Re: [R] Identifying breakpoints/inflection points?
You can try this: library(inflection) #you have to instsall package inflection first a-findiplist(cbind(year),cbind(piproute),1) a The answer: [,1] [,2] [,3] [1,]5 35 1986.0 [2,]5 30 1983.5 shows that the total inflection point is between 1983 and 1986, if we treat data as first concave and then convex, as it can be found from a simple graph. -- View this message in context: http://r.789695.n4.nabble.com/Identifying-breakpoints-inflection-points-tp2065886p4669117.html Sent from the R help mailing list archive at Nabble.com. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Identifying breakpoints/inflection points?
Please quote the question you are answering and also send the answer to the original poster, not only to this *mailing list* the original poster may not be reading himself. Best, Uwe Ligges On 07.06.2013 09:08, dchristop wrote: You can try this: library(inflection) #you have to instsall package inflection first a-findiplist(cbind(year),cbind(piproute),1) a The answer: [,1] [,2] [,3] [1,]5 35 1986.0 [2,]5 30 1983.5 shows that the total inflection point is between 1983 and 1986, if we treat data as first concave and then convex, as it can be found from a simple graph. -- View this message in context: http://r.789695.n4.nabble.com/Identifying-breakpoints-inflection-points-tp2065886p4668889.html Sent from the R help mailing list archive at Nabble.com. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Identifying breakpoints/inflection points?
You can try this: library(inflection) #you have to instsall package inflection first a-findiplist(cbind(year),cbind(piproute),1) a The answer: [,1] [,2] [,3] [1,]5 35 1986.0 [2,]5 30 1983.5 shows that the total inflection point is between 1983 and 1986, if we treat data as first concave and then convex, as it can be found from a simple graph. -- View this message in context: http://r.789695.n4.nabble.com/Identifying-breakpoints-inflection-points-tp2065886p4668889.html Sent from the R help mailing list archive at Nabble.com. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Identifying breakpoints/inflection points?
Hi Charlotte, This may be a bit too late, but I just remembered your question. I have written some functions to extract various features of a time-series, uusing functional data analytic methods. These would be part of an R package that will be soon released. This package can analyze a large collection of time-series. Here is how you can use that to solve your problem: source(features.txt) 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(0.7,0.945945946,1.886363636,1.607843137,4.245614035,3.175675676,2.169014085,2,2.136363636,2.65625,2.080645161,2.114754098,2.090909091,3.012195122,2.935897436,2.592105263,1.075757576,1.210526316,1,1.1875,1.903614458,1.385542169,1.788990826,1.163793103,1.558558559,1.595238095,1.75833,1.858267717,2.169117647,1.403225806,2.859375,3.236220472,2.054263566,3.85417,1.812080537,2.708029197,2.75862069,2.625954198,4.540740741,3.686567164,2.8,2.968253968,3.517730496) ans - features.mat(year, piproute, smoother=glk, plot.it=TRUE) ans ans$cptmat # critical points of the function (minima/maxima) # The answers depend on how you smooth the data. Here is a result showing smoothing using a pemalized spline smoother. ans - features.mat(year, piproute, smoother=spm, plot.it=TRUE) ans ans$cptmat # critical points of the function (minima/maxima) Hope this is helpful, Ravi. Ravi Varadhan, Ph.D. Assistant Professor, Division of Geriatric Medicine and Gerontology School of Medicine Johns Hopkins University Ph. (410) 502-2619 email: rvarad...@jhmi.edu - Original Message - From: Charlotte Chang c.h.w.ch...@gmail.com Date: Tuesday, April 27, 2010 2:25 am Subject: Re: [R] Identifying breakpoints/inflection points? To: Clint Bowman cl...@ecy.wa.gov Cc: r-help@r-project.org 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 cl...@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: cl...@ecy.wa.gov Air Quality Modeler INTERNET: cl...@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(0.7,0.945945946,1.886363636,1.607843137,4.245614035,3.175675676,2.169014085,2,2.136363636,2.65625,2.080645161,2.114754098,2.090909091,3.012195122,2.935897436,2.592105263,1.075757576,1.210526316,1,1.1875,1.903614458,1.385542169,1.788990826,1.163793103,1.558558559,1.595238095,1.75833,1.858267717,2.169117647,1.403225806,2.859375,3.236220472,2.054263566,3.85417,1.812080537,2.708029197,2.75862069,2.625954198,4.540740741,3.686567164,2.8,2.968253968,3.517730496) 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
Re: [R] Identifying breakpoints/inflection points?
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 cl...@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: cl...@ecy.wa.gov Air Quality Modeler INTERNET: cl...@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(0.7,0.945945946,1.886363636,1.607843137,4.245614035,3.175675676,2.169014085,2,2.136363636,2.65625,2.080645161,2.114754098,2.090909091,3.012195122,2.935897436,2.592105263,1.075757576,1.210526316,1,1.1875,1.903614458,1.385542169,1.788990826,1.163793103,1.558558559,1.595238095,1.75833,1.858267717,2.169117647,1.403225806,2.859375,3.236220472,2.054263566,3.85417,1.812080537,2.708029197,2.75862069,2.625954198,4.540740741,3.686567164,2.8,2.968253968,3.517730496) 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 __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Identifying breakpoints/inflection points?
