This function simulates choice data from a probit model.

## Usage

simulate_choices(
form,
N,
T = 1,
J,
re = NULL,
alternatives = NULL,
ordered = FALSE,
ranked = FALSE,
base = NULL,
covariates = NULL,
seed = NULL,
true_parameter = list()
)

## Arguments

form

A formula object that is used to specify the model equation. The structure is choice ~ A | B | C, where

• choice is the name of the dependent variable (the choices),

• A are names of alternative and choice situation specific covariates with a coefficient that is constant across alternatives,

• B are names of choice situation specific covariates with alternative specific coefficients,

• and C are names of alternative and choice situation specific covariates with alternative specific coefficients.

Multiple covariates (of one type) are separated by a + sign. By default, alternative specific constants (ASCs) are added to the model. They can be removed by adding +0 in the second spot.

In the ordered probit model (ordered = TRUE), the formula object has the simple structure choice ~ A. ASCs are not estimated.

N

The number (greater or equal 1) of decision makers.

T

The number (greater or equal 1) of choice occasions or a vector of choice occasions of length N (i.e. a decision maker specific number). Per default, T = 1.

J

The number (greater or equal 2) of choice alternatives.

re

A character (vector) of covariates of form with random effects. If re = NULL (the default), there are no random effects. To have random effects for the ASCs, include "ASC" in re.

alternatives

A character vector with the names of the choice alternatives. If not specified, the choice set is defined by the observed choices. If ordered = TRUE, alternatives is assumed to be specified with the alternatives ordered from worst to best.

ordered

A boolean, FALSE per default. If TRUE, the choice set alternatives is assumed to be ordered from worst to best.

ranked

TBA

base

A character, the name of the base alternative for covariates that are not alternative specific (i.e. type 2 covariates and ASCs). Ignored and set to NULL if the model has no alternative specific covariates (e.g. in the ordered probit model). Per default, base is the last element of alternatives.

covariates

A named list of covariate values. Each element must be a vector of length equal to the number of choice occasions and named according to a covariate. Covariates for which no values are supplied are drawn from a standard normal distribution.

seed

Set a seed for the simulation.

true_parameter

Optionally specify a named list with true parameter values for alpha, C, s, b, Omega, Sigma, Sigma_full, beta, z, or d for the simulation. See the vignette on model definition for definitions of these variables.

## Value

An object of class RprobitB_data.

## Details

See the vignette on choice data for more details.

• check_form() for checking the model formula

• overview_effects() for an overview of the model effects

• create_lagged_cov() for creating lagged covariates

• as_cov_names() for re-labeling alternative-specific covariates

• prepare_data() for preparing empirical choice data

• train_test() for splitting choice data into a train and test subset

## Examples

### simulate data from a binary probit model with two latent classes
data <- simulate_choices(
form = choice ~ cost | income | time,
N = 100,
T = 10,
J = 2,
re = c("cost", "time"),
alternatives = c("car", "bus"),
seed = 1,
true_parameter = list(
"alpha" = c(-1, 1),
"b" = matrix(c(-1, -1, -0.5, -1.5, 0, -1), ncol = 2),
"C" = 2
)
)

### simulate data from an ordered probit model
data <- simulate_choices(
form = opinion ~ age + gender,
N = 10,
T = 1:10,
J = 5,
alternatives = c("very bad", "bad", "indifferent", "good", "very good"),
ordered = TRUE,
covariates = list(
"gender" = rep(sample(c(0,1), 10, replace = TRUE), times = 1:10)
),
seed = 1
)

### simulate data from a ranked probit model
data <- simulate_choices(
form = product ~ price,
N = 10,
T = 1:10,
J = 3,
alternatives = c("A", "B", "C"),
ranked = TRUE,
seed = 1
)