| Title: | Sample Selection Models |
|---|---|
| Description: | In order to facilitate the adjustment of the sample selection models existing in the literature, we created the 'ssmodels' package. Our package allows the adjustment of the classic Heckman model (Heckman (1976), Heckman (1979) <doi:10.2307/1912352>), and the estimation of the parameters of this model via the maximum likelihood method and two-step method, in addition to the adjustment of the Heckman-t models, introduced in the literature by Marchenko and Genton (2012) <doi:10.1080/01621459.2012.656011> and the Heckman-Skew model introduced in the literature by Ogundimu and Hutton (2016) <doi:10.1111/sjos.12171>. We also implemented functions to adjust the generalized version of the Heckman model, introduced by Bastos, Barreto-Souza, and Genton (2021) <doi:10.5705/ss.202021.0068>, that allows the inclusion of covariables to the dispersion and correlation parameters and a function to adjust the Heckman-BS model introduced by Bastos and Barreto-Souza (2020) <doi:10.1080/02664763.2020.1780570> that uses the Birnbaum-Saunders distribution as a joint distribution of the selection and primary regression variables. |
| Authors: | Fernando de Souza Bastos [aut, cre], Wagner Barreto de Souza [aut] |
| Maintainer: | Fernando de Souza Bastos <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.0.1 |
| Built: | 2025-02-24 05:51:29 UTC |
| Source: | https://github.com/fsbmat-ufv/ssmodels |
Estimates the parameters of the classic Heckman model via the two-step method.
HCinitial(selection, outcome, data = sys.frame(sys.parent()))HCinitial(selection, outcome, data = sys.frame(sys.parent()))
selection |
Selection equation. |
outcome |
Primary Regression Equation. |
data |
Database. |
Generally, the two-step method is very useful for finding initial values for the Likelihood Estimation method. In first step performs a probit analysis on a selection equation. The second step analyzes an outcome equation based on the first-step binary probit model.
Returns a numerical vector with estimates of the parameters of the classical Heckman model using the two-step method
data(MEPS2001) attach(MEPS2001) selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income outcomeEq <- lnambx ~ age + female + educ + blhisp + totchr + ins HCinitial(selectEq,outcomeEq, data = MEPS2001)data(MEPS2001) attach(MEPS2001) selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income outcomeEq <- lnambx ~ age + female + educ + blhisp + totchr + ins HCinitial(selectEq,outcomeEq, data = MEPS2001)
Estimates the parameters of the Heckman-BS model
HeckmanBS(selection, outcome, data = sys.frame(sys.parent()), start = NULL)HeckmanBS(selection, outcome, data = sys.frame(sys.parent()), start = NULL)
selection |
Selection equation. |
outcome |
Primary Regression Equation. |
data |
Database. |
start |
initial values. |
The HeckmanBS() function fits the Sample Selection Model based on the Birnbaum–Saunders bivariate distribution, it has the same number of parameters as the classical Heckman model. For more information see Bastos and Barreto-Souza (2020)
Returns a list with the following components.
Coefficients: Returns a numerical vector with the best estimated values of the model parameters;
Value: The value of function to be minimized (or maximized) corresponding to par.
loglik: Negative of value. Minimum (or maximum) of the likelihood function calculated from the estimated coefficients.
counts: Component of the Optim function. A two-element integer vector giving the number of calls to fn and gr respectively. This excludes those calls needed to compute the Hessian, if requested, and any calls to fn to compute a finite-difference approximation to the gradient.
hessian: Component of the Optim function, with pre-defined option hessian=TRUE. A symmetric matrix giving an estimate of the Hessian at the solution found. Note that this is the Hessian of the unconstrained problem even if the box constraints are active.
fisher_infoBS: Fisher information matrix
prop_sigmaBS: Square root of the Fisher information matrix diagonal
level: Selection variable levels
nObs: Numeric value representing the size of the database
nParam: Numerical value representing the number of model parameters
N0: Numerical value representing the number of unobserved entries
N1: Numerical value representing the number of complete entries
NXS: Numerical value representing the number of parameters of the selection model
NXO: Numerical value representing the number of parameters of the regression model
df: Numerical value that represents the difference between the size of the response vector of the selection equation and the number of model parameters
aic: Numerical value representing Akaike's information criterion.
bic: Numerical value representing Schwarz's Bayesian Criterion
initial.value: Numerical vector that represents the input values (Initial Values) used in the parameter estimation.
