How to find all first order neighbors of a collection of points

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How to find all first order neighbors of a collection of points

BL250604
Hi all,

Currently, I am working with U.S. voter data. Below, I included a brief example of the structure of the data with some reproducible code. My data set consists of roughly 233,000 (233k) entries, each specifying a voter and their particular latitude/longitude pair. I have been using the spdep package with the hope of creating a CAR model. To begin the analysis, we need to find all first order neighbors of every point in the data.

While spdep has fantastic commands for finding k nearest neighbors (knearneigh), and a useful command for finding lag of order 3 or more (nblag), I have yet to find a method which is suitable for our purposes (lag = 1, or lag =2). Additionally, I looked into altering the nblag command to accommodate maxlag = 1 or maxlag = 2, but the command relies on an nb format, which is problematic as we are looking for the underlying neighborhood structure.

There has been numerous work done with polygons, or data which already is in “nb” format, but after reading the literature, it seems that polygons are not appropriate, nor are distance based neighbor techniques, due to density fluctuations over the area of interest.

Below is some reproducible code I wrote. I would like to note that I am currently working in R 1.1.453 on a MacBook.

# Create a data frame of 10 voters, picked at random
voter.1 = c(1, -75.52187, 40.62320)
voter.2 = c(2,-75.56373, 40.55216)
voter.3 = c(3,-75.39587, 40.55416)
voter.4 = c(4,-75.42248, 40.64326)
voter.5 = c(5,-75.56654, 40.54948)
voter.6 = c(6,-75.56257, 40.67375)
voter.7 = c(7, -75.51888, 40.59715)
voter.8 = c(8, -75.59879, 40.60014)
voter.9 = c(9, -75.59879, 40.60014)
voter.10 = c(10, -75.50877, 40.53129)

# Bind the vectors together
voter.subset = rbind(voter.1, voter.2, voter.3, voter.4, voter.5, voter.6, voter.7, voter.8, voter.9, voter.10)

# Rename the columns
colnames(voter.subset) = c("Voter.ID", "Longitude", "Latitude")

# Change the class from a matrix to a data frame
voter.subset = as.data.frame(voter.subset)

# Load in the required packages
library(spdep)
library(sp)

# Set the coordinates
coordinates(voter.subset) = c("Longitude", "Latitude")
coords = coordinates(voter.subset)

# Jitter to ensure no duplicate points
coords = jitter(coords, factor = 1)

# Find the first nearest neighbor of each point
one.nn = knearneigh(coords, k=1)

# Convert the first nearest neighbor to format "nb"
one.nn_nb = knn2nb(one.nn, sym = F)

Thank you in advance for any help you may offer, and for taking the time to read this. I have consulted Applied Spatial Data Analysis with R (Bivand, Pebesma, Gomez-Rubio), as well as other Sig-Geo threads, the spdep documentation, and the nb vignette (Bivand, April 3, 2018) from earlier this year.

Warmest,
Ben
--
Benjamin Lieberman
Muhlenberg College 2019
Mobile: 301.299.8928



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Re: How to find all first order neighbors of a collection of points

Facundo Muñoz-2
Dear Benjamin,

I'm not sure how you define "first order neighbors" for a point. The
first thing that comes to my mind is to use their corresponding voronoi
polygons and define neighborhood from there. Following your code:

v <- dismo::voronoi(coords)
par(mfrow = c(1, 2), xaxt = "n", yaxt = "n", mgp = c(0, 0, 0))
plot(coords, type = "n", xlab = NA, ylab = NA)
plot(v, add = TRUE)
text(x = coords[, 1], y = coords[, 2], labels = voter.subset$Voter.ID)
plot(coords, type = "n", xlab = NA, ylab = NA)
plot(poly2nb(v), coords, add = TRUE, col = "gray")

ƒacu.-


On 07/12/2018 09:00 PM, Benjamin Lieberman wrote:

> Hi all,
>
> Currently, I am working with U.S. voter data. Below, I included a brief example of the structure of the data with some reproducible code. My data set consists of roughly 233,000 (233k) entries, each specifying a voter and their particular latitude/longitude pair. I have been using the spdep package with the hope of creating a CAR model. To begin the analysis, we need to find all first order neighbors of every point in the data.
>
> While spdep has fantastic commands for finding k nearest neighbors (knearneigh), and a useful command for finding lag of order 3 or more (nblag), I have yet to find a method which is suitable for our purposes (lag = 1, or lag =2). Additionally, I looked into altering the nblag command to accommodate maxlag = 1 or maxlag = 2, but the command relies on an nb format, which is problematic as we are looking for the underlying neighborhood structure.
>
> There has been numerous work done with polygons, or data which already is in “nb” format, but after reading the literature, it seems that polygons are not appropriate, nor are distance based neighbor techniques, due to density fluctuations over the area of interest.
>
> Below is some reproducible code I wrote. I would like to note that I am currently working in R 1.1.453 on a MacBook.
>
> # Create a data frame of 10 voters, picked at random
> voter.1 = c(1, -75.52187, 40.62320)
> voter.2 = c(2,-75.56373, 40.55216)
> voter.3 = c(3,-75.39587, 40.55416)
> voter.4 = c(4,-75.42248, 40.64326)
> voter.5 = c(5,-75.56654, 40.54948)
> voter.6 = c(6,-75.56257, 40.67375)
> voter.7 = c(7, -75.51888, 40.59715)
> voter.8 = c(8, -75.59879, 40.60014)
> voter.9 = c(9, -75.59879, 40.60014)
> voter.10 = c(10, -75.50877, 40.53129)
>
> # Bind the vectors together
> voter.subset = rbind(voter.1, voter.2, voter.3, voter.4, voter.5, voter.6, voter.7, voter.8, voter.9, voter.10)
>
> # Rename the columns
> colnames(voter.subset) = c("Voter.ID", "Longitude", "Latitude")
>
> # Change the class from a matrix to a data frame
> voter.subset = as.data.frame(voter.subset)
>
> # Load in the required packages
> library(spdep)
> library(sp)
>
> # Set the coordinates
> coordinates(voter.subset) = c("Longitude", "Latitude")
> coords = coordinates(voter.subset)
>
> # Jitter to ensure no duplicate points
> coords = jitter(coords, factor = 1)
>
> # Find the first nearest neighbor of each point
> one.nn = knearneigh(coords, k=1)
>
> # Convert the first nearest neighbor to format "nb"
> one.nn_nb = knn2nb(one.nn, sym = F)
>
> Thank you in advance for any help you may offer, and for taking the time to read this. I have consulted Applied Spatial Data Analysis with R (Bivand, Pebesma, Gomez-Rubio), as well as other Sig-Geo threads, the spdep documentation, and the nb vignette (Bivand, April 3, 2018) from earlier this year.
>
> Warmest,
> Ben
> --
> Benjamin Lieberman
> Muhlenberg College 2019
> Mobile: 301.299.8928
>
>
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo


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Re: How to find all first order neighbors of a collection of points

Roger Bivand
Administrator
On Fri, 13 Jul 2018, Facundo Muñoz wrote:

> Dear Benjamin,
>
> I'm not sure how you define "first order neighbors" for a point. The
> first thing that comes to my mind is to use their corresponding voronoi
> polygons and define neighborhood from there. Following your code:

Thanks, the main source of confusion is that "first order neighbors" are
not defined. A k=1 neighbour could be (as below), as could k=6, or voronoi
neighbours, or sphere of influence etc. So reading vignette("nb") would be
a starting point.

Also note that voronoi and other graph-based neighbours should only use
planar coordinates - including dismo::voronoi, which uses deldir::deldir()
- just like spdep::tri2nb(). Triangulation can lead to spurious neighbours
on the convex hull.

>
> v <- dismo::voronoi(coords)
> par(mfrow = c(1, 2), xaxt = "n", yaxt = "n", mgp = c(0, 0, 0))
> plot(coords, type = "n", xlab = NA, ylab = NA)
> plot(v, add = TRUE)
> text(x = coords[, 1], y = coords[, 2], labels = voter.subset$Voter.ID)
> plot(coords, type = "n", xlab = NA, ylab = NA)
> plot(poly2nb(v), coords, add = TRUE, col = "gray")
>
> ƒacu.-
>
>
> On 07/12/2018 09:00 PM, Benjamin Lieberman wrote:
>> Hi all,
>>
>> Currently, I am working with U.S. voter data. Below, I included a brief
>> example of the structure of the data with some reproducible code. My
>> data set consists of roughly 233,000 (233k) entries, each specifying a
>> voter and their particular latitude/longitude pair.
Using individual voter data is highly dangerous, and must in every case be
subject to the strictest privacy rules. Voter data does not in essence
have position - the only valid voting data that has position is of the
voting station/precinct, and those data are aggregated to preserve
anonymity.

