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Type:

Package

Title:

Heckman Selection Models Based on Bayesian Analysis

Version:

1.0.0

Maintainer:

Heeju Lim <heeju.lim@uconn.edu>

Description:

Implements Heckman selection models using a Bayesian approach via 'Stan' and compares the performance of normal, Student’s t, and contaminated normal distributions in addressing complexities and selection bias (Heeju Lim, Victor E. Lachos, and Victor H. Lachos, Bayesian analysis of flexible Heckman selection models using Hamiltonian Monte Carlo, 2025, under submission).

Imports:

rstan (≥ 2.26.23), mvtnorm (≥ 1.2-3), loo, stats

License:

GPL-3

Encoding:

UTF-8

LazyData:

true

RoxygenNote:

7.3.2

NeedsCompilation:

Packaged:

2025-05-02 19:55:20 UTC; heeju

Author:

Heeju Lim [aut, cre], Victor E. Lachos [aut], Victor H. Lachos [aut]

Depends:

R (≥ 3.5.0)

Repository:

CRAN

Date/Publication:

2025-05-06 08:50:05 UTC

Fit the Heckman Selection Stan model using the Normal, Student-t or Contaminated Normal distributions.

Description

'HeckmanStan()' fits the Heckman selection model using a Bayesian approach to address sample selection bias.

Usage

HeckmanStan(
  y,
  x,
  w,
  cc,
  family = "CN",
  init = "random",
  thin = 5,
  chains = 1,
  iter = 10,
  warmup = 5
)

Arguments

y

A response vector.

x

A covariate matrix for the response y.

w

A covariate matrix for the missing indicator cc.

cc

A missing indicator vector (1=observed, 0=missing) .

family

The distribution family to be used (Normal, T, or CN).

init

Parameters specifies the initial values for model parameters.

thin

An Interval at which samples are retained from the MCMC process to reduce autocorrelation.

chains

The number of chains to run during the MCMC sampling. Running multiple chains is useful for checking convergence.

iter

The total number of iterations for the MCMC sampling, determining how many samples will be drawn.

warmup

The number of initial iterations that will be discarded as the algorithm stabilizes before collecting samples.

Value

An object of class HeckmanStan, which is a list containing two elements:

list[[1]]: Includes inference results from the Stan model, along with EAIC and EBIC.
list[[2]]: Includes the HPC confidence intervals, along with LOOIC, WAIC, and CPO.

Examples


################################################################################
# Simulation
################################################################################
library(mvtnorm)
n<- 100
w<- cbind(1,rnorm(n),rnorm(n))
x<- cbind(w[,1:2])
family="CN"
sigma2<- 1
rho<-0.7
beta<- c(1,0.5)
gamma<- c(1,0.3,-.5)
nu=c(0.1,0.1)
data<-geraHeckman(x,w,beta,gamma,sigma2,rho,nu,family=family)
y<-data$y
cc<-data$cc
# Fit Heckman Normal Stan model
fit.n_stan <- HeckmanStan(y, x, w, cc, family="Normal"
                         , thin = 5, chains = 1, iter = 10000, warmup = 1000)
qoi=c("beta","gamma","sigma_e","sigma2", "rho","EAIC","EBIC")
print(fit.n_stan[[1]],par=qoi)
print(fit.n_stan[[2]])

require(rstan)
plot(fit.n_stan[[1]], pars=qoi)
plot(fit.n_stan[[1]], plotfun="hist", pars=qoi)
plot(fit.n_stan[[1]], plotfun="trace", pars=qoi)
plot(fit.n_stan[[1]], plotfun = "rhat")

MEPS 2001: Ambulatory Expenditures Data

Description

This dataset is an extract from the 2001 Medical Expenditure Panel Survey (MEPS), providing information on ambulatory expenditures and various demographic and health-related variables. It has been used for illustrative examples by Cameron and Trivedi (2009, Chapter 16).

Usage

data(MEPS2001)

Format

A data frame with 3,328 observations on the following 22 variables.

educ: Education status
age: Age
income: Income
female: Gender
vgood: Self-reported health status, very good
good: Self-reported health status, good
hospexp: Hospital expenditures
totchr: Total number of chronic diseases
ffs: Family support
dhospexp: Dummy variable for hospital expenditures
age2: Age squared
agefem: Interaction between age and gender
fairpoor: Self-reported health status, fair or poor
year01: Year of survey
instype: Type of insurance
ambexp: Ambulatory expenditures
lambexp: Log of ambulatory expenditures
blhisp: Ethnicity
instype_s1: Insurance type, version 1
dambexp: Dummy variable for ambulatory expenditures
lnambx: Log-transformed ambulatory expenditures
ins: Insurance status

Source

2001 Medical Expenditure Panel Survey by the Agency for Healthcare Research and Quality.

References

Cameron, C.A. and Trivedi, P.K. (2009). *Microeconometrics Using Stata*. College Station, TX: Stata Press.

Examples


data(MEPS2001)
head(MEPS2001)

Panel Study of Income Dynamics 1976 Extract

Description

Cross-section data originating from the 1976 Panel Study of Income Dynamics (PSID). The dataset includes demographic and economic characteristics of married women and their husbands, and is commonly used for analyzing female labor force participation.

Usage

data(PSID1976)

Format

A data frame with 753 observations on the following 22 variables.

age: age of the woman
city: dummy for living in a city
college: dummy for college education (woman)
education: years of education (woman)
experience: years of labor market experience
feducation: father's years of education
fincome: family income in 1,000s
hage: husband's age
hcollege: dummy for husband's college education
heducation: husband's years of education
hhours: husband's weekly working hours
hours: woman's weekly working hours
hwage: husband's log hourly wage
meducation: mother's years of education
oldkids: number of children older than 6
participation: dummy for woman's labor force participation
repwage: replacement wage (predicted wage if not employed)
tax: marginal tax rate
unemp: state unemployment rate
wage: log hourly wage of the woman
youngkids: number of children 6 or younger

References

Mroz, T. A. (1987). The sensitivity of an empirical model of married women's hours of work to economic and statistical assumptions. *Econometrica*, 55(4), 765–799.

Examples


data(PSID1976)
head(PSID1976)

Generating Heckman data : Normal, Student-t, Slash and Laplace

Description

'geraHeckman()' generates a random sample from the Heckman selection model (Normal, Student-t or CN).

Usage

geraHeckman(x, w, beta, gamma, sigma2, rho, nu, family = "T")

Arguments

x

A covariate matrix for the response y.

w

A covariate matrix for the missing indicator cc.

beta

Values for the beta vector.

gamma

Values for the gamma vector.

sigma2

Value for the variance.

rho

Value for the dependence between the response and missing value.

nu

When using the t- distribution, the initial value for the degrees of freedom.

family

The distribution family to be used (Normal, T, or CN).

Value

Return an object with the response (y) and missing values (cc).

References

Lachos, V. H., Prates, M. O., & Dey, D. K. (2021). Heckman selection-t model: Parameter estimation via the EM-algorithm. Journal of Multivariate Analysis, 184, 104737.

Examples


n <- 100
rho <- .6
cens <- 0.25
nu <- 4
set.seed(20200527)
w <- cbind(1,runif(n,-1,1),rnorm(n))
x <- cbind(w[,1:2])

family <- "T"
c <- qt(cens, df=nu)

sigma2 <- 1
beta <- c(1,0.5)
gamma<- c(1,0.3,-.5)
gamma[1] <- -c*sqrt(sigma2)

data <- geraHeckman(x,w,beta,gamma,sigma2,rho,nu,family=family)