Fernando de Souza Bastos, Wagner Barreto-Souza (2020). “Birnbaum–Saunders sample selection model.” Journal of Applied Statistics.
data(MEPS2001) attach(MEPS2001) selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income outcomeBS <- ambexp ~ age + female + educ + blhisp + totchr + ins HeckmanBS(selectEq, outcomeBS, data = MEPS2001)data(MEPS2001) attach(MEPS2001) selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income outcomeBS <- ambexp ~ age + female + educ + blhisp + totchr + ins HeckmanBS(selectEq, outcomeBS, data = MEPS2001)
Estimates the parameters of the classic Heckman model via Maximum Likelihood method. The initial start is obtained via the two-step method.
HeckmanCL(selection, outcome, data = sys.frame(sys.parent()), start = NULL)HeckmanCL(selection, outcome, data = sys.frame(sys.parent()), start = NULL)
selection |
Selection equation. |
outcome |
Primary Regression Equation. |
data |
Database. |
start |
initial values. |
Returns a list with the following components.
Coefficients: Returns a numerical vector with the best estimated values of the model parameters;
Value: The value of function to be minimized (or maximized) corresponding to par.
loglik: Negative of value. Minimum (or maximum) of the likelihood function calculated from the estimated coefficients.
counts: Component of the Optim function. A two-element integer vector giving the number of calls to fn and gr respectively. This excludes those calls needed to compute the Hessian, if requested, and any calls to fn to compute a finite-difference approximation to the gradient.
hessian: Component of the Optim function, with pre-defined option hessian=TRUE. A symmetric matrix giving an estimate of the Hessian at the solution found. Note that this is the Hessian of the unconstrained problem even if the box constraints are active.
fisher_infoHC: Fisher information matrix
prop_sigmaHC: Square root of the Fisher information matrix diagonal
level: Selection variable levels
nObs: Numeric value representing the size of the database
nParam: Numerical value representing the number of model parameters
N0: Numerical value representing the number of unobserved entries
N1: Numerical value representing the number of complete entries
NXS: Numerical value representing the number of parameters of the selection model
NXO: Numerical value representing the number of parameters of the regression model
df: Numerical value that represents the difference between the size of the response vector of the selection equation and the number of model parameters
aic: Numerical value representing Akaike's information criterion.
bic: Numerical value representing Schwarz's Bayesian Criterion
initial.value: Numerical vector that represents the input values (Initial Values) used in the parameter estimation.
data(MEPS2001) attach(MEPS2001) selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income outcomeEq <- lnambx ~ age + female + educ + blhisp + totchr + ins HeckmanCL(selectEq, outcomeEq, data = MEPS2001)data(MEPS2001) attach(MEPS2001) selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income outcomeEq <- lnambx ~ age + female + educ + blhisp + totchr + ins HeckmanCL(selectEq, outcomeEq, data = MEPS2001)
Estimates the parameters of the Generalized Heckman model
HeckmanGe( selection, outcome, outcomeS, outcomeC, data = sys.frame(sys.parent()), start = NULL )HeckmanGe( selection, outcome, outcomeS, outcomeC, data = sys.frame(sys.parent()), start = NULL )
selection |
Selection equation. |
outcome |
Primary Regression Equation. |
outcomeS |
Matrix with Covariates for fit of the Dispersion Parameter. |
outcomeC |
Matrix with Covariates for fit of the Correlation Parameter. |
data |
Database. |
start |
initial values. |
The HeckmanGe() function fits a generalization of the Heckman sample selection model, allowing sample selection bias and dispersion parameters to depend on covariates. For more information, see Bastos et al. (2022)
Returns a list with the following components.