Why does position and voter data not have position? Which location should
you use - residence, workplace, what? What are these locations proxying?
Nothing valid can be drawn from "just voter data" - you can get
conclusions from carefully constructed stratified exit polls, but there
the key gender/age/ethnicity/social class/etc. confounders are handled by
design. Why should voting decisions be influenced by proximity (they are
not)? The missing element here is looking carefully at relevant covariates
at more aggregated levels (in the US typically zoning controlling social
class positional segregation, etc.).

>> I have been using the spdep package with the hope of creating a CAR
>> model. To begin the analysis, we need to find all first order neighbors
>> of every point in the data.
>>
>> While spdep has fantastic commands for finding k nearest neighbors
>> (knearneigh), and a useful command for finding lag of order 3 or more
>> (nblag), I have yet to find a method which is suitable for our purposes
>> (lag = 1, or lag =2). Additionally, I looked into altering the nblag
>> command to accommodate maxlag = 1 or maxlag = 2, but the command relies
>> on an nb format, which is problematic as we are looking for the
>> underlying neighborhood structure.
>>
>> There has been numerous work done with polygons, or data which already
>> is in “nb” format, but after reading the literature, it seems that
>> polygons are not appropriate, nor are distance based neighbor
>> techniques, due to density fluctuations over the area of interest.
>>
>> Below is some reproducible code I wrote. I would like to note that I am
>> currently working in R 1.1.453 on a MacBook.
You mean RStudio, there is no such version of R.

>>
>> # Create a data frame of 10 voters, picked at random
>> voter.1 = c(1, -75.52187, 40.62320)
>> voter.2 = c(2,-75.56373, 40.55216)
>> voter.3 = c(3,-75.39587, 40.55416)
>> voter.4 = c(4,-75.42248, 40.64326)
>> voter.5 = c(5,-75.56654, 40.54948)
>> voter.6 = c(6,-75.56257, 40.67375)
>> voter.7 = c(7, -75.51888, 40.59715)
>> voter.8 = c(8, -75.59879, 40.60014)
>> voter.9 = c(9, -75.59879, 40.60014)
>> voter.10 = c(10, -75.50877, 40.53129)
>>
These are in geographical coordinates.

>> # Bind the vectors together
>> voter.subset = rbind(voter.1, voter.2, voter.3, voter.4, voter.5, voter.6, voter.7, voter.8, voter.9, voter.10)
>>
>> # Rename the columns
>> colnames(voter.subset) = c("Voter.ID", "Longitude", "Latitude")
>>
>> # Change the class from a matrix to a data frame
>> voter.subset = as.data.frame(voter.subset)
>>
>> # Load in the required packages
>> library(spdep)
>> library(sp)
>>
>> # Set the coordinates
>> coordinates(voter.subset) = c("Longitude", "Latitude")
>> coords = coordinates(voter.subset)
>>
>> # Jitter to ensure no duplicate points
>> coords = jitter(coords, factor = 1)
>>
jitter does not respect geographical coordinated (decimal degree metric).

>> # Find the first nearest neighbor of each point
>> one.nn = knearneigh(coords, k=1)

See the help page (hint: longlat=TRUE to use Great Circle distances, much
slower than planar).

>>
>> # Convert the first nearest neighbor to format "nb"
>> one.nn_nb = knn2nb(one.nn, sym = F)
>>
>> Thank you in advance for any help you may offer, and for taking the
>> time to read this. I have consulted Applied Spatial Data Analysis with
>> R (Bivand, Pebesma, Gomez-Rubio), as well as other Sig-Geo threads, the
>> spdep documentation, and the nb vignette (Bivand, April 3, 2018) from
>> earlier this year.
>>
>> Warmest,
>> Ben
>> --
>> Benjamin Lieberman
>> Muhlenberg College 2019
>> Mobile: 301.299.8928
>>
>>
>>
>> [[alternative HTML version deleted]]
Plain text only, please.

>>
>> _______________________________________________
>> R-sig-Geo mailing list
>> [hidden email]
>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> 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: [hidden email]
http://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
_______________________________________________
R-sig-Geo mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/r-sig-geo
Roger Bivand
Department of Economics
Norwegian School of Economics
Helleveien 30
N-5045 Bergen, Norway
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Re: How to find all first order neighbors of a collection of points

BL250604
Roger anf Facu,

Thank you very much for the help. In terms of the data, I only provided the ID and Lat/Long pairs because they were the only covariates which were necessary. The data set we are using was purchased and contains voter registration information, voter history, and census tract information, after some geocoding took place. The locations are the residents houses, in this instance.

I have rerun the knn with longlat = T, but I am still hung up on the idea of the first order neighbors. I have reread the vignette and section 5 discusses High-Order Neighbors, but there isn’t any mention of first or second order neighbors, as you mentioned above (“first order neighbors are not defined”). One of the pieces of literature I found said that polygons are problematic to work with, as are tesslations for precisely the reason you mentioned, non-planarity. For this reason, I am hung up on the idea of how to find all first order neighbors for a point, especially as the number of first order neighbors varies from point to point, and such knearneigh would not be appropriate here.

If this is something that does not seem feasible, maybe another tactic is necessary.

Again, thank you all for the help.

Warmest
--
Benjamin Lieberman
Muhlenberg College 2019
Mobile: 301.299.8928

> On Jul 13, 2018, at 6:11 AM, Roger Bivand <[hidden email]> wrote:
>
> On Fri, 13 Jul 2018, Facundo Muñoz wrote:
>
>> Dear Benjamin,
>>
>> I'm not sure how you define "first order neighbors" for a point. The
>> first thing that comes to my mind is to use their corresponding voronoi
>> polygons and define neighborhood from there. Following your code:
>
