Estimate the log-likelihood for the gamma/delta transformed convex parameters for tobit regression

Estimate the log-likelihood for the gamma/delta transformed convex parameters for tobit regression

Usage

negLogLik_tobit(
  param,
  x,
  lower_limit,
  upper_limit,
  mask_lower,
  mask_between,
  mask_upper,
  distribution = c("t", "norm")
)

Arguments

param

c(gamma, delta) see details

x

The vector of values

lower_limit, upper_limit

The vector lower and upper limits for censoring

mask_lower, mask_between, mask_upper

Boolean masks indicating if the value is below the lower limit, a point value, or above the upper limit

distribution

The distribution to use

Details

beta = delta/gamma and sigma^2 = gamma^-2. The estimation is based on the convex reformulation of the likelihood function described in Olsen 1978.

References

Olsen RJ. Note on the Uniqueness of the Maximum Likelihood Estimator for the Tobit Model. Econometrica. 1978;46(5):1211. doi:10.2307/1911445