Unable to plot confidence intervals using ggplot, (geom_ribbon() argument)

Question

I am trying to plot 95% confidence intervals on some simulated values but am running into so issues when i am trying to plot the CIs using the geom_ribbon() argument. The trouble I'm having it that my model does not show the CIs when i plot them, like so;

I have included all of my code below if anyone knows where i have gone wrong here;

set.seed(20220520)  
#simulating 200 values between 0 and 1 from a uniform distribution
x = runif(200, min = 0, max = 1) 

lam = exp(0.3+5*x)

y = rpois(200, lambda = lam)

#before we do this each Yi may contain zeros so we need to add a small constant
y <- y + .1 
#combining x and y into a dataframe so we can plot
df = data.frame(x, y)

#fitting a Poisson GLM
model2 <- glm(y ~ x, 
          data = df,
          family = poisson(link='log'))

#make predictions (this may be the same as predictions_mod2)
preds <- predict(model2, type = "response")

#making CI predictions
predictions_mod2 = predict(model2, df, se.fit = TRUE, type = 'response')

#calculate confidence intervals limit
upper_mod2 = predictions_mod2$fit+1.96*predictions_mod2$se.fit 
lower_mod2 = predictions_mod2$fit-1.96*predictions_mod2$se.fit

#transform the CI limit to get one at the level of the mean
upper_mod2 = exp(upper_mod2)/(1+exp(upper_mod2)) 
lower_mod2 = exp(lower_mod2)/(1+exp(lower_mod2))

#combining into a df
predframe = data.frame(lwr=lower_mod2,upr=upper_mod2, x = df$x, y = df$y)

#plot model with 95% confidence intervals using ggplot
ggplot(df, aes(x, y)) +
  geom_ribbon(data = predframe, aes(ymin=lwr, ymax=upr), alpha = 0.4) +
  geom_point() +
  geom_line(aes(x, preds2), col = 'blue')

Answer 1

In a comment to the question, it's asked why not to logit transform the predicted values. The reason why is that the type of prediction asked for is "response" . From the documentation , my emphasis.

type
the type of prediction required. The default is on the scale of the linear predictors; the alternative "response" is on the scale of the response variable . Thus for a default binomial model the default predictions are of log-odds (probabilities on logit scale) and type = "response" gives the predicted probabilities. The "terms" option returns a matrix giving the fitted values of each term in the model formula on the linear predictor scale.

There is a good way to answer, to show the code.

library(ggplot2, quietly = TRUE)

set.seed(20220520)  
#simulating 200 values between 0 and 1 from a uniform distribution
x = runif(200, min = 0, max = 1) 

lam = exp(0.3+5*x)

y = rpois(200, lambda = lam)

#before we do this each Yi may contain zeros so we need to add a small constant
y <- y + 0.1 
#combining x and y into a dataframe so we can plot
df = data.frame(x, y)

#fitting a Poisson GLM
suppressWarnings(
  model2 <- glm(y ~ x, 
                data = df,
                family = poisson(link='log'))
)
#make predictions (this may be the same as predictions_mod2)
preds <- predict(model2, type = "response")

#making CI predictions
predictions_mod2 = predict(model2, df, se.fit = TRUE, type = 'response')

#calculate confidence intervals limit
upper_mod2 = predictions_mod2$fit+1.96*predictions_mod2$se.fit 
lower_mod2 = predictions_mod2$fit-1.96*predictions_mod2$se.fit

#combining into a df
predframe = data.frame(lwr=lower_mod2,upr=upper_mod2, x = df$x, y = df$y)

#plot model with 95% confidence intervals using ggplot
ggplot(df, aes(x, y)) +
  geom_ribbon(data = predframe, aes(ymin=lwr, ymax=upr), alpha = 0.4) +
  geom_point() +
  geom_line(aes(x, preds), col = 'blue')

^{Created on 2022-05-29 by the reprex package (v2.0.1)}