Hi Petr, thanks for your help on this. I will most definitely get this book as it appears to be a good one. I am happy with how nls() and the self starting function appears to be fitting the data set.
What I am wondering about is how to write out this function outside of R. For example, if I sat down with a paper and pencil and wrote this function out in terms of f(x) = ?. In this example (http://www.graphpad.com/curvefit/id203.htm) there is a formula contains for what they are calling the Boltzmann Sigmoid function. In order to have an answer, is this something I need to generate on my own? Or, is there a common form that is being applied by the SSlogis and the SSfpl functions? In Pinheiro and Bates (pg 518) there is a model f(x) = A + B/1+ exp[(scal-x)/expL]. Is this the form of the equation? Or, is there a way to extract the local min and max values from nls () results? Do I have to break apart the individual components of the regression into piecewise functions? Thanks again for your help. Katrina On Tue, Aug 9, 2011 at 12:38 AM, Petr PIKAL <petr.pi...@precheza.cz> wrote: > Hi > >> Hi R help, >> >> I am trying to determine how nls() generates a function based on the >> self-starting SSlogis and what the formula for the function would be. >> I've scoured the help site, and other literature to try and figure >> this out but I still am unsure if I am correct in what I am coming up >> with. > > Thanks for providing data and your code > >> >> >> > ************************************************************************** >> dat <- c(75.44855206,NA,NA,NA,82.70745342,82.5335019,88.56617647,80. >> 00128866,94.15418227,86.63987539,93.91052952,74.10612245,86.62289562,90. >> 47961047,NA,NA,82.45320197,72.14371257,NA,71.44104803,72.59742896,68. >> 36363636,NA,NA,61,NA,NA,71.26502909,NA,85.93333333,84.34248284,79. >> 00522193,79.64223058,97.2074017,88.43700548,96.40413877,95.13511869,92. >> 57379057,93.97498475,NA,97.55995131,89.53321146,97.21728545,93.21980198, >> 77.54054054,95.85392575,86.25684723,97.55325624,80.03950617,NA,91. >> 34023128,92.42906574,88.59433962,65.77272727,89.63772455,NA,NA,NA,NA,74. >> 86344239,83.57594937,70.22516556,65.30543319,NA,NA,67.84852294,60. >> 90909091,54.79303797,NA,52.18735363,33.47003155,NA,41.34693878,24. >> 5047043,NA,NA,NA,NA,9.944444444,13.6875,NA,11.90267176,84.14285714,3. >> 781456954,NA,1.432926829,4.26557377,1.823529412,0.444620253,4. >> > 711155378,NA,6.320284698,0.581632653,0.144578313,3.666666667,0,0,0,0,0,NA, >> 0.032947462,0,0,10.54545455,0,NA,0.561007958,0.75,NA,0.048780488,0. >> 74137931,NA,2.023339318,0,0,0,NA,NA,0.156950673,NA,0.283769634,32. >> > 81818182,NA,NA,0,NA,0,0,0,NA,0.212454212,3.120181406,NA,0.011811024,NA,0, >> > 0.120430108,5.928571429,1.75,0.679292929,0.97,NA,0,NA,NA,1,0.38547486,NA, >> 1.460732984,0.007795889,0.05465288,0.004341534) > >> dat.df.1 <- data.frame(dat) > unnecessary > >> dat.df.2 <- data.frame(x=x.seq, dat.df=dat.df.1) > > some correction > dat.df.2 <- data.frame(x=seq_along(dat), dat=dat) > >> fit.dat <-nls(dat ~ SSlogis(x, Asym, xmid,scal), data = dat.df.2, >> start =list(Asym=90, xmid = 75, scal = -6)) >> plot(dat.df.2, axes=FALSE, ann=FALSE, ylim=c(0,100)) >> lines(dat.df.2$x[complete.cases(dat.df.2)], predict(fit.dat), > ylim=c(0,100)) >> >> summary(fit.dat) >> >> > ************************************************************************** >> Formula: dat ~ SSlogis(x, Asym, xmid, scal) >> >> Parameters: >> Estimate Std. Error t value Pr(>|t|) >> Asym 85.651 1.716 49.900 < 2e-16 *** >> xmid 72.214 1.036 69.697 < 2e-16 *** >> scal -6.150 0.850 -7.236 7.9e-11 *** >> --- >> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 >> >> Residual standard error: 10.33 on 105 degrees of freedom >> >> Number of iterations to convergence: 10 >> Achieved convergence tolerance: 4.405e-06 >> (45 observations deleted due to missingness) >> > ************************************************************************** >> >> >From r-help, SSlogis parameters asym, xmid and scal are defined as: >> >> Asym: a numeric parameter representing the asymptote. >> >> xmid: a numeric parameter representing the x value at the inflection >> point of the curve. The value of SSlogis will be Asym/2 at xmid. >> >> scal: a numeric scale parameter on the input axis. >> >> and it states that the value of SSlogis "is a numeric vector of the >> same length as input. It is the value of the expression >> sym/(1+exp((xmid-input)/scal)). If all of the arguments Asym, xmid, >> and scal are names of objects the gradient matrix with respect to >> these names is attached as an attribute named gradient." >> >> However, how do I get the actual function for the curve that is >> generated? I don't think it can just be: y= >> asym/((1+e^((xmid-x)/scal)))? > > Yes. I think that the best source of information about nonlinear > regression is book by Bates, Pinheiro - Mixed effect models with S and S+. > There you can find how to determine starting parameters, how to construct > and use your own function together with selfstart feature. > >> >> Also, how do you determine the starting parameters to input in for >> asym, xmin, and scal? >> >> Perhaps I need to start at the beginning and define my own function, >> and not rely on SSlogis to provide it? >> >> What I want to be able to do is determine a local maximum for my curve >> (the x value at which this curve inflects (the upper inflection)), and >> the x value for the local minimum (the lower inflection curve), and >> the x value counts in between these values. I think in order to do >> this I need to differentiate the function. > > Maybe I do not understand well but looking at the picture it seems to me > that logistic model is fitting your data quite well. You can use also four > parameter logistic model. > >> fit.dat.2 <-nls(dat ~ SSfpl(x, A, B, xmid,scal), data = dat.df.2, start > =list(A=85.65, B=0, xmid = 72, scal = -6)) >> summary(fit.dat.2) > > Formula: dat ~ SSfpl(x, A, B, xmid, scal) > > Parameters: > Estimate Std. Error t value Pr(>|t|) > A 1.6729 1.5927 1.050 0.296 > B 85.5555 1.7065 50.134 < 2e-16 *** > xmid 71.7628 1.0762 66.679 < 2e-16 *** > scal -5.8051 0.9162 -6.336 6.13e-09 *** > --- > Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > Residual standard error: 10.32 on 104 degrees of freedom > > Number of iterations to convergence: 9 > Achieved convergence tolerance: 7.629e-06 > (45 observations deleted due to missingness) > > As you can see parameter A is insignificant so simple logistic can be used > too. In that case upper asymptote is 85.6, lower asymptote is zero, > inflection point is 72 (x where y is in the middle between both > asymptotes) and scal is rate at which the curve is falling (growing). > > There is however some wave in the beginning of your data > > fit <-loess(dat ~ x, data = dat.df.2, span=0.3) > lines(dat.df.2$x[complete.cases(dat.df.2)], predict(fit), col=3) > > So it is up to you to decide if you are satisfied with getting asymptotic > values from logistic model or you want to set something more elaborated. > > Regards > Petr > >> >> Any insight on this would be greatly appreciated. >> >> Sincerely, >> >> Katrina >> >> ______________________________________________ >> 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.