> Thanks, the main source of confusion is that "first order neighbors" are not defined. A k=1 neighbour could be (as below), as could k=6, or voronoi neighbours, or sphere of influence etc. So reading vignette("nb") would be a starting point.
>
> Also note that voronoi and other graph-based neighbours should only use planar coordinates - including dismo::voronoi, which uses deldir::deldir() - just like spdep::tri2nb(). Triangulation can lead to spurious neighbours on the convex hull.
>
>>
>> v <- dismo::voronoi(coords)
>> par(mfrow = c(1, 2), xaxt = "n", yaxt = "n", mgp = c(0, 0, 0))
>> plot(coords, type = "n", xlab = NA, ylab = NA)
>> plot(v, add = TRUE)
>> text(x = coords[, 1], y = coords[, 2], labels = voter.subset$Voter.ID)
>> plot(coords, type = "n", xlab = NA, ylab = NA)
>> plot(poly2nb(v), coords, add = TRUE, col = "gray")
>>
>> ƒacu.-
>>
>>
>> On 07/12/2018 09:00 PM, Benjamin Lieberman wrote:
>>> Hi all,
>>>
>>> Currently, I am working with U.S. voter data. Below, I included a brief example of the structure of the data with some reproducible code. My data set consists of roughly 233,000 (233k) entries, each specifying a voter and their particular latitude/longitude pair.
>
> Using individual voter data is highly dangerous, and must in every case be subject to the strictest privacy rules. Voter data does not in essence have position - the only valid voting data that has position is of the voting station/precinct, and those data are aggregated to preserve anonymity.
>
> Why does position and voter data not have position? Which location should you use - residence, workplace, what? What are these locations proxying? Nothing valid can be drawn from "just voter data" - you can get conclusions from carefully constructed stratified exit polls, but there the key gender/age/ethnicity/social class/etc. confounders are handled by design. Why should voting decisions be influenced by proximity (they are not)? The missing element here is looking carefully at relevant covariates at more aggregated levels (in the US typically zoning controlling social class positional segregation, etc.).
>
>>> I have been using the spdep package with the hope of creating a CAR model. To begin the analysis, we need to find all first order neighbors of every point in the data.
>>>
>>> While spdep has fantastic commands for finding k nearest neighbors (knearneigh), and a useful command for finding lag of order 3 or more (nblag), I have yet to find a method which is suitable for our purposes (lag = 1, or lag =2). Additionally, I looked into altering the nblag command to accommodate maxlag = 1 or maxlag = 2, but the command relies on an nb format, which is problematic as we are looking for the underlying neighborhood structure.
>>>
>>> There has been numerous work done with polygons, or data which already is in “nb” format, but after reading the literature, it seems that polygons are not appropriate, nor are distance based neighbor techniques, due to density fluctuations over the area of interest.
>>>
>>> Below is some reproducible code I wrote. I would like to note that I am currently working in R 1.1.453 on a MacBook.
>
> You mean RStudio, there is no such version of R.
>
>>>
>>> # Create a data frame of 10 voters, picked at random
>>> voter.1 = c(1, -75.52187, 40.62320)
>>> voter.2 = c(2,-75.56373, 40.55216)
>>> voter.3 = c(3,-75.39587, 40.55416)
>>> voter.4 = c(4,-75.42248, 40.64326)
>>> voter.5 = c(5,-75.56654, 40.54948)
>>> voter.6 = c(6,-75.56257, 40.67375)
>>> voter.7 = c(7, -75.51888, 40.59715)
>>> voter.8 = c(8, -75.59879, 40.60014)
>>> voter.9 = c(9, -75.59879, 40.60014)
>>> voter.10 = c(10, -75.50877, 40.53129)
>>>
>
> These are in geographical coordinates.
>
>>> # Bind the vectors together
>>> voter.subset = rbind(voter.1, voter.2, voter.3, voter.4, voter.5, voter.6, voter.7, voter.8, voter.9, voter.10)
>>>
>>> # Rename the columns
>>> colnames(voter.subset) = c("Voter.ID", "Longitude", "Latitude")
>>>
>>> # Change the class from a matrix to a data frame
>>> voter.subset = as.data.frame(voter.subset)
>>>
>>> # Load in the required packages
>>> library(spdep)
>>> library(sp)
>>>
>>> # Set the coordinates
>>> coordinates(voter.subset) = c("Longitude", "Latitude")
>>> coords = coordinates(voter.subset)
>>>
>>> # Jitter to ensure no duplicate points
>>> coords = jitter(coords, factor = 1)
>>>
>
> jitter does not respect geographical coordinated (decimal degree metric).
>
>>> # Find the first nearest neighbor of each point
>>> one.nn = knearneigh(coords, k=1)
>
> See the help page (hint: longlat=TRUE to use Great Circle distances, much slower than planar).
>
>>>
>>> # Convert the first nearest neighbor to format "nb"
>>> one.nn_nb = knn2nb(one.nn, sym = F)
>>>
>>> Thank you in advance for any help you may offer, and for taking the time to read this. I have consulted Applied Spatial Data Analysis with R (Bivand, Pebesma, Gomez-Rubio), as well as other Sig-Geo threads, the spdep documentation, and the nb vignette (Bivand, April 3, 2018) from earlier this year.
>>>
>>> Warmest,
>>> Ben
>>> --
>>> Benjamin Lieberman
>>> Muhlenberg College 2019
>>> Mobile: 301.299.8928
>>>
>>>
>>>
>>> [[alternative HTML version deleted]]
>
> Plain text only, please.
>
>>>
>>> _______________________________________________
>>> R-sig-Geo mailing list
>>> [hidden email] <mailto:[hidden email]>
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
>>
>>
>> [[alternative HTML version deleted]]
>>
>> _______________________________________________
>> R-sig-Geo mailing list
>> [hidden email] <mailto:[hidden email]>
>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <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: [hidden email] <mailto:[hidden email]>
> http://orcid.org/0000-0003-2392-6140 <http://orcid.org/0000-0003-2392-6140>
> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en_______________________________________________ <https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en_______________________________________________>
> R-sig-Geo mailing list
> [hidden email] <mailto:[hidden email]>
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo>

