[R] How to find inverse of glm model?

[Gregg Powell]

Take a look at this Luigi...

># The model is: logit(p) = β₀ + β₁*Cycles
># Where p is the probability (or normalized value in your case)
>
># The inverse function would be: Cycles = (logit⁻¹(p) - β₀)/β₁
># Where logit⁻¹ is the inverse logit function (also called the expit >function)
>
># Extract coefficients from your model
>intercept <- coef(b_model)[1]
>slope <- coef(b_model)[2]
>
># Define the inverse function
>inverse_predict <- function(p) {
>  # p is the probability or normalized value you want to find the >cycles for
>  # Inverse logit: log(p/(1-p)) which is the logit function
>  logit_p <- log(p/(1-p))
>  

>  # Solve for Cycles: (logit(p) - intercept)/slope
>  cycles <- (logit_p - intercept)/slope
>  

>  return(cycles)
>}
>
># Example: What cycle would give a normalized value of 0.5?
>inverse_predict(0.5)


This function takes a probability (normalized value between 0 and 1) and returns the cycle value that would produce this probability according to your model.
Also:
This works because GLM with binomial family uses the logit link function by default
The inverse function will return values outside your original data range if needed
This won't work for p=0 or p=1 exactly (you'd get -Inf or Inf), so you might want to add checks

All the best,
Gregg









On Tuesday, April 15th, 2025 at 5:57 AM, Luigi Marongiu <marongiu.luigi using gmail.com> wrote:

> 

> 

> I have fitted a glm model to some data; how can I find the inverse
> function of this model? Since I don't know the y=f(x) implemented by
> glm (this works under the hood), I can't define a f⁻¹(y).
> Is there an R function that can find the inverse of a glm model?
> Thank you.
> 

> The working example is:
> `V = c(120.64, 66.14, 34.87, 27.11, 8.87, -5.8, 4.52, -7.16, -17.39, -14.29, -20.26, -14.99, -21.05, -20.64, -8.03, -21.56, -1.28, 15.01, 75.26, 191.76, 455.09, 985.96, 1825.59, 2908.08, 3993.18, 5059.94, 6071.93, 6986.32, 7796.01, 8502.25, 9111.46, 9638.01, 10077.19, 10452.02, 10751.81, 11017.49, 11240.37, 11427.47, 11570.07, 11684.96, 11781.77, 11863.35, 11927.44, 11980.81, 12021.88, 12058.35, 12100.63, 12133.57, 12148.89, 12137.09) df = data.frame(Cycles = 1:35, Values = V[1:35]) M = max(df$Values) df$Norm = df$Values/M df$Norm[df$Norm<0] = 0 b_model = glm(Norm ~ Cycles, data=df, family=binomial) plot(Norm ~ Cycles, df, main="Normalized view", xlab=expression(bold("Time")), ylab=expression(bold("Signal (normalized)")), type="p", col="cyan") lines(b_model$fitted.values ~ df$Cycles, col="blue", lwd=2)`
> 

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