This is a visual approach to evaluating whether my logistic regression estimates are close to the simulated values. Can I instead compute scale and location directly from glm estimates?

sim_logis.R

set.seed(254469)
n=100
xlo=0
xhi=20
loc_logis=5
scale_logis=3


x = runif(n, xlo, xhi)
p_detect = plogis(x, location=loc_logis, scale=scale_logis)
y = rbinom(n, size=1, prob=p_detect)

model = glm(y~x, family=binomial)

lo2p = function(x, int, slope){
	1/(1+exp(-(int+slope*x)))
}

plot(y~x)
lines(xlo:xhi, plogis(xlo:xhi, loc_logis, scale_logis), col="red")
lines(xlo:xhi, lo2p(xlo:xhi, coef(model)[1], coef(model)[2]), col="blue")