Simulate multinomial probit data — simulate_mnp

Generates synthetic choice data from the MNP data-generating process estimated by run_mnprobit(): latent utility differences against the base alternative (alternative 1), $$w_i = X_i \beta + \delta + \varepsilon_i, \qquad \varepsilon_i \sim N_{J-1}(0, \Sigma),$$ with alternative $j > 1$ chosen iff $w_{ij} > \max(0, \max_{k \neq j} w_{ik})$ and the base chosen iff all $w_{ij} < 0$. Covariates are Uniform(-1, 1). Choice sets are balanced (every individual faces all J alternatives), as the MNP estimator requires; there is no outside-option flag — model an outside good as a zero-covariate base alternative instead.

Usage

simulate_mnp_data(
  N = 5000,
  J = 3,
  beta = c(0.8, -0.6),
  delta = NULL,
  Sigma = matrix(c(1, 0.5, 0.5, 1.5), nrow = 2),
  seed = 123
)

Arguments

N: Number of choice situations.
J: Number of alternatives (alternative 1 is the base).
beta: Fixed coefficients for x1..x{K_x} (length K_x = length(beta)).
delta: ASCs of the differenced utilities, one per non-base alternative (length J - 1). Defaults to an alternating pattern of c(0.5, -0.5).
Sigma: Covariance matrix of the differenced errors ((J-1) x (J-1)).
seed: Random seed (NULL skips set.seed()).

Value

A choicer_sim object. true_params contains beta, delta, and Sigma on the identified scale (see Details).

Details

The MNP likelihood only identifies parameters up to scale, so true_params is reported on the identified scale (normalized by $\sigma_{11}$): beta $= \beta / \sqrt{\sigma_{11}}$, delta $= \delta / \sqrt{\sigma_{11}}$, and Sigma $= \Sigma / \sigma_{11}$ — the scale on which run_mnprobit() reports its posterior. With the default Sigma ($\sigma_{11} = 1$) the DGP scale and the identified scale coincide.

Examples

# \donttest{
sim <- simulate_mnp_data(N = 1000, J = 3, seed = 123)
print(sim)
#> <choicer_sim: mnp>
#>   settings:
#>     N = 1000
#>     J = 3
#>     K_x = 2
#>     base_alt = 1
#>   rows in $data: 3000
#>   true_params: beta, delta, Sigma
# }