Coefficients: Returns a numerical vector with the best estimated values of the model parameters;
Value: The value of function to be minimized (or maximized) corresponding to par.
loglik: Negative of value. Minimum (or maximum) of the likelihood function calculated from the estimated coefficients.
counts: Component of the Optim function. A two-element integer vector giving the number of calls to fn and gr respectively. This excludes those calls needed to compute the Hessian, if requested, and any calls to fn to compute a finite-difference approximation to the gradient.
hessian: Component of the Optim function, with pre-defined option hessian=TRUE. A symmetric matrix giving an estimate of the Hessian at the solution found. Note that this is the Hessian of the unconstrained problem even if the box constraints are active.
fisher_infoHG: Fisher information matrix
prop_sigmaHG: Square root of the Fisher information matrix diagonal
level: Selection variable levels
nObs: Numeric value representing the size of the database
nParam: Numerical value representing the number of model parameters
N0: Numerical value representing the number of unobserved entries
N1: Numerical value representing the number of complete entries
NXS: Numerical value representing the number of parameters of the selection model
NXO: Numerical value representing the number of parameters of the regression model
df: Numerical value that represents the difference between the size of the response vector of the selection equation and the number of model parameters
aic: Numerical value representing Akaike's information criterion.
bic: Numerical value representing Schwarz's Bayesian Criterion
initial.value: Numerical vector that represents the input values (Initial Values) used in the parameter estimation.
NE: Numerical value that represents the number of parameters related to the covariates fitted to the dispersion parameter considering the constant parameter.
NV: Numerical value that represents the number of parameters related to the covariates fitted to the correlation parameter considering the constant parameter.
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.
data(MEPS2001) attach(MEPS2001) selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income outcomeEq <- lnambx ~ age + female + educ + blhisp + totchr + ins outcomeS <- cbind(age,female,totchr,ins) outcomeC <- 1 HeckmanGe(selectEq, outcomeEq,outcomeS, outcomeC, data = MEPS2001)data(MEPS2001) attach(MEPS2001) selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income outcomeEq <- lnambx ~ age + female + educ + blhisp + totchr + ins outcomeS <- cbind(age,female,totchr,ins) outcomeC <- 1 HeckmanGe(selectEq, outcomeEq,outcomeS, outcomeC, data = MEPS2001)
Estimates the parameters of the Sample Selection Model with Skew-Normal Distribution
HeckmanSK( selection, outcome, data = sys.frame(sys.parent()), lambda, start = NULL )HeckmanSK( selection, outcome, data = sys.frame(sys.parent()), lambda, start = NULL )
selection |
Selection equation. |
outcome |
Primary Regression Equation. |
data |
Database. |
lambda |
Initial start for asymmetry parameter. |
start |
initial values. |
The HeckmanSK() function fits the Sample Selection Model based on the Skew-normal distribution. For more information see Ogundimu and Hutton (2016)
Returns a list with the following components.
Coefficients: Returns a numerical vector with the best estimated values of the model parameters;
Value: The value of function to be minimized (or maximized) corresponding to par.
loglik: Negative of value. Minimum (or maximum) of the likelihood function calculated from the estimated coefficients.
counts: Component of the Optim function. A two-element integer vector giving the number of calls to fn and gr respectively. This excludes those calls needed to compute the Hessian, if requested, and any calls to fn to compute a finite-difference approximation to the gradient.
hessian: Component of the Optim function, with pre-defined option hessian=TRUE. A symmetric matrix giving an estimate of the Hessian at the solution found. Note that this is the Hessian of the unconstrained problem even if the box constraints are active.
fisher_infoSK: Fisher information matrix
prop_sigmaSK: Square root of the Fisher information matrix diagonal
level: Selection variable levels
nObs: Numeric value representing the size of the database
nParam: Numerical value representing the number of model parameters
N0: Numerical value representing the number of unobserved entries
N1: Numerical value representing the number of complete entries
NXS: Numerical value representing the number of parameters of the selection model
NXO: Numerical value representing the number of parameters of the regression model
df: Numerical value that represents the difference between the size of the response vector of the selection equation and the number of model parameters
aic: Numerical value representing Akaike's information criterion.
bic: Numerical value representing Schwarz's Bayesian Criterion
initial.value: Numerical vector that represents the input values (Initial Values) used in the parameter estimation.
Emmanuel O Ogundimu, Jane L Hutton (2016). “A Sample Selection Model with Skew-normal Distribution.” Scandinavian Journal of Statistics, 43(1), 172–190.
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)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)
Estimates the parameters of the Heckman-t model
HeckmantS(selection, outcome, data = sys.frame(sys.parent()), df, start = NULL)HeckmantS(selection, outcome, data = sys.frame(sys.parent()), df, start = NULL)
selection |
Selection equation. |
outcome |
Primary Regression Equation. |
data |
Database. |
df |
Initial start to the degree of freedom. |
start |
initial values. |
The HeckmantS() function fits the Sample Selection Model based on the Student's t distribution. For more information see Marchenko and Genton (2012)
Returns a list with the following components.
