Choice data

No choice model without choice data, so this vignette1 provides a reference for data management in {RprobitB}. We use the train_choice data set for illustration.

Requirements to choice data

{RprobitB} helps in modeling the choice of individual deciders of one alternative from a finite set of choice alternatives. This choice set has to fulfill three properties (Train 2009): Choices need to be

  1. mutually exclusive (one can choose one and only one alternative that are all different),

  2. exhaustive (the alternatives do not leave other options open),

  3. and finitely many.

Every decider may take one or repeated choices (called choice occasions). The data set thus contains information on

  1. an identifier for each decider (and optionally for each choice situation),

  2. the choices,

  3. alternative and decider specific covariates.

Additionally, {RprobitB} asks the following formal requirements:

  1. The data set must be in “wide” format, that means each row provides the full information for one choice occasion.2

  2. It must contain a column with unique identifiers for each decision maker. Additionally, it can contain a column with identifier for each choice situation of each decider. If this information is missing, these identifier are generated automatically by the appearance of the choices in the data set.3

  3. It can contain a column with the observed choices. Such a column is required for model fitting but not for prediction.

  4. It must contain columns for the values of each alternative specific covariate for each alternative and for each decider specific covariate.


The train_choice data set contains 2929 stated choices by 235 Dutch individuals deciding between two virtual train trip options based on the price, the travel time, the level of comfort, and the number of changes. It fulfills the above requirements: Each row represents one choice occasion, the columns id and choiceid identify the deciders and the choice occasions, respectively. The column choice gives the observed choices. Four alternative-specific covariates are available, namely price, time, change, and comfort. There values are given for each alternative.4

#> 'data.frame':    2929 obs. of  11 variables:
#>  $ deciderID : int  1 1 1 1 1 1 1 1 1 1 ...
#>  $ occasionID: int  1 2 3 4 5 6 7 8 9 10 ...
#>  $ choice    : chr  "A" "A" "A" "B" ...
#>  $ price_A   : num  52.9 52.9 52.9 88.1 52.9 ...
#>  $ time_A    : num  2.5 2.5 1.92 2.17 2.5 ...
#>  $ change_A  : int  0 0 0 0 0 0 0 0 0 0 ...
#>  $ comfort_A : int  1 1 1 1 1 0 1 1 0 1 ...
#>  $ price_B   : num  88.1 70.5 88.1 70.5 70.5 ...
#>  $ time_B    : num  2.5 2.17 1.92 2.5 2.5 ...
#>  $ change_B  : int  0 0 0 0 0 0 0 0 0 0 ...
#>  $ comfort_B : int  1 1 0 0 0 0 1 0 1 0 ...

The model formula

We have to inform {RprobitB} about the covariates we want to include in our model via specifying a formula object. Say we want to model the utility \(U_{n,t,j}\) of decider \(n\) at choice occasion \(t\) for alternative \(j\) via the linear equation

\[U_{n,t,j} = A_{n,t,j} \beta_1 + B_{n,t} \beta_{2,j} + C_{n,t,j} \beta_{3,j} + \epsilon_{n,tj}.\] Here, \(A\) and \(C\) are alternative and choice situation specific covariates, whereas \(B\) is choice situation specific. The coefficient \(\beta_1\) is generic (i.e. the same for each alternative), whereas \(\beta_{2,j}\) and \(\beta_{3,j}\) are alternative specific.

To represent this structure, the formula object is of the form (analogously to {mlogit}) choice ~ A | B | C, where

Specifying a formula object for {RprobitB} must be consistent with the following rules:

To impose random effects for specific variables, we need to define a character vector re with the corresponding variable names. To have random effects for the alternative specific constants, include "ASC" in re.


We specify a model formula for the train_choice data set. Say we want to include all the covariates price, time, comfort, and change, which are all alternative specific (that is, they contain a potentially different value for each alternative, such as different prices for A and B), so either of type 1 or type 3. The difference between type 1 and type 3 is that in the former case, we would estimate a generic coefficient (i.e. a coefficient that is constant across alternatives), whereas in the latter case, we would estimate alternative specific coefficients. Deciding between type 1 and type 3 for these covariates belongs into the topic of model selection, for which we provide a separate vignette. For now, we go with type 1 for all covariates and remove ASCs:

form <- choice ~ price + time + comfort + change | 0

Additionally, we specify random effects for price and time (because we would typically expect heterogeneity here):

re <- c("price", "time")

The prepare_data() function

Before model estimation with {RprobitB}, any empirical choice data set choice_data must pass the prepare_data() function:

data <- prepare_data(form = form, choice_data = choice_data)

The function performs compatibility checks and data transformations and returns an object of class RprobitB_data that can be fed into the estimation routine fit_model(). The following arguments are optional:


Let’s prepare the train_choice data set for estimation with our previous specification of form and re:

data <- prepare_data(form = form, choice_data = train_choice, re = re, id = "deciderID", idc = "occasionID")

The summary and plot methods provide a quick data overview:

#>                  count
#> deciders           235
#> choice occasions  5-19
#> total choices     2929
#> alternatives         2
#> - 'A'             1474
#> - 'B'             1455

Ordered alternatives

The two choice alternatives from the train trip example are unordered. If we had asked “rate your train trip from 1 (horrible) to 7 (great)”, then the respondents would choose from a set of ordered alternatives. Such ordered alternatives can by analyzed by setting ordered = TRUE in prepare_data. In this case, alternatives becomes a mandatory argument, where the alternatives must be named from worst to best.

