>>>>>> for creating the output, and from there, just look-up in the
> >>>>>>>>>> input data.frame. Observations here cannot be their own
> >> neighbours.
> >>>>>>>>>>
> >>>>>>>>>> It would be relevant to know why you need these, are you looking
> >> at
> >>>>>>>>>> variogram clouds?
> >>>>>>>>>>
> >>>>>>>>>> Hope this clarifies,
> >>>>>>>>>>
> >>>>>>>>>> Roger
> >>>>>>>>>>
> >>>>>>>>>>>
> >>>>>>>>>>> ---------
> >>>>>>>>>>> Lom
> >>>>>>>>>>>
> >>>>>>>>>>> On Tue, Jun 2, 2020 at 8:02 PM Kent Johnson <
> kent3737 using gmail.com>
> >>>>>>>> wrote:
> >>>>>>>>>>>
> >>>>>>>>>>>> Roger's example works for me and gives a list of length 101. I
> >> did
> >>>>>>>> have
> >>>>>>>>>>>> some issues that were resolved by updating packages. I'm
> using R
> >>>>>> 3.6.3
> >>>>>>>>>> on
> >>>>>>>>>>>> macOS 10.15.4. I also use rtree successfully on Windows 10
> with
> >> R
> >>>>>>>> 3.6.3.
> >>>>>>>>>>>>
> >>>>>>>>>>>> Kent
> >>>>>>>>>>>>
> >>>>>>>>>>>> On Tue, Jun 2, 2020 at 12:29 PM Roger Bivand <
> >> Roger.Bivand using nhh.no
> >>>>>
> >>>>>>>>>> wrote:
> >>>>>>>>>>>>
> >>>>>>>>>>>>> On Tue, 2 Jun 2020, Kent Johnson wrote:
> >>>>>>>>>>>>>
> >>>>>>>>>>>>>> rtree uses Euclidean distance so the points should be in a
> >>>>>>>> coordinate
> >>>>>>>>>>>>>> system where this makes sense at least as a reasonable
> >>>>>>>> approximation.
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> I tried the original example:
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> remotes::install_github("hunzikp/rtree")
> >>>>>>>>>>>>> library(spData)
> >>>>>>>>>>>>> library(sf)
> >>>>>>>>>>>>> projdata<-st_transform(nz_height, 32759)
> >>>>>>>>>>>>> library(rtree)
> >>>>>>>>>>>>> pts <- st_coordinates(projdata)
> >>>>>>>>>>>>> rt <- RTree(st_coordinates(projdata))
> >>>>>>>>>>>>> bufferR <- c(402.336, 1609.34, 3218.69, 4828.03, 6437.38)
> >>>>>>>>>>>>> wd1 <- withinDistance(rt, pts, bufferR[1])
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> but unfortunately failed (maybe newer Boost headers than
> >> yours?):
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> Error in UseMethod("withinDistance", rTree) :
> >>>>>>>>>>>>> no applicable method for 'withinDistance' applied to an
> >> object
> >>>>>> of
> >>>>>>>>>>>>> class
> >>>>>>>>>>>>> "c('list', 'RTree')"
> >>>>>>>>>>>>>
> >>>>>>>>>>>>>>
> >>>>>>>>>>>>>> Kent
> >>>>>>>>>>>>>>
> >>>>>>>>>>>>>> On Tue, Jun 2, 2020 at 9:59 AM Roger Bivand <
> >>>> Roger.Bivand using nhh.no>
> >>>>>>>>>>>>> wrote:
> >>>>>>>>>>>>>>
> >>>>>>>>>>>>>>> On Tue, 2 Jun 2020, Kent Johnson wrote:
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>> Date: Tue, 2 Jun 2020 02:44:17 -0500
> >>>>>>>>>>>>>>>>> From: Lom Navanyo <lomnavasia using gmail.com>
> >>>>>>>>>>>>>>>>> To: r-sig-geo using r-project.org
> >>>>>>>>>>>>>>>>> Subject: [R-sig-Geo] How to efficiently generate data of
> >>>>>>>>>> neighboring
> >>>>>>>>>>>>>>>>> points within specified radii (distances) for
> each
> >>>>>> point
> >>>>>>>>>> in a
> >>>>>>>>>>>>>>> given
> >>>>>>>>>>>>>>>>> points data set.
> >>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>> Hello,
> >>>>>>>>>>>>>>>>> I have data set of about 3400 location points with which
> I
> >> am
> >>>>>>>>>> trying
> >>>>>>>>>>>>> to
> >>>>>>>>>>>>>>>>> generate data of each point and their neighbors within
> >>>> defined
> >>>>>>>>>> radii
> >>>>>>>>>>>>>>> (eg,
> >>>>>>>>>>>>>>>>> 0.25, 1, and 3 miles).
> >>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>> The rtree package is very fast and memory-efficient for
> >>>>>>>>>>>>> within-distance
> >>>>>>>>>>>>>>>> calculations.
> >>>>>>>>>>>>>>>> https://github.com/hunzikp/rtree
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>> Thanks! Does this also apply when the input points are in
> >>>>>>>>>> geographical
> >>>>>>>>>>>>>>> coordinates?
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>> Roger
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>> Kent Johnson
> >>>>>>>>>>>>>>>> Cambridge, MA
> >>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>> [[alternative HTML version deleted]]
> >>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>> _______________________________________________
> >>>>>>>>>>>>>>>> R-sig-Geo mailing list
> >>>>>>>>>>>>>>>> R-sig-Geo using 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; e-mail: Roger.Bivand using nhh.no
> >>>>>>>>>>>>>>> https://orcid.org/0000-0003-2392-6140
> >>>>>>>>>>>>>>>
> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> --
> >>>>>>>>>>>>> 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 using nhh.no
> >>>>>>>>>>>>> https://orcid.org/0000-0003-2392-6140
> >>>>>>>>>>>>> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
> >>>>>>>>>>>>>
> >>>>>>>>>>>>
> >>>>>>>>>>>
> >>>>>>>>>>
> >>>>>>>>>> --
> >>>>>>>>>> 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 using nhh.no
> >>>>>>>>>> https://orcid.org/0000-0003-2392-6140
> >>>>>>>>>> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
> >>>>>>>>>>
> >>>>>>>>>
> >>>>>>>>
> >>>>>>>> --
> >>>>>>>> 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 using nhh.no
> >>>>>>>> https://orcid.org/0000-0003-2392-6140
> >>>>>>>> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
> >>>>>>>>
> >>>>>>>
> >>>>>>
> >>>>>> --
> >>>>>> 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 using nhh.no
> >>>>>> https://orcid.org/0000-0003-2392-6140
> >>>>>> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
> >>>>>>
> >>>>>
> >>>>
> >>>> --
> >>>> 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 using nhh.no
> >>>> https://orcid.org/0000-0003-2392-6140
> >>>> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
> >>>>
> >>>
> >>
> >> --
> >> 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 using nhh.no
> >> https://orcid.org/0000-0003-2392-6140
> >> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
> >>
> >
>
> --
> 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 using nhh.no
> https://orcid.org/0000-0003-2392-6140
> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
>
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