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Re: How to find all first order neighbors of a collection of points

BL250604
All-

I would like to note that as the data is proprietary, and for obvious privacy concerns, the lat/long pairs were randomly generated, and were not taken directly from the data.


--
Benjamin Lieberman
Muhlenberg College 2019
Mobile: 301.299.8928

> On Jul 13, 2018, at 6:58 AM, Benjamin Lieberman <[hidden email]> wrote:
>
> Roger anf Facu,
>
> Thank you very much for the help. In terms of the data, I only provided the ID and Lat/Long pairs because they were the only covariates which were necessary. The data set we are using was purchased and contains voter registration information, voter history, and census tract information, after some geocoding took place. The locations are the residents houses, in this instance.
>
> I have rerun the knn with longlat = T, but I am still hung up on the idea of the first order neighbors. I have reread the vignette and section 5 discusses High-Order Neighbors, but there isn’t any mention of first or second order neighbors, as you mentioned above (“first order neighbors are not defined”). One of the pieces of literature I found said that polygons are problematic to work with, as are tesslations for precisely the reason you mentioned, non-planarity. For this reason, I am hung up on the idea of how to find all first order neighbors for a point, especially as the number of first order neighbors varies from point to point, and such knearneigh would not be appropriate here.
>
> If this is something that does not seem feasible, maybe another tactic is necessary.
>
> Again, thank you all for the help.
>
> Warmest
> --
> Benjamin Lieberman
> Muhlenberg College 2019
> Mobile: 301.299.8928
>
>> On Jul 13, 2018, at 6:11 AM, Roger Bivand <[hidden email] <mailto:[hidden email]>> wrote:
>>
>> On Fri, 13 Jul 2018, Facundo Muñoz wrote:
>>
>>> Dear Benjamin,
>>>
>>> I'm not sure how you define "first order neighbors" for a point. The
>>> first thing that comes to my mind is to use their corresponding voronoi
>>> polygons and define neighborhood from there. Following your code:
>>
>> Thanks, the main source of confusion is that "first order neighbors" are not defined. A k=1 neighbour could be (as below), as could k=6, or voronoi neighbours, or sphere of influence etc. So reading vignette("nb") would be a starting point.
>>
>> Also note that voronoi and other graph-based neighbours should only use planar coordinates - including dismo::voronoi, which uses deldir::deldir() - just like spdep::tri2nb(). Triangulation can lead to spurious neighbours on the convex hull.
>>
>>>
>>> v <- dismo::voronoi(coords)
>>> par(mfrow = c(1, 2), xaxt = "n", yaxt = "n", mgp = c(0, 0, 0))
>>> plot(coords, type = "n", xlab = NA, ylab = NA)
>>> plot(v, add = TRUE)
>>> text(x = coords[, 1], y = coords[, 2], labels = voter.subset$Voter.ID)
>>> plot(coords, type = "n", xlab = NA, ylab = NA)
>>> plot(poly2nb(v), coords, add = TRUE, col = "gray")
>>>
>>> ƒacu.-
>>>
>>>
>>> On 07/12/2018 09:00 PM, Benjamin Lieberman wrote:
>>>> Hi all,
>>>>
>>>> Currently, I am working with U.S. voter data. Below, I included a brief example of the structure of the data with some reproducible code. My data set consists of roughly 233,000 (233k) entries, each specifying a voter and their particular latitude/longitude pair.
>>
>> Using individual voter data is highly dangerous, and must in every case be subject to the strictest privacy rules. Voter data does not in essence have position - the only valid voting data that has position is of the voting station/precinct, and those data are aggregated to preserve anonymity.
>>
>> Why does position and voter data not have position? Which location should you use - residence, workplace, what? What are these locations proxying? Nothing valid can be drawn from "just voter data" - you can get conclusions from carefully constructed stratified exit polls, but there the key gender/age/ethnicity/social class/etc. confounders are handled by design. Why should voting decisions be influenced by proximity (they are not)? The missing element here is looking carefully at relevant covariates at more aggregated levels (in the US typically zoning controlling social class positional segregation, etc.).
>>
>>>> I have been using the spdep package with the hope of creating a CAR model. To begin the analysis, we need to find all first order neighbors of every point in the data.
>>>>
>>>> While spdep has fantastic commands for finding k nearest neighbors (knearneigh), and a useful command for finding lag of order 3 or more (nblag), I have yet to find a method which is suitable for our purposes (lag = 1, or lag =2). Additionally, I looked into altering the nblag command to accommodate maxlag = 1 or maxlag = 2, but the command relies on an nb format, which is problematic as we are looking for the underlying neighborhood structure.
>>>>
>>>> There has been numerous work done with polygons, or data which already is in “nb” format, but after reading the literature, it seems that polygons are not appropriate, nor are distance based neighbor techniques, due to density fluctuations over the area of interest.
>>>>
>>>> Below is some reproducible code I wrote. I would like to note that I am currently working in R 1.1.453 on a MacBook.
>>
>> You mean RStudio, there is no such version of R.
>>
>>>>
>>>> # Create a data frame of 10 voters, picked at random
>>>> voter.1 = c(1, -75.52187, 40.62320)
>>>> voter.2 = c(2,-75.56373, 40.55216)
>>>> voter.3 = c(3,-75.39587, 40.55416)
>>>> voter.4 = c(4,-75.42248, 40.64326)
>>>> voter.5 = c(5,-75.56654, 40.54948)
>>>> voter.6 = c(6,-75.56257, 40.67375)
>>>> voter.7 = c(7, -75.51888, 40.59715)
>>>> voter.8 = c(8, -75.59879, 40.60014)
>>>> voter.9 = c(9, -75.59879, 40.60014)
>>>> voter.10 = c(10, -75.50877, 40.53129)
>>>>
>>
>> These are in geographical coordinates.
>>
>>>> # Bind the vectors together
>>>> voter.subset = rbind(voter.1, voter.2, voter.3, voter.4, voter.5, voter.6, voter.7, voter.8, voter.9, voter.10)
>>>>
>>>> # Rename the columns
>>>> colnames(voter.subset) = c("Voter.ID", "Longitude", "Latitude")
>>>>
>>>> # Change the class from a matrix to a data frame
>>>> voter.subset = as.data.frame(voter.subset)
>>>>
>>>> # Load in the required packages
>>>> library(spdep)
>>>> library(sp)
>>>>
>>>> # Set the coordinates
>>>> coordinates(voter.subset) = c("Longitude", "Latitude")
>>>> coords = coordinates(voter.subset)
>>>>
>>>> # Jitter to ensure no duplicate points
>>>> coords = jitter(coords, factor = 1)
>>>>
>>
>> jitter does not respect geographical coordinated (decimal degree metric).
>>
>>>> # Find the first nearest neighbor of each point
>>>> one.nn = knearneigh(coords, k=1)
>>
>> See the help page (hint: longlat=TRUE to use Great Circle distances, much slower than planar).
>>
>>>>
>>>> # Convert the first nearest neighbor to format "nb"
>>>> one.nn_nb = knn2nb(one.nn, sym = F)
>>>>
>>>> Thank you in advance for any help you may offer, and for taking the time to read this. I have consulted Applied Spatial Data Analysis with R (Bivand, Pebesma, Gomez-Rubio), as well as other Sig-Geo threads, the spdep documentation, and the nb vignette (Bivand, April 3, 2018) from earlier this year.
>>>>
>>>> Warmest,
>>>> Ben
>>>> --
>>>> Benjamin Lieberman
>>>> Muhlenberg College 2019
>>>> Mobile: 301.299.8928
>>>>
>>>>
>>>>
>>>> [[alternative HTML version deleted]]
>>
>> Plain text only, please.
>>
>>>>
>>>> _______________________________________________
>>>> R-sig-Geo mailing list
>>>> [hidden email] <mailto:[hidden email]>
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
>>>
>>>
>>> [[alternative HTML version deleted]]
>>>
>>> _______________________________________________
>>> R-sig-Geo mailing list
>>> [hidden email] <mailto:[hidden email]>
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <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: [hidden email] <mailto:[hidden email]>
>> http://orcid.org/0000-0003-2392-6140 <http://orcid.org/0000-0003-2392-6140>
>> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en_______________________________________________ <https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en_______________________________________________>
>> R-sig-Geo mailing list
>> [hidden email] <mailto:[hidden email]>
>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo>


