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Model:

mylogit <- glm(Result ~ kickLength, data = RegFg, family = "binomial")

Probability plot:

plot.dat <- data.frame(prob = RegFg$NumMade/RegFg$NumKick, 
    kl = RegFg$kickLength, 
    fit = predict(mylogit, RegFg))

plot.dat$fit_prob <- exp(plot.dat$fit)/(1+exp(plot.dat$fit)) 

g1<-ggplot(plot.dat, aes(x=kl, y=prob)) +  
   geom_point() + geom_line(aes(x=kl, y=fit_prob))

Probability fit line (I think):

geom_line(aes(x=kl, y=fit_prob))

I am looking to find the derivative of probability with respect to kick length at each kick length.

NelsonGon
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Teddy Taylor
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  • I think `coef(mylogit)["kickLength"]*binomial()$mu.eta(predict(kickLength, type = "link")` will do it, but I'd have to check/think about it some more ... – Ben Bolker Dec 28 '21 at 19:04

1 Answers1

2

If you want to do it without knowing the formula then that implies numeric differentiation. Now the input is missing from the question so let us use the example in the Note at the end so that it can actually be run -- next time please provide a complete runnable example. Then use numeric differentiation from the numDeriv package.

library(numDeriv)

prob <- function(x) predict(fm, list(x = x), type = "response")
grad1 <- grad(prob, x)  # find derivative at each x value

# check against formula in Ben Bolker's comment
grad2 <- coef(fm)["x"] * binomial()$mu.eta(predict(fm, list(x = x), type = "link"))
all.equal(grad1, grad2, check.attributes = FALSE)
## [1] TRUE

Note

set.seed(123)
success <- rep(0:1, each = 3)
x <- rnorm(6)
fm <- glm(success ~ x, family = binomial)
G. Grothendieck
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  • I did the following input: `prob <- function(x) predict(mylogit, list(x = x), type = "response")' 'grad1 <- grad(prob, x)` This outputted "object "kickLength" could not be found" I am unsure what I can do to prevent this from happening. Right now, I just am stuck at how to convert the line of best fit to a function of kick length. What was the original input you suggested I added in your previous comment? Maybe that can help. – Teddy Taylor Dec 28 '21 at 20:21
  • You have specified your variable to be x but there is no variable named x in your problem. – G. Grothendieck Dec 28 '21 at 20:27