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
angular statistics
6 messages · Holland, Jeffrey D, Peter Nelson, Don McKenzie +1 more
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
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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
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R-sig-ecology at r-project.org
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Don McKenzie
Affiliate Professor
School of Environmental and Forest Sciences
University of Washington
dmck at uw.edu
Peter, For my purposes (I.e., estimating exposure and drying potential in northern hemisphere temperate forests), I simply subtract 45 degrees from the measured aspect in degrees, convert to radians, and then take the cosine of the adjusted angle. If I want to make exposure positive, I then reverse the sign. In this way, southwest-facing slopes get the maximum value (1) and northeast-facing slopes get the lowest (-1). As others have mentioned, this approach gives equal weight to east-west and north-south variation in exposure, which may or may not be valid for a given situation. In your case, it sounds like you want to assume the east-facing aspects are maximally exposed. In that case, I would just subtract 90 degrees from your degrees measurement, convert to radians, and then take the cosine, which I believe amounts to the same approach that Don suggested. East-facing slopes should end up with a value of 1 and west-facing slopes a value of -1 (due north and south will have values of 0). If you want to give north-facing aspects less exposure than south-facing aspects (I don't know whether you are in the northern or southern hemisphere), then you could subtract 135 degrees from your measurements, making southeast aspects the most exposed. Steve J. Stephen Brewer Professor Department of Biology PO Box 1848 University of Mississippi University, Mississippi 38677-1848 Brewer web page - http://home.olemiss.edu/~jbrewer/ FAX - 662-915-5144 Phone - 662-915-1077
On 10/15/13 11:59 AM, "Peter Nelson" <pnelson at cfr-west.org> 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
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