HeckmanSK: Skew-Normal Sample Selection Model Fit Function

In ssmodels: Sample Selection Models

Skew-Normal Sample Selection Model Fit Function

Description

Fits a sample selection model based on the Skew-Normal distribution using Maximum Likelihood Estimation (MLE). This model allows for asymmetry in the distribution of the outcome variable's error term, addressing potential skewness.

Usage

HeckmanSK(
  selection,
  outcome,
  data = sys.frame(sys.parent()),
  lambda,
  start = NULL
)

Arguments

selection	A formula specifying the selection equation.
outcome	A formula specifying the outcome equation.
data	A data frame containing the variables.
lambda	Initial start value for the skewness parameter (lambda).
start	Optional numeric vector of initial parameter values.

Details

The function implements MLE for a sample selection model where the outcome equation's errors follow a Skew-Normal distribution, as proposed in \insertCiteogundimu2016sample;textualssmodels. The optimization is performed via the BFGS algorithm.

The results include estimates for:

• Selection equation coefficients.

• Outcome equation coefficients.

• Standard deviation of the error term (sigma).

• Correlation between the selection and outcome errors (rho).

• Skewness parameter (lambda).

• Robust standard errors from the Fisher information matrix.

Value

A list containing:

• coefficients: Named vector of estimated model parameters.

• value: The (negative) log-likelihood at convergence.

• loglik: The maximum log-likelihood.

• counts: Number of gradient evaluations.

• hessian: Hessian matrix at the optimum.

• fisher_infoSK: Approximate Fisher information matrix.

• prop_sigmaSK: Standard errors for the estimates.

• level: Levels of the selection variable.

• nObs: Number of observations.

• nParam: Number of model parameters.

• N0: Number of censored (unobserved) observations.

• N1: Number of observed (uncensored) observations.

• NXS: Number of covariates in the selection equation.

• NXO: Number of covariates in the outcome equation.

• df: Degrees of freedom (observations minus parameters).

• aic: Akaike Information Criterion.

• bic: Bayesian Information Criterion.

• initial.value: Initial parameter values used.

References

\insertRef

ogundimu2016samplessmodels

Examples

data("Mroz87")
attach(Mroz87)
selectEq <- lfp ~ huswage + kids5 + mtr + fatheduc + educ + city
outcomeEq <- log(wage) ~ educ + city
HeckmanSK(selectEq, outcomeEq, data = Mroz87, lambda = -1.5)

ssmodels documentation built on June 8, 2025, 10:49 a.m.