The ssmodels package provides functions to fit data affected by sample selection bias.
It includes several extensions of the classical Heckman selection model, allowing for different
assumptions about the joint distribution of the selection and outcome equations.
Details
The following models are implemented:
HeckmanCLClassic Heckman model (Tobit-2).
HeckmantSHeckman model with Student's t-distribution.
HeckmanSKHeckman model with Skew-Normal distribution.
HeckmanBSHeckman model with Birnbaum-Saunders distribution.
HeckmanGeGeneralized Heckman model with covariates in the dispersion and correlation structures.
The package also includes helper functions for computing Inverse Mills Ratios (IMR), post-processing parameter vectors, and two-step initial value estimation.
References
James J Heckman (1976). “The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimator for such models.” In Annals of Economic and Social Measurement, Volume 5, number 4, 475–492. NBER.
James J Heckman (1979). “Sample selection bias as a specification error.” Econometrica: Journal of the econometric society, 153–161.
Thomas A Mroz (1987). “The sensitivity of an empirical model of married women's hours of work to economic and statistical assumptions.” Econometrica: Journal of the Econometric Society, 765–799.
Ott Toomet, Arne Henningsen (2008). “Sample Selection Models in R: Package sampleSelection.” Journal of Statistical Software, 27(7). https://www.jstatsoft.org/article/view/v027i07.
Yulia V Marchenko, Marc G Genton (2012). “A Heckman selection-t model.” Journal of the American Statistical Association, 107(497), 304–317.
Emmanuel O Ogundimu, Jane L Hutton (2016). “A Sample Selection Model with Skew-normal Distribution.” Scandinavian Journal of Statistics, 43(1), 172–190.
Mikhail Zhelonkin, Marc G Genton, Elvezio Ronchetti (2016). “Robust inference in sample selection models.” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 78(4), 805–827.
Mikhail Zhelonkin, Marc G. Genton, Elvezio Ronchetti (2019). ssmrob: Robust Estimation and Inference in Sample Selection Models. R package version 0.7, https://CRAN.R-project.org/package=ssmrob.
Emmanuel O Ogundimu, Gary S Collins (2019). “A robust imputation method for missing responses and covariates in sample selection models.” Statistical methods in medical research, 28(1), 102–116.
Fernando de Souza Bastos, Wagner Barreto-Souza (2020). “Birnbaum–Saunders sample selection model.” Journal of Applied Statistics.
Fernando de Souza Bastos, Wagner Barreto-Souza, Marc G Genton (2022). “A Generalized Heckman Model With Varying Sample Selection Bias and Dispersion Parameters.” Statistica Sinica.