Simulate hierarchical multinomial probit data — simulate_hmnp

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).

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).

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.

Examples

# \donttest{
sim <- simulate_hmnp_data(N = 100, T = 4, J = 4, seed = 123)
print(sim)
#> <choicer_sim: hmnp>
#>   settings:
#>     N = 100
#>     T = 4
#>     J = 4
#>     K_x = 2
#>     P = 2
#>     include_outside = TRUE
#>     vary_choice_set = FALSE
#>     sigma = 1
#>   rows in $data: 1600
#>   true_params: beta, W, theta, sigma_d, delta, xi, Z
sim$true_params$delta
#> [1] 1.4492921 0.3046101 0.6374623 1.0511186
# }