[R-sig-eco] angular statistics
Michael Marsh
swamp at blarg.net
Fri Oct 18 05:16:09 CEST 2013
If you want a measure of exposure, i. e., heat, I suggest using the
"heatload" transformation suggested by McCune and Grace (2002). Their
assumption is that mid-afternoon, when the sun is in the southwest, is
usually the warmest time of day. The formula at the end of Chapter 3
follows:
heat load index=(1-cos(degrees-45))/2
McCune, Bruce and James B. Grace. 2002. Analysis of ecological
communities. MJM Software Design. Gleneden Beach, Oregon. USA
Mike Marsh
On 10/16/2013 3:00 AM, r-sig-ecology-request at r-project.org wrote:
> Send R-sig-ecology mailing list submissions to
> r-sig-ecology at r-project.org
>
> To subscribe or unsubscribe via the World Wide Web, visit
> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
> or, via email, send a message with subject or body 'help' to
> r-sig-ecology-request at r-project.org
>
> You can reach the person managing the list at
> r-sig-ecology-owner at r-project.org
>
> When replying, please edit your Subject line so it is more specific
> than "Re: Contents of R-sig-ecology digest..."
>
>
> Today's Topics:
>
> 1. angular statistics (Peter Nelson)
> 2. Re: angular statistics (Holland, Jeffrey D)
> 3. Re: angular statistics (Don McKenzie)
> 4. Re: angular statistics (Peter Nelson)
> 5. Re: angular statistics (Donald McKenzie)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Tue, 15 Oct 2013 09:59:38 -0700
> From: Peter Nelson <pnelson at cfr-west.org>
> To: r-sig-ecology at r-project.org
> Subject: [R-sig-eco] angular statistics
> Message-ID: <0C3C26EA-5599-4570-B205-5FEECB70BCC5 at cfr-west.org>
> Content-Type: text/plain; charset=us-ascii
>
> I want to include the exposure (measured in degrees, for example, East-facing is 90) of various coastal sites in GLM and CCA analyses. Is there an appropriate transformation that I can apply to these measurements that will allow me to do this? I've found plenty of information on comparing headings, calculating means, etc, but nothing on how exposure might be used as a continuous independent variable.
>
> Treating exposure as a categorical variable (East, Southwest, etc) seems like a fallback option, but then there is just as much of a 'difference' between SE and E sites as there is between SE and NW sites!
>
> Thanks, Pete
>
>
> ------------------------------
>
> Message: 2
> Date: Tue, 15 Oct 2013 17:10:43 +0000
> From: "Holland, Jeffrey D" <jdhollan at purdue.edu>
> To: "R-sig-ecology at r-project.org" <R-sig-ecology at r-project.org>
> Subject: Re: [R-sig-eco] angular statistics
> Message-ID:
> <30A9CCE0A986F74C837D6F87F9C581861367E631 at WPVEXCMBX01.purdue.lcl>
> Content-Type: text/plain; charset="us-ascii"
>
> Hello Pete,
> You could include the sine and cosine of the angles. A good book on this kind of analysis:
> Fisher, N.I. 1993. Statistical Analysis of Circular Data. Cambridge Univ. Press.
> To make this closer to exposure, perhaps you could first "rotate" the compass so that 360' is facing the direction of maximum exposure, and back-transform later? Just a thought.
> Cheers, Jeff
>
> ____________________
> Jeffrey D. Holland (765) 494-7739
> Assoc. Prof. of Landscape Ecology & Biodiversity jdhollan #at# purdue.edu
> Dept. of Entomology, Purdue University Smith Hall B17, 901 W. State St., West Lafayette, IN 47907
>
>
> -----Original Message-----
> From: r-sig-ecology-bounces at r-project.org [mailto:r-sig-ecology-bounces at r-project.org] On Behalf Of Peter Nelson
> Sent: Tuesday, October 15, 2013 1:00 PM
> To: r-sig-ecology at r-project.org
> Subject: [R-sig-eco] angular statistics
>
> I want to include the exposure (measured in degrees, for example, East-facing is 90) of various coastal sites in GLM and CCA analyses. Is there an appropriate transformation that I can apply to these measurements that will allow me to do this? I've found plenty of information on comparing headings, calculating means, etc, but nothing on how exposure might be used as a continuous independent variable.
>
> Treating exposure as a categorical variable (East, Southwest, etc) seems like a fallback option, but then there is just as much of a 'difference' between SE and E sites as there is between SE and NW sites!
>
> Thanks, Pete
> _______________________________________________
> R-sig-ecology mailing list
> R-sig-ecology at r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
>
>
>
> ------------------------------
>
> Message: 3
> Date: Tue, 15 Oct 2013 11:45:14 -0700
> From: Don McKenzie <dmck at u.washington.edu>
> To: Peter Nelson <pnelson at cfr-west.org>
> Cc: r-sig-ecology at r-project.org
> Subject: Re: [R-sig-eco] angular statistics
> Message-ID: <CD8BB4BE-0DB6-4863-B8AF-1D7443D79CF8 at u.washington.edu>
> Content-Type: text/plain
>
> There is precedent in the ecological literature for using a cosine transformation IF you have reason to believe that your predictor varies continuously and symmetrically in its effects around a circle. For example, if due east were the "most" exposure, and due west the least, with due north and south being roughly equal, you could create a new predictor called "east.exposure" with (most basically)
>
> east.exposure = cos(exposure - PI/2)
>
> Many more complicated extensions of this idea are possible, associated with nonlinear or asymmetrical gradients, but I will leave that to you or others on the list.
