Thank your, Pr. Nash, for your perspective on the issue. Here is an example of binary data/response (resp) that were simulated and re-estimated assuming a non linear effect of the predictor (x) on the likelihood of response. For re-estimation, I have used gnlm::bnlr for the logistic regression. The accuracy of the parameter estimates is so-so, probably due to the low number of data points (8*nx). For illustration, I have also include a glm call to an incorrect linear model of x.
#install.packages(gnlm) #require(gnlm) set.seed(12345) nx <- 10 x <- c( rep(0, 3*nx), rep(c(10, 30, 100, 500, 1000), each = nx) ) rnd <- runif(length(x)) a <- log(0.2/(1-0.2)) b <- log(0.7/(1-0.7)) - a c <- 30 likelihood <- a + b*x/(c+x) p <- exp(likelihood) / (1 + exp(likelihood)) resp <- ifelse(rnd <= p, 1, 0) df <- data.frame( x = x, resp = resp, nresp = 1- resp ) head(df) # glm can only assume linear effect of x, which is the wrong model glm_mod <- glm( resp~x, data = df, family = 'binomial' ) glm_mod # Using gnlm package, estimate a model model with just intercept, and a model with predictor effect int_mod <- gnlm::bnlr( y = df[,2:3], link = 'logit', mu = ~ p_a, pmu = c(a) ) emax_mod <- gnlm::bnlr( y = df[,2:3], link = 'logit', mu = ~ p_a + p_b*x/(p_c+x), pmu = c(a, b, c) ) int_mod emax_mod ________________________________ From: J C Nash <profjcn...@gmail.com> Sent: Tuesday, July 28, 2020 14:16 To: Sebastien Bihorel <sebastien.biho...@cognigencorp.com>; r-help@r-project.org <r-help@r-project.org> Subject: Re: [R] Nonlinear logistic regression fitting There is a large literature on nonlinear logistic models and similar curves. Some of it is referenced in my 2014 book Nonlinear Parameter Optimization Using R Tools, which mentions nlxb(), now part of the nlsr package. If useful, I could put the Bibtex refs for that somewhere. nls() is now getting long in the tooth. It has a lot of flexibility and great functionality, but it did very poorly on the Hobbs problem that rather forced me to develop the codes that are 3/5ths of optim() and also led to nlsr etc. The Hobbs problem dated from 1974, and with only 12 data points still defeats a majority of nonlinear fit programs. nls() poops out because it has no LM stabilization and a rather weak forward difference derivative approximation. nlsr tries to generate analytic derivatives, which often help when things are very badly scaled. Another posting suggests an example problem i.e., some data and a model, though you also need the loss function (e.g., Max likelihood, weights, etc.). Do post some data and functions so we can provide more focussed advice. JN On 2020-07-28 10:13 a.m., Sebastien Bihorel via R-help wrote: > Hi > > I need to fit a logistic regression model using a saturable Michaelis-Menten > function of my predictor x. The likelihood could be expressed as: > > L = intercept + emax * x / (EC50+x) > > Which I guess could be expressed as the following R model > > ~ emax*x/(ec50+x) > > As far as I know (please, correct me if I am wrong), fitting such a model is > to not doable with glm, since the function is not linear. > > A Stackoverflow post recommends the bnlr function from the gnlm > (https://stackoverflow.com/questions/45362548/nonlinear-logistic-regression-package-in-r)... > I would be grateful for any opinion on this package or for any alternative > recommendation of package/function. > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > 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 -- To UNSUBSCRIBE and more, see 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.