Ranked choices

Rather than recording only the single most preferred alternative, some surveys ask for a full ranking of all the alternatives, which reveals far more about the underlying preferences. Ranked choices can by analyzed by setting ranked = TRUE in prepare_data(). The choice column of the data set must provide the full ranking for each choice occasion (from most preferred to least preferred), where the alternatives are separated by commas.

The ranked probit model follows directly from the basic multivariate case. The only difference is that we take flexible utility differences such that the differenced utility vector is always negative. Thereby, we incorporate information of the full ranking.

Simulate choices

The simulate_choices function simulates discrete choice data from a prespecified probit model. Say we want to simulate the choices of N deciders in T choice occasions7 among J alternatives from a model formulation form, we have to call

data <- simulate_choices(form = form, N = N, T = T, J = J)

The function simulate_choices() has the following optional arguments:

We can specify the true parameters8 by adding a named list with values for

True parameters that are not specified will be set at random.


For illustration, we simulate the choices of N = 100 deciders at T = 10 choice occasions between the alternatives A and B:

N <- 100
T <- 10
alternatives <- c("A", "B")
base <- "B"
form <- choice ~ var1 | var2 | var3
re <- c("ASC", "var2")

{RprobitB} provides the function overview_effects() which can be used to get an overview of the effects for which parameters can be specified:

overview_effects(form = form, re = re, alternatives = alternatives, base = base)
#>   effect as_value as_coef random
#> 1   var1     TRUE   FALSE  FALSE
#> 2 var3_A     TRUE    TRUE  FALSE
#> 3 var3_B     TRUE    TRUE  FALSE
#> 4 var2_A    FALSE    TRUE   TRUE
#> 5  ASC_A    FALSE    TRUE   TRUE

Hence, the coefficient vector alpha must be of length 3, where the elements 1 to 3 correspond to var1, var3_A, and var3_B, respectively. The matrix b must be of dimension 2 x C, where (by default) C = 1 and row 1 and 2 correspond to var2_A and ASC_A, respectively.

data <- simulate_choices(
  form = form,
  N = N,
  T = T,
  J = 2,
  re = re,
  alternatives = alternatives,
  seed = 1,
  true_parameter = list(
    alpha = c(-1, 0, 1),
    b = matrix(c(2, -0.5), ncol = 1)
#>                  count
#> deciders           100
#> choice occasions    10
#> total choices     1000
#> alternatives         2
#> - 'A'              435
#> - 'B'              565

We can visualize the covariates grouped by the chosen alternatives:

plot(data, by_choice = TRUE)

What we see is consistent with our specification: Higher values of var1_A for example correspond more frequently to choice B (upper-right panel), because the coefficient of var1 (the first value of alpha) is negative.

Train and test data set

The function train_test() can be used to split the output of prepare_data() or simulate_choices() into a train and a test subset. This is useful when evaluating the prediction performance of a fitted model. For example, the following code puts 70% of deciders from our simulated data into the train subsample and 30% of deciders in the test subsample:

train_test(data, test_proportion = 0.3, by = "N")
#> $train
#> Simulated data of 700 choices.
#> $test
#> Simulated data of 300 choices.

Alternatively, the following code puts 2 randomly chosen choice occasions per decider from data into the test subsample, the rest goes into the train subsample:

train_test(data, test_number = 2, by = "T", random = TRUE, seed = 1)
#> $train
#> Simulated data of 800 choices.
#> $test
#> Simulated data of 200 choices.


Train, K. 2009. Discrete Choice Methods with Simulation. Cambridge University Press.

  1. This vignette is build using R 4.1.2 with the {RprobitB} 1.1.4 package.↩︎

  2. The{tidyr}package [contains functionality]( that can transform adata.frame` into this format.↩︎

  3. The choice situation identifier are irrelevant for model estimation because {RprobitB} does not model correlation over choice occasions. They are useful to identify specific choice occasions later on.↩︎

  4. For alternative specific variables, the alternative names must be added to the covariates via the _ separator.↩︎

  5. Mind that not all alternative specific coefficients of type 2-covariates are identified. This is because the probit model is estimated on utility differences since the level of the utility is irrelevant, see the vignette on the model definition. Therefore, the coefficient of the last alternative of each type 2-covariate is set to 0.↩︎

  6. ASCs capture the average effect on utility of all factors that are not included in the model. Due to identifiability, we cannot estimate ASCs for all the alternatives. Therefore, they are added for all except for the last alternative.↩︎

  7. T can be either a positive number, representing a fixed number of choice occasions for each decision maker, or a vector of length N with decision maker specific numbers of choice occasions.↩︎

  8. See the vignette on the model definition for more details, especially for the meaning of the parameters.↩︎