mxl_hessian_parallel: Analytical Hessian of the log-likelihood v2

In choicer: Discrete Choice Models for Economic Applications

Analytical Hessian of the log-likelihood v2

Description

Computes the Hessian of the log-likelihood for the Mixed Logit model using OpenMP for parallelization. Mirrors the parameters of mxl_loglik_gradient_parallel.

Usage

mxl_hessian_parallel(
  theta,
  X,
  W,
  alt_idx,
  choice_idx,
  M,
  weights,
  eta_draws,
  rc_dist,
  rc_correlation = TRUE,
  rc_mean = FALSE,
  use_asc = TRUE,
  include_outside_option = FALSE,
  gen_seed = -1L,
  gen_scramble = 1L,
  gen_S = 0L
)

Arguments

theta	vector collecting model parameters (beta, mu, L, delta (ASCs))
X	design matrix for covariates with fixed coefficients; sum(M_i) x K_x
W	design matrix for covariates with random coefficients; sum(M_i) x K_w or J x K_w
alt_idx	sum(M) x 1 vector with indices of alternatives within each choice set; 1-based indexing
choice_idx	N x 1 vector with indices of chosen alternatives; 1-based indexing relative to X; 0 is used if include_outside_option=True
M	N x 1 vector with number of alternatives for each individual
weights	N x 1 vector with weights for each observation
eta_draws	Array with choice situation draws; K_w x S x N
rc_dist	K_w x 1 integer vector indicating distribution of random coefficients: 0 = normal, 1 = log-normal
rc_correlation	whether random coefficients should be correlated
rc_mean	whether to estimate means for random coefficients.
use_asc	whether to use alternative-specific constants.
include_outside_option	whether to include outside option normalized to 0 (if so, the outside option is not included in the data)
gen_seed	Integer master seed for the on-the-fly Halton generator. < 0 (default) uses the materialized eta_draws cube; >= 0 generates draws on the fly from this seed.
gen_scramble	Integer scramble mode for on-the-fly generation: 0 = identity permutations (plain Halton, compat), 1 = seeded position-wise digit permutations.
gen_S	Integer number of draws per individual, used only when gen_seed >= 0.

Value

Hessian evaluated at input arguments

Note

For log-normal random coefficients (rc_dist=1) with rc_mean=TRUE, the distribution is a shifted log-normal: beta_k = exp(mu_k) + exp(L_k * eta), where exp(mu_k) shifts the location and exp(L_k * eta) ~ LogNormal(0, sigma_k^2). This differs from the textbook parameterization exp(mu_k + L_k * eta).

Examples

library(data.table)
set.seed(42)
N <- 50; J <- 3
dt <- data.table(id = rep(1:N, each = J), alt = rep(1:J, N))
dt[, `:=`(x1 = rnorm(.N), w1 = rnorm(.N))]
dt[, choice := 0L]
dt[, choice := sample(c(1L, rep(0L, J - 1))), by = id]
d <- prepare_mxl_data(dt, "id", "alt", "choice", "x1", "w1")
eta <- get_halton_normals(50, d$N, ncol(d$W))
theta <- rep(0, ncol(d$X) + ncol(d$W) + nrow(d$alt_mapping) - 1)
H <- choicer:::mxl_hessian_parallel(theta, d$X, d$W, d$alt_idx, d$choice_idx,
  d$M, d$weights, eta, rc_dist = rep(0L, ncol(d$W)),
  rc_correlation = FALSE, rc_mean = FALSE)
dim(H)

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