simulate_hmnp_data: Simulate hierarchical multinomial probit data

In choicer: Discrete Choice Models for Economic Applications

Simulate hierarchical multinomial probit data

Description

Generates synthetic panel choice data from the hierarchical probit DGP with iid normal utility shocks:

U_{ijt} = x_{ijt}'\beta_i + \delta_j + \epsilon_{ijt}, \qquad U_{iot} = \epsilon_{iot}, \qquad \epsilon \sim N(0, \sigma^2),

choice by argmax within the task. The outside option is stochastic — it carries its own N(0, \sigma^2) shock on top of systematic utility 0, exactly as in the estimator. \beta_i \sim N(\beta, W) (normal only) and \delta_j = z_j'\theta + \xi_j, \xi_j \sim N(0, \sigma_d^2), as in simulate_hmnl_data().

Usage

simulate_hmnp_data(
  N = 500,
  T = 10,
  J = 4,
  beta = c(0.8, -0.6),
  W = NULL,
  theta = c(0.5, -0.4),
  sigma_d = 0.5,
  Z = NULL,
  include_outside = TRUE,
  seed = 123,
  vary_choice_set = FALSE,
  sigma = 1
)

Arguments

N	Number of respondents.
T	Number of choice situations per respondent.
J	Number of inside alternatives.
beta	Population means of the structural random coefficients (length K_x = length(beta)); all coordinates are normal.
W	Covariance of the random coefficients (K_x x K_x). Defaults to diag(0.5, K_x).
theta	Mean-function coefficients for \delta_j = z_j'\theta + \xi_j; the first entry is the intercept, entries ⁠2..P⁠ load on the alternative-level covariates.
sigma_d	Standard deviation of the alternative-level effects \xi_j.
Z	Optional ⁠J x (length(theta) - 1)⁠ matrix of alternative-level covariates (excluding the intercept). Default NULL draws them Uniform(-1, 1).
include_outside	Logical; if TRUE (default) every choice set also contains an outside option with systematic utility 0 and its own normal shock. The outside good is implicit in the returned data (matching the prepare_hmnp_data() convention): no physical row is emitted, and a choice situation the outside option wins has an all-zeros choice column.
seed	Random seed (NULL skips set.seed()).
vary_choice_set	Logical; if TRUE choice-set size is sampled uniformly from 2:J per task. Default FALSE.
sigma	Standard deviation of the iid utility shocks (DGP scale).

Details

The iid-probit likelihood identifies parameters only up to the common scale \sigma, so true_params is reported on the identified scale: beta = \beta/\sigma, W = W/\sigma^2, theta = \theta/\sigma, sigma_d = \sigma_d/\sigma, delta = \delta/\sigma, xi = \xi/\sigma. With the default sigma = 1 the DGP scale and the identified scale coincide.

Value

A choicer_sim object. true_params contains beta, W, theta, sigma_d, the realized delta and xi, and the full mean-function design Z — all on the identified scale (see Details).

Examples

sim <- simulate_hmnp_data(N = 100, T = 4, J = 4, seed = 123)
print(sim)
sim$true_params$delta

choicer documentation built on Sept. 5, 2026, 1:07 a.m.