>
> On Oct 15, 2013, at 9:59 AM, Peter Nelson wrote:
>
>> I want to include the exposure (measured in degrees, for example, East-facing is 90) of various coastal sites in GLM and CCA analyses. Is there an appropriate transformation that I can apply to these measurements that will allow me to do this? I've found plenty of information on comparing headings, calculating means, etc, but nothing on how exposure might be used as a continuous independent variable.
>>
>> Treating exposure as a categorical variable (East, Southwest, etc) seems like a fallback option, but then there is just as much of a 'difference' between SE and E sites as there is between SE and NW sites!
>>
>> Thanks, Pete
>> _______________________________________________
>> R-sig-ecology mailing list
>> R-sig-ecology at r-project.org
>> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
>
>
>
> Don McKenzie
>
> Affiliate Professor
> School of Environmental and Forest Sciences
> University of Washington
>
> dmck at uw.edu
>
>
>
>
>
> [[alternative HTML version deleted]]
>
>
>
> ------------------------------
>
> Message: 4
> Date: Tue, 15 Oct 2013 14:19:54 -0700
> From: Peter Nelson <pnelson at cfr-west.org>
> To: Don McKenzie <dmck at u.washington.edu>
> Cc: r-sig-ecology at r-project.org
> Subject: Re: [R-sig-eco] angular statistics
> Message-ID: <13AB12EA-E808-4217-9E06-62AFC3A7C656 at cfr-west.org>
> Content-Type: text/plain
>
> Thanks Don. I tried the transformation you suggested, but the results don't appear promising (0 deg doesn't = 360 deg, intervals vary):
>
> 0 6.12574E-17
> 10 -0.544021111
> 20 0.912945251
> 30 -0.988031624
> 40 0.74511316
> 50 -0.262374854
> 60 -0.304810621
> 70 0.773890682
> 80 -0.993888654
> 90 0.893996664
>
> I tried
>
> east.exposure=cos(exposure*PI/180)
>
> This seems better (e.g., 0 degrees = 360 degrees) see below), but the absolute values of the intervals aren't consistent. No surprise, I suppose, but what to do?
>
> Thanks, Peter
>
> 0 1
> 10 0.984807753
> 20 0.939692621
> 30 0.866025404
> 40 0.766044443
> 50 0.64278761
> 60 0.5
> 70 0.342020143
> 80 0.173648178
> 90 6.12574E-17
> 100 -0.173648178
> 110 -0.342020143
> 120 -0.5
> 130 -0.64278761
> 140 -0.766044443
> 150 -0.866025404
> 160 -0.939692621
> 170 -0.984807753
> 180 -1
> 190 -0.984807753
> 200 -0.939692621
> 210 -0.866025404
> 220 -0.766044443
> 230 -0.64278761
> 240 -0.5
> 250 -0.342020143
> 260 -0.173648178
> 270 -1.83772E-16
> 280 0.173648178
> 290 0.342020143
> 300 0.5
> 310 0.64278761
> 320 0.766044443
> 330 0.866025404
> 340 0.939692621
> 350 0.984807753
> 360 1
> On Oct 15, 2013, at 11:45 AM, Don McKenzie <dmck at u.washington.edu> wrote:
>
>> There is precedent in the ecological literature for using a cosine transformation IF you have reason to believe that your predictor varies continuously and symmetrically in its effects around a circle. For example, if due east were the "most" exposure, and due west the least, with due north and south being roughly equal, you could create a new predictor called "east.exposure" with (most basically)
>>
>> east.exposure = cos(exposure - PI/2)
>>
>> Many more complicated extensions of this idea are possible, associated with nonlinear or asymmetrical gradients, but I will leave that to you or others on the list.
>>
>> On Oct 15, 2013, at 9:59 AM, Peter Nelson wrote:
>>
>>> I want to include the exposure (measured in degrees, for example, East-facing is 90) of various coastal sites in GLM and CCA analyses. Is there an appropriate transformation that I can apply to these measurements that will allow me to do this? I've found plenty of information on comparing headings, calculating means, etc, but nothing on how exposure might be used as a continuous independent variable.
>>>
>>> Treating exposure as a categorical variable (East, Southwest, etc) seems like a fallback option, but then there is just as much of a 'difference' between SE and E sites as there is between SE and NW sites!
