conf intervals for point-wise prediction

#https://stats.stackexchange.com/questions/29044/plotting-confidence-intervals-for-the-predicted-probabilities-from-a-logistic-re

library(tidyverse)
library(magrittr)


set.seed(1234)

# create fake data on gambling. Does prob win depend on bid size? 
mydat <- data.frame(
  won=as.factor(sample(c(0, 1), 250, replace=TRUE)), 
  bid=runif(250, min=0, max=1000)
)

# logistic regression model: 
mod1 <- glm(won~bid, data=mydat, family=binomial(link="logit"))

# new predictor values to use for prediction: 
plotdat <- data.frame(bid=(0:1000))

# df with predictions, lower and upper limits of CIs: 
preddat <- predict(mod1,
               type = "link",
               newdata=plotdat,
               se.fit=TRUE) %>% 
  as.data.frame() %>% 
  mutate(bid = (0:1000), 

         # model object mod1 has a component called linkinv that 
         # is a function that inverts the link function of the GLM:
         lower = mod1$family$linkinv(fit - 1.96*se.fit), 
         point.estimate = mod1$family$linkinv(fit), 
         upper = mod1$family$linkinv(fit + 1.96*se.fit)) 


# plotting with ggplot: 
preddat %>% ggplot(aes(x = bid, 
                   y = point.estimate)) + 
  geom_line(colour = "blue") + 
  geom_ribbon(aes(ymin = lower,
                  ymax = upper), 
              alpha = 0.5) + 
  scale_y_continuous(limits = c(0,1))
  
  ###https://stats.stackexchange.com/questions/167324/variance-covariance-matrix-of-logit-with-matrix-computation
  

   library(Matrix)
 library(sandwich)
 mydata <- read.csv("http://www.ats.ucla.edu/stat/data/binary.csv")
 mylogit <- glm(admit ~ gre + gpa, data = mydata, family = "binomial")
 X <- as.matrix(cbind(1, mydata[,c('gre','gpa')]))
 n <- nrow(X)

 pi<-mylogit$fit

 w<-pi*(1-pi)

 v<-Diagonal(n, x = w)
 var_b<-solve(t(X)%*%v%*%X)
 var_b

         x 3 Matrix of class "dgeMatrix"
          [,1]          [,2]          [,3]
[1,]  1.1558251135 -2.818944e-04 -0.2825632388
[2,] -0.0002818944  1.118288e-06 -0.0001144821
[3,] -0.2825632388 -1.144821e-04  0.1021349767


vcov(mylogit)

         (Intercept)           gre           gpa
(Intercept)  1.1558247051 -2.818942e-04 -0.2825631552
gre         -0.0002818942  1.118287e-06 -0.0001144821
gpa         -0.2825631552 -1.144821e-04  0.1021349526