Hi: You're fitting y as a function of x; as in any regression model, the x's are assumed to be conditionally fixed. If you want to model x as a function of y, that's a calibration problem.
There are several issues at play: 1. In the model, you have assumed x is fixed, but afterward, you want to treat it as random. 2. You're implicitly assuming that the relationship between Y and X is invertible. If this were a math problem, you would be right: y = a exp(b * x) => x = (1/b) log(y/a). Unfortunately, this is a statistical problem, and several problems arise, among them: - the X and Y scales are very different, which suggests rather strongly that the distribution associated with random variation in Y is not the same as the distribution associated with random variation in X. - the distribution of random errors in Y is quite likely not going to have the same relationship to the distribution of random errors in X as the functional relationship between x and y above. More succinctly, the problem is a lack of invariance, so you can't simply invert the problem at the end. 3. Predictions are only as valid/reliable as the underlying model and its attendant assumptions. Your request to predict x as a function of y is essentially acknowledging that the prediction is useless before it is ever made, by point (1). Chemometrics deals with calibration problems regularly - I presume that many calibration functions are nonlinear, so you may find something useful by hunting in that area. In econometrics, a related (but not equivalent) problem is the so-called 'errors in variables', in which both y and x are assumed to be random. Of course, you could model the problem from a Bayesian perspective and hope that MCMC comes to the rescue :) The bottom line is that a statistical relationship between y and x does not translate to a corresponding relationship between x and y (through mathematical inversion). Basically, they are treated as separate problems, which makes sense because the conditional distribution of Y|X = x is not the same as that of X|Y = y. HTH, Dennis 2010/9/8 åÌÅÎÁ âÅÌÙÈ <da...@rambler.ru> > > Dear colleagues! > Is it possible to make predictions in R? > there is an exponential relationship detween y and x > x<-c(0.001,0.003,0.01,0.16,0.3,0.7,0.9) > y<-c(38.8,41.5,44.2,27,26.9,6.9,3) > f<-function(x,a,b){a*exp(b*x)} > fm<-nls(y~f(x,a,b), start=c(a=1,b=1)) > > How one can predict x when y=10 and is it possible to calculate standard > error of x? > The task is equal to function ED in drc package, but it use logistic > regression only. > > Best regards, > Elena. > > -- > da...@rambler.ru. > > ______________________________________________ > 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. > [[alternative HTML version deleted]]
______________________________________________ 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.