Coefficients: Returns a numerical vector with the best estimated values of the model parameters;
Value: The value of function to be minimized (or maximized) corresponding to par.
loglik: Negative of value. Minimum (or maximum) of the likelihood function calculated from the estimated coefficients.
counts: Component of the Optim function. A two-element integer vector giving the number of calls to fn and gr respectively. This excludes those calls needed to compute the Hessian, if requested, and any calls to fn to compute a finite-difference approximation to the gradient.
hessian: Component of the Optim function, with pre-defined option hessian=TRUE. A symmetric matrix giving an estimate of the Hessian at the solution found. Note that this is the Hessian of the unconstrained problem even if the box constraints are active.
fisher_infotS: Fisher information matrix
prop_sigmatS: Square root of the Fisher information matrix diagonal
level: Selection variable levels
nObs: Numeric value representing the size of the database
nParam: Numerical value representing the number of model parameters
N0: Numerical value representing the number of unobserved entries
N1: Numerical value representing the number of complete entries
NXS: Numerical value representing the number of parameters of the selection model
NXO: Numerical value representing the number of parameters of the regression model
df: Numerical value that represents the difference between the size of the response vector of the selection equation and the number of model parameters
aic: Numerical value representing Akaike's information criterion.
bic: Numerical value representing Schwarz's Bayesian Criterion
initial.value: Numerical vector that represents the input values (Initial Values) used in the parameter estimation.
Yulia V Marchenko, Marc G Genton (2012). “A Heckman selection-t model.” Journal of the American Statistical Association, 107(497), 304–317.
data(MEPS2001) attach(MEPS2001) selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income outcomeEq <- lnambx ~ age + female + educ + blhisp + totchr + ins HeckmantS(selectEq, outcomeEq, data = MEPS2001, df=12)data(MEPS2001) attach(MEPS2001) selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income outcomeEq <- lnambx ~ age + female + educ + blhisp + totchr + ins HeckmantS(selectEq, outcomeEq, data = MEPS2001, df=12)
Column vector of the inverse ratio of Mills
IMR(selection, data = sys.frame(sys.parent()))IMR(selection, data = sys.frame(sys.parent()))
selection |
Selection equation. |
data |
Database. |
Return column vector of the inverse ratio of Mills
data(MEPS2001) attach(MEPS2001) selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income IMR(selectEq)data(MEPS2001) attach(MEPS2001) selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income IMR(selectEq)
The MEPS is a set of large-scale surveys of families, individuals and their medical providers (doctors, hospitals, pharmacies, etc.) in the United States. It has data on the health services Americans use, how often they use them, the cost of these services and how they are paid, as well as data on the cost and reach of health insurance available to American workers. The sample is restricted to persons aged between 21 and 64 years and contains a variable response with 3328 observations of outpatient costs, of which 526 (15.8%) correspond to unobserved expenditure values and identified as zero expenditure for adjustment of the models. It also includes the following explanatory variables:
educ: education status
age: Age
income: income
female: gender
vgood: a numeric vector
good: a numeric vector
hospexp: a numeric vector
totchr: number of chronic diseases
ffs: a numeric vector
dhospexp: a numeric vector
age2: a numeric vector
agefem: a numeric vector
fairpoor: a numeric vector
year01: a numeric vector
instype: a numeric vector
ambexp: a numeric vector
lambexp: log ambulatory expenditures
blhisp: ethnicity
instype_s1: a numeric vector
dambexp: dummy variable, ambulatory expenditures
lnambx: a numeric vector
ins: insurance status
MEPS2001MEPS2001
An object of class data.frame with 3328 rows and 22 columns.
2001 Medical Expenditure Panel Survey by the Agency for Healthcare Research and Quality.
Cameron A Colin, Pravin K Trivedi (2009). “Microeconometrics using STATA.” Lakeway Drive, TX: Stata Press Books.
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.
