Calcular intervalos de predicción para regresión logística

Me gustaría entender cómo generar intervalos de predicción para estimaciones de regresión logística.

Me aconsejaron que siguiera los procedimientos en Collett's Modeling Binary Data , 2nd Ed p.98-99. Después de implementar este procedimiento y compararlo con los R predict.glm, en realidad creo que este libro muestra el procedimiento para calcular los intervalos de confianza , no los intervalos de predicción.

La implementación del procedimiento de Collett, con una comparación con predict.glm, se muestra a continuación.

Me gustaría saber: ¿cómo hago para producir un intervalo de predicción en lugar de un intervalo de confianza?

#Derived from Collett 'Modelling Binary Data' 2nd Edition p.98-99
#Need reproducible "random" numbers.
seed <- 67

num.students <- 1000
which.student <- 1

#Generate data frame with made-up data from students:
set.seed(seed) #reset seed
v1 <- rbinom(num.students,1,0.7)
v2 <- rnorm(length(v1),0.7,0.3)
v3 <- rpois(length(v1),1)

#Create df representing students
students <- data.frame(
    intercept = rep(1,length(v1)),
    outcome = v1,
    score1 = v2,
    score2 = v3
)
print(head(students))

predict.and.append <- function(input){
    #Create a vanilla logistic model as a function of score1 and score2
    data.model <- glm(outcome ~ score1 + score2, data=input, family=binomial)

    #Calculate predictions and SE.fit with the R package's internal method
    # These are in logits.
    predictions <- as.data.frame(predict(data.model, se.fit=TRUE, type='link'))

    predictions$actual <- input$outcome
    predictions$lower <- plogis(predictions$fit - 1.96 * predictions$se.fit)
    predictions$prediction <- plogis(predictions$fit)
    predictions$upper <- plogis(predictions$fit + 1.96 * predictions$se.fit)


    return (list(data.model, predictions))
}

output <- predict.and.append(students)

data.model <- output[[1]]

#summary(data.model)

#Export vcov matrix 
model.vcov <- vcov(data.model)

# Now our goal is to reproduce 'predictions' and the se.fit manually using the vcov matrix
this.student.predictors <- as.matrix(students[which.student,c(1,3,4)])

#Prediction:
this.student.prediction <- sum(this.student.predictors * coef(data.model))
square.student <- t(this.student.predictors) %*% this.student.predictors
se.student <- sqrt(sum(model.vcov * square.student))

manual.prediction <- data.frame(lower = plogis(this.student.prediction - 1.96*se.student), 
    prediction = plogis(this.student.prediction), 
    upper = plogis(this.student.prediction + 1.96*se.student))

print("Data preview:")
print(head(students))
print(paste("Point estimate of the outcome probability for student", which.student,"(2.5%, point prediction, 97.5%) by Collett's procedure:"))
manual.prediction
print(paste("Point estimate of the outcome probability for student", which.student,"(2.5%, point prediction, 97.5%) by R's predict.glm:"))    
print(output[[2]][which.student,c('lower','prediction','upper')])

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