        [[alternative HTML version deleted]]

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Re: How to find all first order neighbors of a collection of points

Roger Bivand
Administrator
In reply to this post by BL250604
On Fri, 13 Jul 2018, Benjamin Lieberman wrote:

> Roger anf Facu,
>
> Thank you very much for the help. In terms of the data, I only provided
> the ID and Lat/Long pairs because they were the only covariates which
> were necessary. The data set we are using was purchased and contains
> voter registration information, voter history, and census tract
> information, after some geocoding took place. The locations are the
> residents houses, in this instance.
>
> I have rerun the knn with longlat = T, but I am still hung up on the
> idea of the first order neighbors. I have reread the vignette and
> section 5 discusses High-Order Neighbors, but there isn’t any mention of
> first or second order neighbors, as you mentioned above (“first order
> neighbors are not defined”). One of the pieces of literature I found
> said that polygons are problematic to work with, as are tesslations for
> precisely the reason you mentioned, non-planarity. For this reason, I am
> hung up on the idea of how to find all first order neighbors for a
> point, especially as the number of first order neighbors varies from
> point to point, and such knearneigh would not be appropriate here.
So project them, and use Euclidean distances in distance or graph-based
methods (or knn). You still have not defined "first order neighbors". That
is your call alone. If you believe that voter behaviour is like a
contagious disease, define contagion, and from that "first order
neighbours". If you are simply accounting for missing background
covariates that have a larger spatial footprint rather than voter-voter
interaction, it probably doesn't matter much. What is the implied model
here - that voters behave by observing the behaviour of their proximate
neighbours (giving similar behaviour for near neighbours) or that voters
are patched/segregated by residence, and near neighbours behave similarly
not because of information spillovers between voters, but because the
voters are subject to aggregate social/economic conditions?

Roger

>
> If this is something that does not seem feasible, maybe another tactic
> is necessary.
>
> Again, thank you all for the help.
>
> Warmest
> --
> Benjamin Lieberman
> Muhlenberg College 2019
> Mobile: 301.299.8928
>
>> On Jul 13, 2018, at 6:11 AM, Roger Bivand <[hidden email]> wrote:
>>
>> On Fri, 13 Jul 2018, Facundo Muñoz wrote:
>>
>>> Dear Benjamin,
>>>
>>> I'm not sure how you define "first order neighbors" for a point. The
>>> first thing that comes to my mind is to use their corresponding voronoi
>>> polygons and define neighborhood from there. Following your code:
>>
>> Thanks, the main source of confusion is that "first order neighbors" are not defined. A k=1 neighbour could be (as below), as could k=6, or voronoi neighbours, or sphere of influence etc. So reading vignette("nb") would be a starting point.
>>
>> Also note that voronoi and other graph-based neighbours should only use planar coordinates - including dismo::voronoi, which uses deldir::deldir() - just like spdep::tri2nb(). Triangulation can lead to spurious neighbours on the convex hull.
>>
>>>
>>> v <- dismo::voronoi(coords)
>>> par(mfrow = c(1, 2), xaxt = "n", yaxt = "n", mgp = c(0, 0, 0))
>>> plot(coords, type = "n", xlab = NA, ylab = NA)
>>> plot(v, add = TRUE)
>>> text(x = coords[, 1], y = coords[, 2], labels = voter.subset$Voter.ID)
>>> plot(coords, type = "n", xlab = NA, ylab = NA)
>>> plot(poly2nb(v), coords, add = TRUE, col = "gray")
>>>
>>> ƒacu.-
>>>
>>>
>>> On 07/12/2018 09:00 PM, Benjamin Lieberman wrote:
>>>> Hi all,
>>>>
>>>> Currently, I am working with U.S. voter data. Below, I included a brief example of the structure of the data with some reproducible code. My data set consists of roughly 233,000 (233k) entries, each specifying a voter and their particular latitude/longitude pair.
>>
>> Using individual voter data is highly dangerous, and must in every case be subject to the strictest privacy rules. Voter data does not in essence have position - the only valid voting data that has position is of the voting station/precinct, and those data are aggregated to preserve anonymity.
>>
>> Why does position and voter data not have position? Which location should you use - residence, workplace, what? What are these locations proxying? Nothing valid can be drawn from "just voter data" - you can get conclusions from carefully constructed stratified exit polls, but there the key gender/age/ethnicity/social class/etc. confounders are handled by design. Why should voting decisions be influenced by proximity (they are not)? The missing element here is looking carefully at relevant covariates at more aggregated levels (in the US typically zoning controlling social class positional segregation, etc.).
>>
>>>> I have been using the spdep package with the hope of creating a CAR model. To begin the analysis, we need to find all first order neighbors of every point in the data.
>>>>
>>>> While spdep has fantastic commands for finding k nearest neighbors (knearneigh), and a useful command for finding lag of order 3 or more (nblag), I have yet to find a method which is suitable for our purposes (lag = 1, or lag =2). Additionally, I looked into altering the nblag command to accommodate maxlag = 1 or maxlag = 2, but the command relies on an nb format, which is problematic as we are looking for the underlying neighborhood structure.
>>>>
>>>> There has been numerous work done with polygons, or data which already is in “nb” format, but after reading the literature, it seems that polygons are not appropriate, nor are distance based neighbor techniques, due to density fluctuations over the area of interest.
>>>>
>>>> Below is some reproducible code I wrote. I would like to note that I am currently working in R 1.1.453 on a MacBook.
>>
>> You mean RStudio, there is no such version of R.
>>
>>>>
>>>> # Create a data frame of 10 voters, picked at random
>>>> voter.1 = c(1, -75.52187, 40.62320)
>>>> voter.2 = c(2,-75.56373, 40.55216)
>>>> voter.3 = c(3,-75.39587, 40.55416)
>>>> voter.4 = c(4,-75.42248, 40.64326)
>>>> voter.5 = c(5,-75.56654, 40.54948)
>>>> voter.6 = c(6,-75.56257, 40.67375)
>>>> voter.7 = c(7, -75.51888, 40.59715)
>>>> voter.8 = c(8, -75.59879, 40.60014)
>>>> voter.9 = c(9, -75.59879, 40.60014)
>>>> voter.10 = c(10, -75.50877, 40.53129)
>>>>
>>
>> These are in geographical coordinates.
>>
>>>> # Bind the vectors together
>>>> voter.subset = rbind(voter.1, voter.2, voter.3, voter.4, voter.5, voter.6, voter.7, voter.8, voter.9, voter.10)
>>>>
>>>> # Rename the columns
>>>> colnames(voter.subset) = c("Voter.ID", "Longitude", "Latitude")
>>>>
>>>> # Change the class from a matrix to a data frame
>>>> voter.subset = as.data.frame(voter.subset)
>>>>
>>>> # Load in the required packages
>>>> library(spdep)
>>>> library(sp)
>>>>
>>>> # Set the coordinates
>>>> coordinates(voter.subset) = c("Longitude", "Latitude")
>>>> coords = coordinates(voter.subset)
>>>>
>>>> # Jitter to ensure no duplicate points
>>>> coords = jitter(coords, factor = 1)
>>>>
>>
>> jitter does not respect geographical coordinated (decimal degree metric).
>>
>>>> # Find the first nearest neighbor of each point
>>>> one.nn = knearneigh(coords, k=1)
>>
>> See the help page (hint: longlat=TRUE to use Great Circle distances, much slower than planar).
>>
>>>>
>>>> # Convert the first nearest neighbor to format "nb"
>>>> one.nn_nb = knn2nb(one.nn, sym = F)
>>>>
>>>> Thank you in advance for any help you may offer, and for taking the time to read this. I have consulted Applied Spatial Data Analysis with R (Bivand, Pebesma, Gomez-Rubio), as well as other Sig-Geo threads, the spdep documentation, and the nb vignette (Bivand, April 3, 2018) from earlier this year.
>>>>
>>>> Warmest,
>>>> Ben
>>>> --
>>>> Benjamin Lieberman
>>>> Muhlenberg College 2019
>>>> Mobile: 301.299.8928
>>>>
>>>>
>>>>
>>>> [[alternative HTML version deleted]]
>>
>> Plain text only, please.
>>
>>>>
>>>> _______________________________________________
>>>> R-sig-Geo mailing list
>>>> [hidden email] <mailto:[hidden email]>
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
>>>
>>>
>>> [[alternative HTML version deleted]]
>>>
>>> _______________________________________________
>>> R-sig-Geo mailing list
>>> [hidden email] <mailto:[hidden email]>
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <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: [hidden email] <mailto:[hidden email]>
>> http://orcid.org/0000-0003-2392-6140 <http://orcid.org/0000-0003-2392-6140>
>> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en_______________________________________________ <https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en_______________________________________________>
>> R-sig-Geo mailing list
>> [hidden email] <mailto:[hidden email]>
>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> 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: [hidden email]
http://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
_______________________________________________
R-sig-Geo mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/r-sig-geo
Roger Bivand
Department of Economics
Norwegian School of Economics
Helleveien 30
N-5045 Bergen, Norway
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Re: How to find all first order neighbors of a collection of points

