[R] Fitting a modified logistic with glm?

[Ken Knoblauch]

Mike Lawrence <mike <at> thatmike.com> writes:
> Where f(x) is a logistic function, I have data that follow:
> g(x) = f(x)*.5 + .5

> How would you suggest I modify the standard glm(..., family='binomial')
> function to fit this? Here's an example of a clearly ill-advised attempt to
> simply use the standard glm(..., family='binomial') approach:
> #define the scale and location of the modified logistic to be fit
> location = 20
> scale = 30
> x = runif(200,-200,200)
> x.noise = runif(length(x),-10,10)
> prob.success = plogis(x+x.noise,location,scale)*.5 + .5
> y = rep(NA,length(x))
> for(i in 1:length(x)){
>     y[i] = sample(
>         x = c(1,0)
>         , size = 1
>         , prob = c(prob.success[i], 1-prob.success[i])
>     )
> }
> plot(x,y)
> curve(plogis(x,location,scale)*.5 + .5,add=T)
Hi,

You might try the link mafc.logit(m = 2) defined in the 
psyphy package.  Continuing with your example,
library(psyphy)
fit <- glm(y ~ x, binomial(mafc.logit(2)), 
  control = glm.control(maxit = 100))  # default didn't converge
x.ord <- order(x)
lines(x[x.ord], fitted(fit)[x.ord], col = "red", lwd = 3)

HTH,

Ken

-- 
Ken Knoblauch
Inserm U846
Institut Cellule Souche et Cerveau
Département Neurosciences Intégratives
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