[R-sig-Geo] How to efficiently generate data of neighboring points

[Roger Bivand]

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