Charlotte, Try: library(msProcess) # you may have to install msProcess year[peaks(birds.pr$fit)] -- Clint BowmanINTERNET: cl...@ecy.wa.gov Air Quality Modeler INTERNET: cl...@math.utah.edu Department of Ecology VOICE: (360) 407-6815 PO Box 47600FAX:(360) 407-7534 Olympia, WA 98504-7600 On Mon, 26 Apr 2010, Charlotte Chang wrote: 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 cl...@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: cl...@ecy.wa.gov Air Quality Modeler INTERNET: cl...@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(0.7,0.945945946,1.886363636,1.607843137,4.245614035,3.175675676,2.169014085,2,2.136363636,2.65625,2.080645161,2.114754098,2.090909091,3.012195122,2.935897436,2.592105263,1.075757576,1.210526316,1,1.1875,1.903614458,1.385542169,1.788990826,1.163793103,1.558558559,1.595238095,1.75833,1.858267717,2.169117647,1.403225806,2.859375,3.236220472,2.054263566,3.85417,1.812080537,2.708029197,2.75862069,2.625954198,4.540740741,3.686567164,2.8,2.968253968,3.517730496) 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 __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Identifying breakpoints/inflection points?
... but you should be warned that this is an inherently difficult issue. You are trying to estimate a second derivative from noisy data. The result is likely to be **very** dependent on the fitting methods and parameters chosen (e.g. span of a kernel smoother), even if the fit itself is fairly robust. I suggest you try some sensitivity analyses and/or bootstrapping of your results if the software does not already provide uncertainty estimates. Cheers, Bert Bert Gunter Genentech Nonclinical Biostatistics -Original Message- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of Clint Bowman Sent: Tuesday, April 27, 2010 9:32 AM To: Charlotte Chang Cc: r-help@r-project.org Subject: Re: [R] Identifying breakpoints/inflection points? Charlotte, Try: library(msProcess) # you may have to install msProcess year[peaks(birds.pr$fit)] -- Clint BowmanINTERNET: cl...@ecy.wa.gov Air Quality Modeler INTERNET: cl...@math.utah.edu Department of Ecology VOICE: (360) 407-6815 PO Box 47600FAX:(360) 407-7534 Olympia, WA 98504-7600 On Mon, 26 Apr 2010, Charlotte Chang wrote: 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 cl...@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: cl...@ecy.wa.gov Air Quality Modeler INTERNET: cl...@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(1967,1968,1969,1970,1971,1972,1973,1974,1975,1976,1977,1978,1979,198 0,1981,1982,1983,1984,1985,1986,1987,1988,1989,1990,1991,1992,1993,1994,1995 ,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005,2006,2007,2008,2009) piproute-c(0.7,0.945945946,1.886363636,1.607843137,4.245614035,3.17 5675676,2.169014085,2,2.136363636,2.65625,2.080645161,2.114754098,2.09090909 1,3.012195122,2.935897436,2.592105263,1.075757576,1.210526316,1,1.1875,1.903 614458,1.385542169,1.788990826,1.163793103,1.558558559,1.595238095,1.758 33,1.858267717,2.169117647,1.403225806,2.859375,3.236220472,2.054263566,3.85 417,1.812080537,2.708029197,2.75862069,2.625954198,4.540740741,3.6865671 64,2.8,2.968253968,3.517730496) 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 __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained
[R] Identifying breakpoints/inflection points?
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(0.7,0.945945946,1.886363636,1.607843137,4.245614035,3.175675676,2.169014085,2,2.136363636,2.65625,2.080645161,2.114754098,2.090909091,3.012195122,2.935897436,2.592105263,1.075757576,1.210526316,1,1.1875,1.903614458,1.385542169,1.788990826,1.163793103,1.558558559,1.595238095,1.75833,1.858267717,2.169117647,1.403225806,2.859375,3.236220472,2.054263566,3.85417,1.812080537,2.708029197,2.75862069,2.625954198,4.540740741,3.686567164,2.8,2.968253968,3.517730496) 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 __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Identifying breakpoints/inflection points?
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 BowmanINTERNET: cl...@ecy.wa.gov Air Quality Modeler INTERNET: cl...@math.utah.edu Department of Ecology VOICE: (360) 407-6815 PO Box 47600FAX:(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(0.7,0.945945946,1.886363636,1.607843137,4.245614035,3.175675676,2.169014085,2,2.136363636,2.65625,2.080645161,2.114754098,2.090909091,3.012195122,2.935897436,2.592105263,1.075757576,1.210526316,1,1.1875,1.903614458,1.385542169,1.788990826,1.163793103,1.558558559,1.595238095,1.75833,1.858267717,2.169117647,1.403225806,2.859375,3.236220472,2.054263566,3.85417,1.812080537,2.708029197,2.75862069,2.625954198,4.540740741,3.686567164,2.8,2.968253968,3.517730496) 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 __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.