[R] Identifying breakpoints/inflection points?

[Charlotte Chang]

Hi Clint,

Thank you for your help with the code. The span recommendation really
improved the fit of my LOESS curve. I appreciate your thoughtful
assistance!

My remaining question is how could I go about identifying the
inflection points for the LOESS curve? I was thinking about trying to
find the 2nd derivative and then using the uniroot function.

My code is here (but it's buggy and doesn't work):

birds.lo<-loess.smooth(x,y,span=0.45)
d2 <- function(x) {
	predict(birds.lo, x, deriv=2)$y
}
x<-year
y<-piproute

> d2(x)
Error in predict(birds.lo, x, deriv = 2)$y :
  $ operator is invalid for atomic vectors

#Desired next step:
uniroot(d2,c(7,10))

Any ideas about this would be profoundly appreciated! I'm hitting a dead end.

Yours,

Charlotte

On Mon, Apr 26, 2010 at 3:32 PM, Clint Bowman <clint at ecy.wa.gov> wrote:
> Charlotte,
>
> Try:
>
> birds.lo <- loess(piproute~year,span=.25)
> # play with span to see your desired pattern
> birds.pr<-predict(birds.lo, data.frame(year = seq(1967, 2009, 1)), se =
> FALSE)
> #
> plot($year,birds.pr$fit,ylim=c(0,5))
> par(new=T)
> plot(year,birds.pr$fit,pch="+",col=2,ylim=c(0,5))
>
>
> --
> Clint Bowman                    INTERNET:       clint at ecy.wa.gov
> Air Quality Modeler             INTERNET:       clint at math.utah.edu
> Department of Ecology           VOICE:          (360) 407-6815
> PO Box 47600                    FAX:            (360) 407-7534
> Olympia, WA 98504-7600
>
> On Mon, 26 Apr 2010, Charlotte Chang wrote:
>
>> Hello!
>> I have a dataset with the following two vectors:
>>
>>
>> year<-c(1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,1980,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009)
>>
>>
>> piproute<-c(0.733333333,0.945945946,1.886363636,1.607843137,4.245614035,3.175675676,2.169014085,2,2.136363636,2.65625,2.080645161,2.114754098,2.090909091,3.012195122,2.935897436,2.592105263,1.075757576,1.210526316,1,1.1875,1.903614458,1.385542169,1.788990826,1.163793103,1.558558559,1.595238095,1.758333333,1.858267717,2.169117647,1.403225806,2.859375,3.236220472,2.054263566,3.854166667,1.812080537,2.708029197,2.75862069,2.625954198,4.540740741,3.686567164,2.8,2.968253968,3.517730496)
>>
>> Pipits is the response variable (it is the number of birds counted at
>> each survey site in each year) and year is the independent variable.
>> If you plot it in R (plot(year,piproute,pch=19)), you'll see that the
>> relationship looks like a quintic polynomial.
>>
>> Initially I was trying to fit this curve using an iterative equation,
>> but it's not working. I suspect that the curve-fitting equation itself
>> is inappropriate (it's a modified version of the logistic growth
>> equation). Now what I'd like to do is identify the 3 break/inflection
>> points in the population trend. That way, I can make an argument that
>> the break points corresponded to shifts in government policy with
>> respect to land use management. I've been looking at the segmented
>> package, and initially I looked at change.pt test in the circ.stats
>> package (which is inappropriate b/c my data is not amenable to
>> circular statistical analysis). Any ideas on what I could do would be
>> appreciated!
>>
>> Thank you!
>>
>> -Charlotte
>>
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>>
>