Estimating equation for Tobit regression (Type I)

Handles left and/or right censored outcomes using standard normal PDF/CDF. Theta is (beta, log(sigma)), a vector of length b + 1.

Usage

ee_tobit(
  theta,
  X,
  y,
  lower = NULL,
  upper = NULL,
  weights = NULL,
  offset = NULL
)

Arguments

theta: Numeric vector of length b + 1.
X: Numeric n-by-b design matrix.
y: Numeric vector of n observed (possibly censored) outcome values.
lower: Numeric lower censoring limit, or NULL (default, no left censoring).
upper: Numeric upper censoring limit, or NULL (default, no right censoring).
weights: Optional numeric vector of n weights. Default NULL.
offset: Optional numeric vector of n offsets. Default NULL.

Value

A (b+1)-by-n matrix. The rows are named X_1 through X_b for the columns of X, and the final row is named log_sigma.

Examples

# A latent outcome observed only down to zero, so the negative values are
# left censored at the limit.
set.seed(123)
n <- 200
X <- cbind(1, rnorm(n))
y <- pmax(1 + 0.5 * X[, 2] + rnorm(n), 0)

psi <- function(theta) ee_tobit(theta, X = X, y = y, lower = 0)

# The last parameter is log(sigma), started at the log of the observed
# standard deviation.
m <- m_estimate(
  stacked_equations = psi,
  init = c(mean(y), 0, log(sd(y)))
)
coef(m)
#>          X_1          X_2    log_sigma 
#>  1.040942234  0.477997107 -0.002076965