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I have been struggling with the following problem for some time and would be very grateful for any help. I am running a logit model in R using the mlogit function and am able to generate the predicted probability of choosing each alternative for a given value of the predictors as follows:

library(mlogit)
data("Fishing", package = "mlogit")
Fish <- mlogit.data(Fishing, varying = c(2:9), shape = "wide", choice = "mode")

Fish_fit<-Fish[-(1:4),]
Fish_test<-Fish[1:4,]
m <- mlogit(mode ~price+ catch | income, data = Fish_fit)
predict(m,newdata=Fish_test,)

I cannot, however, work out how to add confidence intervals to the predicted probability estimates. I have already tried adding arguments to the predict function, but none seem to generate them. Any ideas on how it can be achieved would be much appreciated.

James
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1 Answers1

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One approach here is Monte Carlo simulation. You'd simulate repeated draws from a multivariate-normal sampling distribution whose parameters are given by your model results.

For each simulation, estimate your predicted probabilities, and use their empirical distribution over simulations to get your confidence intervals.

library(MASS)

est_betas <- m$coefficients
est_preds <- predict(m, newdata = Fish_test)

sim_betas <- mvrnorm(1000, m$coefficients, vcov(m))
sim_preds <- apply(sim_betas, 1, function(x) {
  m$coefficients <- x
  predict(m, newdata = Fish_test)
})
sim_ci <- apply(sim_preds, 1, quantile, c(.025, .975))

cbind(prob = est_preds, t(sim_ci))
#              prob       2.5%     97.5%
# beach   0.1414336 0.10403634 0.1920795
# boat    0.3869535 0.33521346 0.4406527
# charter 0.3363766 0.28751240 0.3894717
# pier    0.1352363 0.09858375 0.1823240
effel
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