mnl_bhhh_parallel: BHHH/OPG information matrix for multinomial logit model

In choicer: Discrete Choice Models for Economic Applications

BHHH/OPG information matrix for multinomial logit model

Description

Computes the weighted outer product of per-individual scores \sum_i w_i\, s_i s_i^\top for the Multinomial Logit model. The per-individual score s_i is the (positive) gradient of individual i's log-likelihood contribution and is weight-free; the supplied weights enter only as the leading multiplier. Passing weights = w yields the ordinary weighted BHHH/OPG information; passing weights = w^2 yields the sandwich meat B = \sum_i w_i^2 s_i s_i^\top used for robust (WESML) inference.

Usage

mnl_bhhh_parallel(
  theta,
  X,
  alt_idx,
  choice_idx,
  M,
  weights,
  use_asc = TRUE,
  include_outside_option = FALSE
)

Arguments

theta	K + J - 1 or K + J vector with model parameters
X	sum(M) x K design matrix with covariates. Stacks M[i] x K matrices for individual i.
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
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)

Value

A symmetric positive-semidefinite information matrix \sum_i w_i\, s_i s_i^\top (same sign convention as the negated Hessian).

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), x2 = rnorm(.N))]
dt[, choice := 0L]
dt[, choice := sample(c(1L, rep(0L, J - 1))), by = id]
fit <- run_mnlogit(dt, "id", "alt", "choice", c("x1", "x2"))
B <- choicer:::mnl_bhhh_parallel(coef(fit), fit$data$X, fit$data$alt_idx,
  fit$data$choice_idx, fit$data$M, fit$data$weights)
dim(B)

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