Rers: I have some ecological data (stream velocity vs. % cover of submerged weeds) that shows strong evidence of a thresholding step-function, e.g. below some velocity, % cover ranges from 0% to 100% (with no apparent relationship to velocity within this range of velocities), but above a certain "threshold" velocity, the % cover does not appear to exceed, say, 10%. There are good mechanistic reasons for believing there is a step function there, so I'm trying to determine the velocity position and significance of this threshold. I came up with the following approach, but I was hoping to find out if there is a more "standardized" way of doing this: 1) Give small velocity steps ranging from 0 to max velocity, classify all samples (% cover vs. velocity) into "above threshold" and "below threshold". 2) Perform a t-test on these two groups, store the p-value to an array, building up a database of p-value vs. velocity threshold. 3) Determine the minimum p-value from the previous step, which should be the velocity threshold -- the p-value at this threshold is the significance of the threshold. Does this make sense? Is there a better way of doing this? When I ran this on the data, you see a nice, nearly parabolic relationship around what the threshold appears to be of p-value vs. threshold. --j -- Jonathan A. Greenberg, PhD Postdoctoral Scholar Center for Spatial Technologies and Remote Sensing (CSTARS) University of California, Davis One Shields Avenue The Barn, Room 250N Davis, CA 95616 Cell: 415-794-5043 AIM: jgrn307, MSN: jgrn307 at hotmail.com, Gchat: jgrn307
Hi Jonathan, I don't know if I got the point, but for thresholds assessments, give a look at segmented package. bests milton brazil=toronto On Tue, Jun 16, 2009 at 5:23 PM, Jonathan Greenberg <greenberg@ucdavis.edu>wrote:> Rers: > > I have some ecological data (stream velocity vs. % cover of submerged > weeds) that shows strong evidence of a thresholding step-function, e.g. > below some velocity, % cover ranges from 0% to 100% (with no apparent > relationship to velocity within this range of velocities), but above a > certain "threshold" velocity, the % cover does not appear to exceed, say, > 10%. There are good mechanistic reasons for believing there is a step > function there, so I'm trying to determine the velocity position and > significance of this threshold. I came up with the following approach, but > I was hoping to find out if there is a more "standardized" way of doing > this: > > 1) Give small velocity steps ranging from 0 to max velocity, classify all > samples (% cover vs. velocity) into "above threshold" and "below threshold". > 2) Perform a t-test on these two groups, store the p-value to an array, > building up a database of p-value vs. velocity threshold. > 3) Determine the minimum p-value from the previous step, which should be > the velocity threshold -- the p-value at this threshold is the significance > of the threshold. > > Does this make sense? Is there a better way of doing this? When I ran > this on the data, you see a nice, nearly parabolic relationship around what > the threshold appears to be of p-value vs. threshold. > > --j > > -- > > Jonathan A. Greenberg, PhD > Postdoctoral Scholar > Center for Spatial Technologies and Remote Sensing (CSTARS) > University of California, Davis > One Shields Avenue > The Barn, Room 250N > Davis, CA 95616 > Cell: 415-794-5043 > AIM: jgrn307, MSN: jgrn307@hotmail.com, Gchat: jgrn307 > > ______________________________________________ > R-help@r-project.org mailing list > stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > R-project.org/posting-guide.html<r-project.org/posting-guide.html> > and provide commented, minimal, self-contained, reproducible code. >[[alternative HTML version deleted]]
Hi Threshold models with time series for ecology have been quite famous with bookf from Tong (1990, nonlinear time series), who studied lynx population and showed evidence of threshold (regime specific) effects, and built a model called "threshold autoregressive" Many of those functions are available in package tsDyn, (dev version on code.google.com/p/tsdyn/wiki/ThresholdCointegration contains many new features). If you have time series, this package should be convenient for you. Otherwise, basically, your approach is right with a known threshold, means if you know a priori what is the threshold, then you can apply usual inference, resp t tests. If the threshold is unknown, you need to estimate it by estimating all threshold, and tests have non standard distribution due to the presence of a parameter unidentified unfer the null ("Davies problem"). A good point to start with would be Sample splitting and threshold estimation," Econometrica, (2000), 68, 575-603 available at: ssc.wisc.edu/~bhansen/papers/ecnmt_00.html Hope this helps Mat Jonathan Greenberg-2 wrote:> > Rers: > > I have some ecological data (stream velocity vs. % cover of submerged > weeds) that shows strong evidence of a thresholding step-function, e.g. > below some velocity, % cover ranges from 0% to 100% (with no apparent > relationship to velocity within this range of velocities), but above a > certain "threshold" velocity, the % cover does not appear to exceed, > say, 10%. There are good mechanistic reasons for believing there is a > step function there, so I'm trying to determine the velocity position > and significance of this threshold. I came up with the following > approach, but I was hoping to find out if there is a more "standardized" > way of doing this: > > 1) Give small velocity steps ranging from 0 to max velocity, classify > all samples (% cover vs. velocity) into "above threshold" and "below > threshold". > 2) Perform a t-test on these two groups, store the p-value to an array, > building up a database of p-value vs. velocity threshold. > 3) Determine the minimum p-value from the previous step, which should be > the velocity threshold -- the p-value at this threshold is the > significance of the threshold. > > Does this make sense? Is there a better way of doing this? When I ran > this on the data, you see a nice, nearly parabolic relationship around > what the threshold appears to be of p-value vs. threshold. > > --j > > -- > > Jonathan A. Greenberg, PhD > Postdoctoral Scholar > Center for Spatial Technologies and Remote Sensing (CSTARS) > University of California, Davis > One Shields Avenue > The Barn, Room 250N > Davis, CA 95616 > Cell: 415-794-5043 > AIM: jgrn307, MSN: jgrn307 at hotmail.com, Gchat: jgrn307 > > ______________________________________________ > R-help at r-project.org mailing list > stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > >-- View this message in context: nabble.com/Statistically-detecting-thresholds...-tp24063180p24071317.html Sent from the R help mailing list archive at Nabble.com.