Discrete choice models explain decisions between mutually exclusive alternatives through the utility a decider attaches to each of them. RprobitB estimates such models in a Bayesian probit framework, for binary, multinomial, ordered, and ranked responses, observed once per decider or repeatedly in panel data. Preferences may vary across the population, either through random coefficients or latent classes. The posterior draws obtained from the Gibbs sampler support choice prediction, marginal effects, and model comparison by information criteria and Bayes factors.
Install the released version from CRAN:
install.packages("RprobitB")We use 2929 stated choices by 235 Dutch individuals deciding between
two hypothetical train trip options "A" and
"B" based on the price, the travel time, the number of
rail-to-rail transfers (changes), and the level of comfort (where
0 is the best comfort and 2 the worst). The
data set Train of the mlogit
package records the prices in cents of Dutch guilders and the travel
times in minutes, which we convert to euro and hours:
data("Train", package = "mlogit")
Train$price_A <- Train$price_A / 100 / 2.20371
Train$price_B <- Train$price_B / 100 / 2.20371
Train$time_A <- Train$time_A / 60
Train$time_B <- Train$time_B / 60
head(Train)
#> choiceid id choice price_A price_B time_A time_B change_A change_B
#> 1 1 1 A 10.89073 18.15121 2.500000 2.500000 0 0
#> 2 2 1 A 10.89073 14.52097 2.500000 2.166667 0 0
#> 3 3 1 A 10.89073 18.15121 1.916667 1.916667 0 0
#> 4 4 1 B 18.15121 14.52097 2.166667 2.500000 0 0
#> 5 5 1 B 10.89073 14.52097 2.500000 2.500000 0 0
#> 6 6 1 B 18.15121 10.89073 1.916667 2.166667 0 0
#> comfort_A comfort_B
#> 1 1 1
#> 2 1 1
#> 3 1 0
#> 4 1 0
#> 5 1 0
#> 6 0 0Choice models in RprobitB are estimated with the
function fit():
library(RprobitB)
set.seed(1)
train_model <- fit(
choice ~ price + time + change + factor(comfort) | 0, # model formula
data = Train, # choice data
column_decider = "id", # decider identifiers
column_occasion = "choiceid" # occasion identifiers
)summary() reports the posterior together with
convergence diagnostics:
summary(train_model)
#> Bayesian probit choice model
#> Formula: choice ~ price + time + change + factor(comfort) | 0 | 0
#> Samples: 500 retained per chain, 4 chains
#>
#> variable mean mode sd rhat ess_bulk
#> beta[price] -0.197 -0.199 0.00895 1.00 437
#> beta[time] -1.052 -1.052 0.09190 1.00 652
#> beta[change] -0.202 -0.207 0.03463 1.00 748
#> beta[factor(comfort)1] -0.397 -0.398 0.04403 1.00 672
#> beta[factor(comfort)2] -1.335 -1.344 0.07909 1.01 602plot() displays the results via bayesplot:
plot(train_model, type = "interval")
The negative estimate signs indicate that a higher fare, a longer trip, an extra change, and a poorer comfort class each lower the utility of an alternative (as expected). Beyond the signs, the ratios of the coefficients can be interpreted as trade-offs:
compensation <- interpret(train_model, reference = "price")
compensation
#> 1 `time` compensates -5.35 `price` (95% interval -6.14 to -4.53)
#> 1 `change` compensates -1.03 `price` (95% interval -1.35 to -0.698)
#> 1 `factor(comfort)1` compensates -2.02 `price` (95% interval -2.44 to -1.6)
#> 1 `factor(comfort)2` compensates -6.8 `price` (95% interval -7.57 to -6.05)Read this way, deciders would pay
The fitted model can also be used to predict choices for trips that
the data do not contain. Below, trip "B" saves an hour over
trip "A" and charges a premium of 2, 5, or 8 euro for
it:
scenario <- data.frame(
price_A = 20, price_B = c(22, 25, 28),
time_A = 2.5, time_B = 1.5,
change_A = 0, change_B = 0,
comfort_A = 1, comfort_B = 1
)
predict(train_model, newdata = scenario)
#> id choiceid .prediction probability_A probability_B
#> 1 1 1 B 0.2557624 0.7442376
#> 2 2 1 B 0.4725960 0.5274040
#> 3 3 1 A 0.6980868 0.3019132The prediction turns where the premium passes the 5.35 euro that the hour is worth: the faster trip is the predicted choice at 2 euro, the two are almost tied at 5 euro, and the slower trip wins at 8 euro.
Besides prices, are the other three choice attributes worth modeling
at all? update() refits the model with a changed
specification on the same data, and bayes_factor() compares
the two:
train_model_small <- update(train_model, . ~ price) # using only price
comparison <- bayes_factor(train_model, train_model_small, log = TRUE)
comparison
#> Estimated log Bayes factor in favor of model1 over model2: 150.68432The log Bayes factor of 151 is decisive: travel time, changes, and comfort carry information about the choices that the price alone does not.
The RprobitB function fit() estimates
the following model variants:
Five vignettes cover the details:
Posterior draws are stored in the posterior format. Chains run in parallel through a future plan. The examples use data sets of the mlogit, AER, MASS, and choicedata packages, which are introduced in the vignettes.
citation("RprobitB")
#> Um Paket 'RprobitB' in Publikationen zu zitieren, nutzen Sie bitte:
#>
#> Oelschläger L (2026). _RprobitB: Bayesian Probit Choice Modeling_. R
#> package version 2.0.0, <https://loelschlaeger.de/RprobitB/>.
#>
#> Ein BibTeX-Eintrag für LaTeX-Benutzer ist
#>
#> @Manual{,
#> title = {RprobitB: Bayesian Probit Choice Modeling},
#> author = {Lennart Oelschläger},
#> year = {2026},
#> note = {R package version 2.0.0},
#> url = {https://loelschlaeger.de/RprobitB/},
#> }The broader methodological foundation is described in Oelschläger (2026), Overcoming Challenges in Modeling Choice Behavior Heterogeneity, doctoral dissertation, Bielefeld University, https://pub.uni-bielefeld.de/record/3014719. The latent-class mixed multinomial probit model is introduced in Oelschläger and Bauer (2021), Bayes Estimation of Latent Class Mixed Multinomial Probit Models, TRB Annual Meeting 2021, https://trid.trb.org/view/1759753.