Roger Bivand
Administrator
In reply to this post by BL250604
On Fri, 13 Jul 2018, Benjamin Lieberman wrote:

> All-
>
> I would like to note that as the data is proprietary, and for obvious
> privacy concerns, the lat/long pairs were randomly generated, and were
> not taken directly from the data.

Thanks for the clarification. Note that if the data are a sample, that is
not a complete listing for one or more study areas, you don't know who the
first order neighbour (the most proximate other voter) is, because that
indidivual may not be in the sample. Your fallback then is to treat the
data as aggregates, unless you rule out local sampling variability.

Roger

>
>
> --
> Benjamin Lieberman
> Muhlenberg College 2019
> Mobile: 301.299.8928
>
>> On Jul 13, 2018, at 6:58 AM, Benjamin Lieberman <[hidden email]> wrote:
>>
>> Roger anf Facu,
>>
>> Thank you very much for the help. In terms of the data, I only provided the ID and Lat/Long pairs because they were the only covariates which were necessary. The data set we are using was purchased and contains voter registration information, voter history, and census tract information, after some geocoding took place. The locations are the residents houses, in this instance.
>>
>> I have rerun the knn with longlat = T, but I am still hung up on the idea of the first order neighbors. I have reread the vignette and section 5 discusses High-Order Neighbors, but there isn’t any mention of first or second order neighbors, as you mentioned above (“first order neighbors are not defined”). One of the pieces of literature I found said that polygons are problematic to work with, as are tesslations for precisely the reason you mentioned, non-planarity. For this reason, I am hung up on the idea of how to find all first order neighbors for a point, especially as the number of first order neighbors varies from point to point, and such knearneigh would not be appropriate here.
>>
>> If this is something that does not seem feasible, maybe another tactic is necessary.
>>
>> Again, thank you all for the help.
>>
>> Warmest
>> --
>> Benjamin Lieberman
>> Muhlenberg College 2019
>> Mobile: 301.299.8928
>>
>>> On Jul 13, 2018, at 6:11 AM, Roger Bivand <[hidden email] <mailto:[hidden email]>> wrote:
>>>
>>> On Fri, 13 Jul 2018, Facundo Muñoz wrote:
>>>
>>>> Dear Benjamin,
>>>>
>>>> I'm not sure how you define "first order neighbors" for a point. The
>>>> first thing that comes to my mind is to use their corresponding voronoi
>>>> polygons and define neighborhood from there. Following your code:
>>>
>>> Thanks, the main source of confusion is that "first order neighbors" are not defined. A k=1 neighbour could be (as below), as could k=6, or voronoi neighbours, or sphere of influence etc. So reading vignette("nb") would be a starting point.
>>>
>>> Also note that voronoi and other graph-based neighbours should only use planar coordinates - including dismo::voronoi, which uses deldir::deldir() - just like spdep::tri2nb(). Triangulation can lead to spurious neighbours on the convex hull.
>>>
>>>>
>>>> v <- dismo::voronoi(coords)
>>>> par(mfrow = c(1, 2), xaxt = "n", yaxt = "n", mgp = c(0, 0, 0))
>>>> plot(coords, type = "n", xlab = NA, ylab = NA)
>>>> plot(v, add = TRUE)
>>>> text(x = coords[, 1], y = coords[, 2], labels = voter.subset$Voter.ID)
>>>> plot(coords, type = "n", xlab = NA, ylab = NA)
>>>> plot(poly2nb(v), coords, add = TRUE, col = "gray")
>>>>
>>>> ƒacu.-
>>>>
>>>>
>>>> On 07/12/2018 09:00 PM, Benjamin Lieberman wrote:
>>>>> Hi all,
>>>>>
>>>>> Currently, I am working with U.S. voter data. Below, I included a brief example of the structure of the data with some reproducible code. My data set consists of roughly 233,000 (233k) entries, each specifying a voter and their particular latitude/longitude pair.
>>>
>>> Using individual voter data is highly dangerous, and must in every case be subject to the strictest privacy rules. Voter data does not in essence have position - the only valid voting data that has position is of the voting station/precinct, and those data are aggregated to preserve anonymity.
>>>
>>> Why does position and voter data not have position? Which location should you use - residence, workplace, what? What are these locations proxying? Nothing valid can be drawn from "just voter data" - you can get conclusions from carefully constructed stratified exit polls, but there the key gender/age/ethnicity/social class/etc. confounders are handled by design. Why should voting decisions be influenced by proximity (they are not)? The missing element here is looking carefully at relevant covariates at more aggregated levels (in the US typically zoning controlling social class positional segregation, etc.).
>>>
>>>>> I have been using the spdep package with the hope of creating a CAR model. To begin the analysis, we need to find all first order neighbors of every point in the data.
>>>>>
>>>>> While spdep has fantastic commands for finding k nearest neighbors (knearneigh), and a useful command for finding lag of order 3 or more (nblag), I have yet to find a method which is suitable for our purposes (lag = 1, or lag =2). Additionally, I looked into altering the nblag command to accommodate maxlag = 1 or maxlag = 2, but the command relies on an nb format, which is problematic as we are looking for the underlying neighborhood structure.
>>>>>
>>>>> There has been numerous work done with polygons, or data which already is in “nb” format, but after reading the literature, it seems that polygons are not appropriate, nor are distance based neighbor techniques, due to density fluctuations over the area of interest.
>>>>>
>>>>> Below is some reproducible code I wrote. I would like to note that I am currently working in R 1.1.453 on a MacBook.
>>>
>>> You mean RStudio, there is no such version of R.
>>>
>>>>>
>>>>> # Create a data frame of 10 voters, picked at random
>>>>> voter.1 = c(1, -75.52187, 40.62320)
>>>>> voter.2 = c(2,-75.56373, 40.55216)
>>>>> voter.3 = c(3,-75.39587, 40.55416)
>>>>> voter.4 = c(4,-75.42248, 40.64326)
>>>>> voter.5 = c(5,-75.56654, 40.54948)
>>>>> voter.6 = c(6,-75.56257, 40.67375)
>>>>> voter.7 = c(7, -75.51888, 40.59715)
>>>>> voter.8 = c(8, -75.59879, 40.60014)
>>>>> voter.9 = c(9, -75.59879, 40.60014)
>>>>> voter.10 = c(10, -75.50877, 40.53129)
>>>>>
>>>
>>> These are in geographical coordinates.
>>>
>>>>> # Bind the vectors together
>>>>> voter.subset = rbind(voter.1, voter.2, voter.3, voter.4, voter.5, voter.6, voter.7, voter.8, voter.9, voter.10)
>>>>>
>>>>> # Rename the columns
>>>>> colnames(voter.subset) = c("Voter.ID", "Longitude", "Latitude")
>>>>>
>>>>> # Change the class from a matrix to a data frame
>>>>> voter.subset = as.data.frame(voter.subset)
>>>>>
>>>>> # Load in the required packages
>>>>> library(spdep)
>>>>> library(sp)
>>>>>
>>>>> # Set the coordinates
>>>>> coordinates(voter.subset) = c("Longitude", "Latitude")
>>>>> coords = coordinates(voter.subset)
>>>>>
>>>>> # Jitter to ensure no duplicate points
>>>>> coords = jitter(coords, factor = 1)
>>>>>
>>>
>>> jitter does not respect geographical coordinated (decimal degree metric).
>>>
>>>>> # Find the first nearest neighbor of each point
>>>>> one.nn = knearneigh(coords, k=1)
>>>
>>> See the help page (hint: longlat=TRUE to use Great Circle distances, much slower than planar).
>>>
>>>>>
>>>>> # Convert the first nearest neighbor to format "nb"
>>>>> one.nn_nb = knn2nb(one.nn, sym = F)
>>>>>
>>>>> Thank you in advance for any help you may offer, and for taking the time to read this. I have consulted Applied Spatial Data Analysis with R (Bivand, Pebesma, Gomez-Rubio), as well as other Sig-Geo threads, the spdep documentation, and the nb vignette (Bivand, April 3, 2018) from earlier this year.
>>>>>
>>>>> Warmest,
>>>>> Ben
>>>>> --
>>>>> Benjamin Lieberman
>>>>> Muhlenberg College 2019
>>>>> Mobile: 301.299.8928
>>>>>
>>>>>
>>>>>
>>>>> [[alternative HTML version deleted]]
>>>
>>> Plain text only, please.
>>>
>>>>>
>>>>> _______________________________________________
>>>>> R-sig-Geo mailing list
>>>>> [hidden email] <mailto:[hidden email]>
>>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
>>>>
>>>>
>>>> [[alternative HTML version deleted]]
>>>>
>>>> _______________________________________________
>>>> R-sig-Geo mailing list
>>>> [hidden email] <mailto:[hidden email]>
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <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: [hidden email] <mailto:[hidden email]>
>>> http://orcid.org/0000-0003-2392-6140 <http://orcid.org/0000-0003-2392-6140>
>>> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en_______________________________________________ <https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en_______________________________________________>
>>> R-sig-Geo mailing list
>>> [hidden email] <mailto:[hidden email]>
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
>
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> 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: [hidden email]
http://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
_______________________________________________
R-sig-Geo mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/r-sig-geo
Roger Bivand
Department of Economics
Norwegian School of Economics
Helleveien 30
N-5045 Bergen, Norway
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Re: How to find all first order neighbors of a collection of points

