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
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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 ********************************************