Just a quick note about jargon: you are using the word "likelihood" in
a way that I (and maybe some others) find confusing. (In fact, I think
you used it two different ways, but maybe I'm just confused.) I would
say that likelihood is the probability of observing the entire data set,
considered as a function of the parameters. You appear to be using it
(at first) as the probability that a particular observation is equal to
1, and then as the argument to a logit function to give that probability.
What you probably want to do is find the parameters that maximize the
likelihood (in my sense). The usual practice is to maximize the log of
the likelihood; it tends to be easier to work with. In your notation
below, the log likelihood would be
loglik <- sum( resp*log(p) + (1-resp)*log1p(-p) )
When you have a linear logistic regression model, this simplifies a bit,
and there are fast algorithms that are usually stable to optimize it.
With a nonlinear model, you lose some of that, and I'd suggest directly
optimizing it.
Duncan Murdoch
On 29/07/2020 8:56 a.m., Sebastien Bihorel via R-help wrote:
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.
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
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