BL250604
Roger-

Thank you so much for the help. In our case, first order neighbors are all neighbors who are adjacent to a voter. Second order neighbors are then all neighbors who are adjacent to the first order neighbors. Hope that this could clarify what I have been referencing this time.

I will try the method you suggested, thank you.

Best,
Ben
--
Benjamin Lieberman
Muhlenberg College 2019
Mobile: 301.299.8928

> On Jul 13, 2018, at 7:30 AM, Roger Bivand <[hidden email]> wrote:
>
> On Fri, 13 Jul 2018, Benjamin Lieberman wrote:
>
>> All-
>>
>> I would like to note that as the data is proprietary, and for obvious privacy concerns, the lat/long pairs were randomly generated, and were not taken directly from the data.
>
> Thanks for the clarification. Note that if the data are a sample, that is not a complete listing for one or more study areas, you don't know who the first order neighbour (the most proximate other voter) is, because that indidivual may not be in the sample. Your fallback then is to treat the data as aggregates, unless you rule out local sampling variability.
>
> Roger
>
>>
>>
>> --
>> Benjamin Lieberman
>> Muhlenberg College 2019
>> Mobile: 301.299.8928
>>
>>> On Jul 13, 2018, at 6:58 AM, Benjamin Lieberman <[hidden email]> wrote:
>>>
>>> Roger anf Facu,
>>>
>>> Thank you very much for the help. In terms of the data, I only provided the ID and Lat/Long pairs because they were the only covariates which were necessary. The data set we are using was purchased and contains voter registration information, voter history, and census tract information, after some geocoding took place. The locations are the residents houses, in this instance.
>>>
>>> I have rerun the knn with longlat = T, but I am still hung up on the idea of the first order neighbors. I have reread the vignette and section 5 discusses High-Order Neighbors, but there isn’t any mention of first or second order neighbors, as you mentioned above (“first order neighbors are not defined”). One of the pieces of literature I found said that polygons are problematic to work with, as are tesslations for precisely the reason you mentioned, non-planarity. For this reason, I am hung up on the idea of how to find all first order neighbors for a point, especially as the number of first order neighbors varies from point to point, and such knearneigh would not be appropriate here.
>>>
>>> If this is something that does not seem feasible, maybe another tactic is necessary.
>>>
>>> Again, thank you all for the help.
>>>
>>> Warmest
>>> --
>>> Benjamin Lieberman
>>> Muhlenberg College 2019
>>> Mobile: 301.299.8928
>>>
>>>> On Jul 13, 2018, at 6:11 AM, Roger Bivand <[hidden email] <mailto:[hidden email]> <mailto:[hidden email] <mailto:[hidden email]>>> wrote:
>>>>
>>>> On Fri, 13 Jul 2018, Facundo Muñoz wrote:
>>>>
>>>>> Dear Benjamin,
>>>>>
>>>>> I'm not sure how you define "first order neighbors" for a point. The
>>>>> first thing that comes to my mind is to use their corresponding voronoi
>>>>> polygons and define neighborhood from there. Following your code:
>>>>
>>>> Thanks, the main source of confusion is that "first order neighbors" are not defined. A k=1 neighbour could be (as below), as could k=6, or voronoi neighbours, or sphere of influence etc. So reading vignette("nb") would be a starting point.
>>>>
>>>> Also note that voronoi and other graph-based neighbours should only use planar coordinates - including dismo::voronoi, which uses deldir::deldir() - just like spdep::tri2nb(). Triangulation can lead to spurious neighbours on the convex hull.
>>>>
>>>>>
>>>>> v <- dismo::voronoi(coords)
>>>>> par(mfrow = c(1, 2), xaxt = "n", yaxt = "n", mgp = c(0, 0, 0))
>>>>> plot(coords, type = "n", xlab = NA, ylab = NA)
>>>>> plot(v, add = TRUE)
>>>>> text(x = coords[, 1], y = coords[, 2], labels = voter.subset$Voter.ID)
>>>>> plot(coords, type = "n", xlab = NA, ylab = NA)
>>>>> plot(poly2nb(v), coords, add = TRUE, col = "gray")
>>>>>
>>>>> ƒacu.-
>>>>>
>>>>>
>>>>> On 07/12/2018 09:00 PM, Benjamin Lieberman wrote:
>>>>>> Hi all,
>>>>>>
>>>>>> Currently, I am working with U.S. voter data. Below, I included a brief example of the structure of the data with some reproducible code. My data set consists of roughly 233,000 (233k) entries, each specifying a voter and their particular latitude/longitude pair.
>>>>
>>>> Using individual voter data is highly dangerous, and must in every case be subject to the strictest privacy rules. Voter data does not in essence have position - the only valid voting data that has position is of the voting station/precinct, and those data are aggregated to preserve anonymity.
>>>>
>>>> Why does position and voter data not have position? Which location should you use - residence, workplace, what? What are these locations proxying? Nothing valid can be drawn from "just voter data" - you can get conclusions from carefully constructed stratified exit polls, but there the key gender/age/ethnicity/social class/etc. confounders are handled by design. Why should voting decisions be influenced by proximity (they are not)? The missing element here is looking carefully at relevant covariates at more aggregated levels (in the US typically zoning controlling social class positional segregation, etc.).
>>>>
>>>>>> I have been using the spdep package with the hope of creating a CAR model. To begin the analysis, we need to find all first order neighbors of every point in the data.
>>>>>>
>>>>>> While spdep has fantastic commands for finding k nearest neighbors (knearneigh), and a useful command for finding lag of order 3 or more (nblag), I have yet to find a method which is suitable for our purposes (lag = 1, or lag =2). Additionally, I looked into altering the nblag command to accommodate maxlag = 1 or maxlag = 2, but the command relies on an nb format, which is problematic as we are looking for the underlying neighborhood structure.
>>>>>>
>>>>>> There has been numerous work done with polygons, or data which already is in “nb” format, but after reading the literature, it seems that polygons are not appropriate, nor are distance based neighbor techniques, due to density fluctuations over the area of interest.
>>>>>>
>>>>>> Below is some reproducible code I wrote. I would like to note that I am currently working in R 1.1.453 on a MacBook.
>>>>
>>>> You mean RStudio, there is no such version of R.
>>>>
>>>>>>
>>>>>> # Create a data frame of 10 voters, picked at random
>>>>>> voter.1 = c(1, -75.52187, 40.62320)
>>>>>> voter.2 = c(2,-75.56373, 40.55216)
>>>>>> voter.3 = c(3,-75.39587, 40.55416)
>>>>>> voter.4 = c(4,-75.42248, 40.64326)
>>>>>> voter.5 = c(5,-75.56654, 40.54948)
>>>>>> voter.6 = c(6,-75.56257, 40.67375)
>>>>>> voter.7 = c(7, -75.51888, 40.59715)
>>>>>> voter.8 = c(8, -75.59879, 40.60014)
>>>>>> voter.9 = c(9, -75.59879, 40.60014)
>>>>>> voter.10 = c(10, -75.50877, 40.53129)
>>>>>>
>>>>
>>>> These are in geographical coordinates.
>>>>
>>>>>> # Bind the vectors together
>>>>>> voter.subset = rbind(voter.1, voter.2, voter.3, voter.4, voter.5, voter.6, voter.7, voter.8, voter.9, voter.10)
>>>>>>
>>>>>> # Rename the columns
>>>>>> colnames(voter.subset) = c("Voter.ID", "Longitude", "Latitude")
>>>>>>
>>>>>> # Change the class from a matrix to a data frame
>>>>>> voter.subset = as.data.frame(voter.subset)
>>>>>>
>>>>>> # Load in the required packages
>>>>>> library(spdep)
>>>>>> library(sp)
>>>>>>
>>>>>> # Set the coordinates
>>>>>> coordinates(voter.subset) = c("Longitude", "Latitude")
>>>>>> coords = coordinates(voter.subset)
>>>>>>
>>>>>> # Jitter to ensure no duplicate points
>>>>>> coords = jitter(coords, factor = 1)
>>>>>>
>>>>
>>>> jitter does not respect geographical coordinated (decimal degree metric).
>>>>
>>>>>> # Find the first nearest neighbor of each point
>>>>>> one.nn = knearneigh(coords, k=1)
>>>>
>>>> See the help page (hint: longlat=TRUE to use Great Circle distances, much slower than planar).
>>>>
>>>>>>
>>>>>> # Convert the first nearest neighbor to format "nb"
>>>>>> one.nn_nb = knn2nb(one.nn, sym = F)
>>>>>>
>>>>>> Thank you in advance for any help you may offer, and for taking the time to read this. I have consulted Applied Spatial Data Analysis with R (Bivand, Pebesma, Gomez-Rubio), as well as other Sig-Geo threads, the spdep documentation, and the nb vignette (Bivand, April 3, 2018) from earlier this year.
>>>>>>
>>>>>> Warmest,
>>>>>> Ben
>>>>>> --
>>>>>> Benjamin Lieberman
>>>>>> Muhlenberg College 2019
>>>>>> Mobile: 301.299.8928
>>>>>>
>>>>>>
>>>>>>
>>>>>> [[alternative HTML version deleted]]
>>>>
>>>> Plain text only, please.
>>>>
>>>>>>
>>>>>> _______________________________________________
>>>>>> R-sig-Geo mailing list
>>>>>> [hidden email] <mailto:[hidden email]> <mailto:[hidden email] <mailto:[hidden email]>>
>>>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo> <https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo>>
>>>>>
>>>>>
>>>>> [[alternative HTML version deleted]]
>>>>>
>>>>> _______________________________________________
>>>>> R-sig-Geo mailing list
>>>>> [hidden email] <mailto:[hidden email]> <mailto:[hidden email] <mailto:[hidden email]>>
>>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo> <https://stat.ethz.ch/mailman/listinfo/r-sig-geo <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: [hidden email] <mailto:[hidden email]> <mailto:[hidden email] <mailto:[hidden email]>>
>>>> http://orcid.org/0000-0003-2392-6140 <http://orcid.org/0000-0003-2392-6140> <http://orcid.org/0000-0003-2392-6140 <http://orcid.org/0000-0003-2392-6140>>
>>>> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en_______________________________________________ <https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en_______________________________________________><https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en_______________________________________________ <https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en_______________________________________________>>
>>>> R-sig-Geo mailing list
>>>> [hidden email] <mailto:[hidden email]> <mailto:[hidden email] <mailto:[hidden email]>>
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo> <https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo>>
>>
>>
>> [[alternative HTML version deleted]]
>>
>> _______________________________________________
>> R-sig-Geo mailing list
>> [hidden email] <mailto:[hidden email]>
>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <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: [hidden email] <mailto:[hidden email]>
> http://orcid.org/0000-0003-2392-6140 <http://orcid.org/0000-0003-2392-6140>
> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en <https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en>

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Re: How to find all first order neighbors of a collection of points

Roger Bivand
Administrator
On Fri, 13 Jul 2018, Benjamin Lieberman wrote:

> Roger-
>
> Thank you so much for the help. In our case, first order neighbors are
> all neighbors who are adjacent to a voter. Second order neighbors are
> then all neighbors who are adjacent to the first order neighbors. Hope
> that this could clarify what I have been referencing this time.

So you need to define what you mean by adjacent for the purposes of your
study. This depends on knowing the underlying behavioural patterns
affecting interaction.

