Log-likelihood function of the (normally mixed) multinomial probit model

Usage

f_ll_mnp(
  theta,
  data,
  neg = FALSE,
  normal_cdf = mvtnorm::pmvnorm,
  threshold = 1e-06
)

Arguments

theta

A numeric, the vector of model coefficients. The order of theta is c(b, o, l), see the details.

data

A data.frame, the output of sim_mnp.

neg

Set to TRUE to return the negative log-likelihood value.

normal_cdf

A function that evaluates the n-variate normal CDF. It must take the arguments

lower, the vector of lower limits of length n,
upper, the vector of upper limits of length n,
mean, the mean vector of length n,
sigma, the n times n covariance matrix,

and return a single numeric.

By default, normal_cdf = mvtnorm::pmvnorm.

threshold

A small numeric between 0 and 1. Choice probabilities below this value are set to this value to avoid numerical problems.

Value

A numeric, the log-likelihood value at theta given data.

Details

The order of theta is supposed to be c(b, o, l), where

b is the vector of mean effects without the first entry,
o the lower-triangular elements of the lower-triangular Cholesky root of the effect covariance matrix Omega (if any),
and l the lower-triangular elements of the lower-triangular Cholesky root of the differenced (with respect to the last alternative) error term covariance matrix Sigma.

References

https://en.wikipedia.org/wiki/Multinomial_probit

Examples

data <- sim_mnp(N = 500, J = 3, P = 2, b = c(1, 3), Sigma = diag(3))
theta <- attr(data, "true")
f_ll_mnp(theta = theta, data = data)
#> [1] -160.4119
# \donttest{
nlm(f_ll_mnp, p = theta, data = data, neg = TRUE)$estimate
#> [1] 2.7968937 1.1491481 0.5971256 1.1336704
# }