>>>
>>> Thanks, Pete
>>> _______________________________________________
>>> R-sig-ecology mailing list
>>> R-sig-ecology at r-project.org
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
>>
>>
>>
>> Don McKenzie
>>
>> Affiliate Professor
>> School of Environmental and Forest Sciences
>> University of Washington
>>
>> dmck at uw.edu
>>
>>
>>
>>
>
> [[alternative HTML version deleted]]
>
>
>
> ------------------------------
>
> Message: 5
> Date: Tue, 15 Oct 2013 14:53:21 -0700 (PDT)
> From: Donald McKenzie <dmck at u.washington.edu>
> To: Peter Nelson <pnelson at cfr-west.org>
> Cc: r-sig-ecology at r-project.org
> Subject: Re: [R-sig-eco] angular statistics
> Message-ID:
> <alpine.LRH.2.01.1310151453210.15539 at hymn03.u.washington.edu>
> Content-Type: text/plain; charset="iso-8859-15"; Format="flowed"
>
> Make sure you use consistent units. PI/2 in radians, 90 in degrees. cos(90-90) = 1, cos(270 - 90) = -1. So west (270) has the lowest value, east the highest.
>
> On Tue, 15 Oct 2013, Peter Nelson wrote:
>
>> Thanks Don.?I tried the transformation you suggested, but the results don't
>> appear promising (0 deg doesn't = 360 deg, intervals vary):
>> 0
>> 6.12574E-17
>> 10
>> -0.544021111
>> 20
>> 0.912945251
>> 30
>> -0.988031624
>> 40
>> 0.74511316
>> 50
>> -0.262374854
>> 60
>> -0.304810621
>> 70
>> 0.773890682
>> 80
>> -0.993888654
>> 90
>> 0.893996664
>>
>> I tried?
>>
>> east.exposure=cos(exposure*PI/180)?
>>
>> This seems better (e.g., 0 degrees = 360 degrees) see below), but the
>> absolute values of the intervals aren't consistent. No surprise, I suppose,
>> but what to do? ?
>>
>> Thanks, Peter
>>
>> 0
>> 1
>> 10
>> 0.984807753
>> 20
>> 0.939692621
>> 30
>> 0.866025404
>> 40
>> 0.766044443
>> 50
>> 0.64278761
>> 60
>> 0.5
>> 70
>> 0.342020143
>> 80
>> 0.173648178
>> 90
>> 6.12574E-17
>> 100
>> -0.173648178
>> 110
>> -0.342020143
>> 120
>> -0.5
>> 130
>> -0.64278761
>> 140
>> -0.766044443
>> 150
>> -0.866025404
>> 160
>> -0.939692621
>> 170
>> -0.984807753
>> 180
>> -1
>> 190
>> -0.984807753
>> 200
>> -0.939692621
>> 210
>> -0.866025404
>> 220
>> -0.766044443
>> 230
>> -0.64278761
>> 240
>> -0.5
>> 250
>> -0.342020143
>> 260
>> -0.173648178
>> 270
>> -1.83772E-16
>> 280
>> 0.173648178
>> 290
>> 0.342020143
>> 300
>> 0.5
>> 310
>> 0.64278761
>> 320
>> 0.766044443
>> 330
>> 0.866025404
>> 340
>> 0.939692621
>> 350
>> 0.984807753
>> 360
>> 1 On Oct 15, 2013, at 11:45 AM, Don McKenzie <dmck at u.washington.edu> wrote:
>>
>> There is precedent in the ecological literature for using a
>> cosine transformation IF you have reason to believe that your
>> predictor varies continuously and symmetrically in its effects
>> around a circle. ?For example, if due east were the "most"
>> exposure, and due west the least, with due north and south
>> being roughly equal, you could create a new predictor
>> called?"east.exposure" with (most basically)
>> east.exposure = cos(exposure - PI/2)
>>
>> Many more complicated extensions of this idea are possible,
>> associated with nonlinear or asymmetrical gradients, but I will leave
>> that to you or others on the list.
>>
>> On Oct 15, 2013, at 9:59 AM, Peter Nelson wrote:
>>
>> I want to include the exposure (measured in degrees, for
>> example, East-facing is 90) of various coastal sites in
>> GLM and CCA analyses. Is there an appropriate
>> transformation that I can apply to these measurements
>> that will allow me to do this? I've found plenty of
>> information on comparing headings, calculating means,
>> etc, but nothing on how exposure might be used as a
>> continuous independent variable.
>>
>> Treating exposure as a categorical variable (East,
>> Southwest, etc) seems like a fallback option, but then
>> there is just as much of a 'difference' between SE and E
>> sites as there is between SE and NW sites!
>>
>> Thanks, Pete
>> _______________________________________________
>> R-sig-ecology mailing list
>> R-sig-ecology at r-project.org
>> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
>>
>>
>>
>>
>>
>> Don McKenzie
>>
>> Affiliate Professor
>> School of Environmental and Forest Sciences
>> University of Washington
>>
>> dmck at uw.edu
>>
>>
>>
>>
>>
>>
>>
> ------------------------------
>
> _______________________________________________
> R-sig-ecology mailing list
> R-sig-ecology at r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
>
>
> End of R-sig-ecology Digest, Vol 67, Issue 7
> ********************************************
>
>
More information about the R-sig-ecology
mailing list