Roger

>
> I will try the method you suggested, thank you.
>
> Best,
> Ben
> --
> Benjamin Lieberman
> Muhlenberg College 2019
> Mobile: 301.299.8928
>
>> On Jul 13, 2018, at 7:30 AM, Roger Bivand <[hidden email]> wrote:
>>
>> On Fri, 13 Jul 2018, Benjamin Lieberman wrote:
>>
>>> All-
>>>
>>> I would like to note that as the data is proprietary, and for obvious privacy concerns, the lat/long pairs were randomly generated, and were not taken directly from the data.
>>
>> Thanks for the clarification. Note that if the data are a sample, that is not a complete listing for one or more study areas, you don't know who the first order neighbour (the most proximate other voter) is, because that indidivual may not be in the sample. Your fallback then is to treat the data as aggregates, unless you rule out local sampling variability.
>>
>> Roger
>>
>>>
>>>
>>> --
>>> Benjamin Lieberman
>>> Muhlenberg College 2019
>>> Mobile: 301.299.8928
>>>
>>>> On Jul 13, 2018, at 6:58 AM, Benjamin Lieberman <[hidden email]> wrote:
>>>>
>>>> Roger anf Facu,
>>>>
>>>> Thank you very much for the help. In terms of the data, I only provided the ID and Lat/Long pairs because they were the only covariates which were necessary. The data set we are using was purchased and contains voter registration information, voter history, and census tract information, after some geocoding took place. The locations are the residents houses, in this instance.
>>>>
>>>> I have rerun the knn with longlat = T, but I am still hung up on the idea of the first order neighbors. I have reread the vignette and section 5 discusses High-Order Neighbors, but there isn’t any mention of first or second order neighbors, as you mentioned above (“first order neighbors are not defined”). One of the pieces of literature I found said that polygons are problematic to work with, as are tesslations for precisely the reason you mentioned, non-planarity. For this reason, I am hung up on the idea of how to find all first order neighbors for a point, especially as the number of first order neighbors varies from point to point, and such knearneigh would not be appropriate here.
>>>>
>>>> If this is something that does not seem feasible, maybe another tactic is necessary.
>>>>
>>>> Again, thank you all for the help.
>>>>
>>>> Warmest
>>>> --
>>>> Benjamin Lieberman
>>>> Muhlenberg College 2019
>>>> Mobile: 301.299.8928
>>>>
>>>>> On Jul 13, 2018, at 6:11 AM, Roger Bivand <[hidden email] <mailto:[hidden email]> <mailto:[hidden email] <mailto:[hidden email]>>> wrote:
>>>>>
>>>>> On Fri, 13 Jul 2018, Facundo Muñoz wrote:
>>>>>
>>>>>> Dear Benjamin,
>>>>>>
>>>>>> I'm not sure how you define "first order neighbors" for a point. The
>>>>>> first thing that comes to my mind is to use their corresponding voronoi
>>>>>> polygons and define neighborhood from there. Following your code:
>>>>>
>>>>> Thanks, the main source of confusion is that "first order neighbors" are not defined. A k=1 neighbour could be (as below), as could k=6, or voronoi neighbours, or sphere of influence etc. So reading vignette("nb") would be a starting point.
>>>>>
>>>>> Also note that voronoi and other graph-based neighbours should only use planar coordinates - including dismo::voronoi, which uses deldir::deldir() - just like spdep::tri2nb(). Triangulation can lead to spurious neighbours on the convex hull.
>>>>>
>>>>>>
>>>>>> v <- dismo::voronoi(coords)
>>>>>> par(mfrow = c(1, 2), xaxt = "n", yaxt = "n", mgp = c(0, 0, 0))
>>>>>> plot(coords, type = "n", xlab = NA, ylab = NA)
>>>>>> plot(v, add = TRUE)
>>>>>> text(x = coords[, 1], y = coords[, 2], labels = voter.subset$Voter.ID)
>>>>>> plot(coords, type = "n", xlab = NA, ylab = NA)
>>>>>> plot(poly2nb(v), coords, add = TRUE, col = "gray")
>>>>>>
>>>>>> ƒacu.-
>>>>>>
>>>>>>
>>>>>> On 07/12/2018 09:00 PM, Benjamin Lieberman wrote:
>>>>>>> Hi all,
>>>>>>>
>>>>>>> Currently, I am working with U.S. voter data. Below, I included a brief example of the structure of the data with some reproducible code. My data set consists of roughly 233,000 (233k) entries, each specifying a voter and their particular latitude/longitude pair.
>>>>>
>>>>> Using individual voter data is highly dangerous, and must in every case be subject to the strictest privacy rules. Voter data does not in essence have position - the only valid voting data that has position is of the voting station/precinct, and those data are aggregated to preserve anonymity.
>>>>>
>>>>> Why does position and voter data not have position? Which location should you use - residence, workplace, what? What are these locations proxying? Nothing valid can be drawn from "just voter data" - you can get conclusions from carefully constructed stratified exit polls, but there the key gender/age/ethnicity/social class/etc. confounders are handled by design. Why should voting decisions be influenced by proximity (they are not)? The missing element here is looking carefully at relevant covariates at more aggregated levels (in the US typically zoning controlling social class positional segregation, etc.).
>>>>>
>>>>>>> I have been using the spdep package with the hope of creating a CAR model. To begin the analysis, we need to find all first order neighbors of every point in the data.
>>>>>>>
>>>>>>> While spdep has fantastic commands for finding k nearest neighbors (knearneigh), and a useful command for finding lag of order 3 or more (nblag), I have yet to find a method which is suitable for our purposes (lag = 1, or lag =2). Additionally, I looked into altering the nblag command to accommodate maxlag = 1 or maxlag = 2, but the command relies on an nb format, which is problematic as we are looking for the underlying neighborhood structure.
>>>>>>>
>>>>>>> There has been numerous work done with polygons, or data which already is in “nb” format, but after reading the literature, it seems that polygons are not appropriate, nor are distance based neighbor techniques, due to density fluctuations over the area of interest.
>>>>>>>
>>>>>>> Below is some reproducible code I wrote. I would like to note that I am currently working in R 1.1.453 on a MacBook.
>>>>>
>>>>> You mean RStudio, there is no such version of R.
>>>>>
>>>>>>>
>>>>>>> # Create a data frame of 10 voters, picked at random
>>>>>>> voter.1 = c(1, -75.52187, 40.62320)
>>>>>>> voter.2 = c(2,-75.56373, 40.55216)
>>>>>>> voter.3 = c(3,-75.39587, 40.55416)
>>>>>>> voter.4 = c(4,-75.42248, 40.64326)
>>>>>>> voter.5 = c(5,-75.56654, 40.54948)
>>>>>>> voter.6 = c(6,-75.56257, 40.67375)
>>>>>>> voter.7 = c(7, -75.51888, 40.59715)
>>>>>>> voter.8 = c(8, -75.59879, 40.60014)
>>>>>>> voter.9 = c(9, -75.59879, 40.60014)
>>>>>>> voter.10 = c(10, -75.50877, 40.53129)
>>>>>>>
>>>>>
>>>>> These are in geographical coordinates.
>>>>>
>>>>>>> # Bind the vectors together
>>>>>>> voter.subset = rbind(voter.1, voter.2, voter.3, voter.4, voter.5, voter.6, voter.7, voter.8, voter.9, voter.10)
>>>>>>>
>>>>>>> # Rename the columns
>>>>>>> colnames(voter.subset) = c("Voter.ID", "Longitude", "Latitude")
>>>>>>>
>>>>>>> # Change the class from a matrix to a data frame
>>>>>>> voter.subset = as.data.frame(voter.subset)
>>>>>>>
>>>>>>> # Load in the required packages
>>>>>>> library(spdep)
>>>>>>> library(sp)
>>>>>>>
>>>>>>> # Set the coordinates
>>>>>>> coordinates(voter.subset) = c("Longitude", "Latitude")
>>>>>>> coords = coordinates(voter.subset)
>>>>>>>
>>>>>>> # Jitter to ensure no duplicate points
>>>>>>> coords = jitter(coords, factor = 1)
>>>>>>>
>>>>>
>>>>> jitter does not respect geographical coordinated (decimal degree metric).
>>>>>
>>>>>>> # Find the first nearest neighbor of each point
>>>>>>> one.nn = knearneigh(coords, k=1)
>>>>>
>>>>> See the help page (hint: longlat=TRUE to use Great Circle distances, much slower than planar).
>>>>>
>>>>>>>
>>>>>>> # Convert the first nearest neighbor to format "nb"
>>>>>>> one.nn_nb = knn2nb(one.nn, sym = F)
>>>>>>>
>>>>>>> Thank you in advance for any help you may offer, and for taking the time to read this. I have consulted Applied Spatial Data Analysis with R (Bivand, Pebesma, Gomez-Rubio), as well as other Sig-Geo threads, the spdep documentation, and the nb vignette (Bivand, April 3, 2018) from earlier this year.
>>>>>>>
>>>>>>> Warmest,
>>>>>>> Ben
>>>>>>> --
>>>>>>> Benjamin Lieberman
>>>>>>> Muhlenberg College 2019
>>>>>>> Mobile: 301.299.8928
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> [[alternative HTML version deleted]]
>>>>>
>>>>> Plain text only, please.
>>>>>
>>>>>>>
>>>>>>> _______________________________________________
>>>>>>> R-sig-Geo mailing list
>>>>>>> [hidden email] <mailto:[hidden email]> <mailto:[hidden email] <mailto:[hidden email]>>
>>>>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo> <https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo>>
>>>>>>
>>>>>>
>>>>>> [[alternative HTML version deleted]]
>>>>>>
>>>>>> _______________________________________________
>>>>>> R-sig-Geo mailing list
>>>>>> [hidden email] <mailto:[hidden email]> <mailto:[hidden email] <mailto:[hidden email]>>
>>>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo> <https://stat.ethz.ch/mailman/listinfo/r-sig-geo <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: [hidden email] <mailto:[hidden email]> <mailto:[hidden email] <mailto:[hidden email]>>
>>>>> http://orcid.org/0000-0003-2392-6140 <http://orcid.org/0000-0003-2392-6140> <http://orcid.org/0000-0003-2392-6140 <http://orcid.org/0000-0003-2392-6140>>
>>>>> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en_______________________________________________ <https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en_______________________________________________><https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en_______________________________________________ <https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en_______________________________________________>>
>>>>> R-sig-Geo mailing list
>>>>> [hidden email] <mailto:[hidden email]> <mailto:[hidden email] <mailto:[hidden email]>>
>>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo> <https://stat.ethz.ch/mailman/listinfo/r-sig-geo <https://stat.ethz.ch/mailman/listinfo/r-sig-geo>>
>>>
>>>
>>> [[alternative HTML version deleted]]
>>>
>>> _______________________________________________
>>> R-sig-Geo mailing list
>>> [hidden email] <mailto:[hidden email]>
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo <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: [hidden email] <mailto:[hidden email]>
>> http://orcid.org/0000-0003-2392-6140 <http://orcid.org/0000-0003-2392-6140>
>> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en <https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en>
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> 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: [hidden email]
http://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
_______________________________________________
R-sig-Geo mailing list
[hidden email]
https://stat.ethz.ch/mailman/listinfo/r-sig-geo
Roger Bivand
Department of Economics
Norwegian School of Economics
Helleveien 30
N-5045 Bergen, Norway