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.
data(MEPS2001) attach(MEPS2001) hist(lnambx) selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income outcomeEq <- lnambx ~ age + female + educ + blhisp + totchr + ins HeckmanCL(selectEq, outcomeEq, data = MEPS2001)data(MEPS2001) attach(MEPS2001) hist(lnambx) selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income outcomeEq <- lnambx ~ age + female + educ + blhisp + totchr + ins HeckmanCL(selectEq, outcomeEq, data = MEPS2001)
The Mroz87 data frame contains data about 753 married women. These data are collected within the "Panel Study of Income Dynamics" (PSID). Of the 753 observations, the first 428 are for women with positive hours worked in 1975, while the remaining 325 observations are for women who did not work for pay in 1975. A more complete discussion of the data is found in Mroz (1987). It also includes the following explanatory variables:
lfp: Dummy variable for labor-force participation.
hours: Wife's hours of work in 1975.
kids5: Number of children 5 years old or younger.
kids618: Number of children 6 to 18 years old.
Age: Wife's age.
Educ: Wife's educational attainment, in years.
wage: Wife's average hourly earnings, in 1975 dollars.
repwage: Wife's wage reported at the time of the 1976 interview.
hushrs: Husband's hours worked in 1975.
husage: Husband's age.
huseduc: Husband's educational attainment, in years.
huswage: Husband's wage, in 1975 dollars.
faminc: Family income, in 1975 dollars.
mtr: Marginal tax rate facing the wife.
motheduc: Wife's mother's educational attainment, in years.
fatheduc: Wife's father's educational attainment, in years.
unem: Unemployment rate in county of residence, in percentage points.
city: Dummy variable = 1 if live in large city, else 0.
exper: Actual years of wife's previous labor market experience.
nwifeinc: Non-wife income.
wifecoll: Dummy variable for wife's college attendance.
huscoll: Dummy variable for husband's college attendance.
Mroz87Mroz87
An object of class data.frame with 753 rows and 22 columns.
PSID Staff, The Panel Study of Income Dynamics, Institute for Social ResearchPanel Study of Income Dynamics, University of Michigan, https://psidonline.isr.umich.edu/
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.
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.
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.
Jeffrey M Wooldridge (2016). Introductory econometrics: A modern approach. Nelson Education.
# Wooldridge(2016): page 247 data(Mroz87) attach(Mroz87) selectEq <- lfp ~ nwifeinc + educ + exper + I(exper^2) + age + kids5 + kids618 outcomeEq <- log(wage) ~ educ + exper + I(exper^2) outcomeS <- cbind(educ, exper) outcomeC <- cbind(educ, exper) outcomeBS <- wage ~ educ + exper + I(exper^2) outcomeBS <- wage ~ educ + exper + I(exper^2) HeckmanCL(selectEq, outcomeEq, data = Mroz87) HeckmanBS(selectEq, outcomeBS, data = Mroz87) HeckmanSK(selectEq, outcomeEq, data = Mroz87, lambda = 1) HeckmantS(selectEq, outcomeEq, data = Mroz87, df=5) HeckmanGe(selectEq, outcomeEq, outcomeS, outcomeC, data = Mroz87)# Wooldridge(2016): page 247 data(Mroz87) attach(Mroz87) selectEq <- lfp ~ nwifeinc + educ + exper + I(exper^2) + age + kids5 + kids618 outcomeEq <- log(wage) ~ educ + exper + I(exper^2) outcomeS <- cbind(educ, exper) outcomeC <- cbind(educ, exper) outcomeBS <- wage ~ educ + exper + I(exper^2) outcomeBS <- wage ~ educ + exper + I(exper^2) HeckmanCL(selectEq, outcomeEq, data = Mroz87) HeckmanBS(selectEq, outcomeBS, data = Mroz87) HeckmanSK(selectEq, outcomeEq, data = Mroz87, lambda = 1) HeckmantS(selectEq, outcomeEq, data = Mroz87, df=5) HeckmanGe(selectEq, outcomeEq, outcomeS, outcomeC, data = Mroz87)
The US National Health and Nutrition Examination Study (NHANES) is a survey data collected by the US National Center for Health Statistics. The survey data dates back to 1999, where individuals of all ages are interviewed in their home annually and complete the health examination component of the survey. The study variables include demographic variables (e.g. age and annual household income), physical measurements (e.g. BMI – body mass index), health variables (e.g. diabetes status), and lifestyle variables (e.g. smoking status). This data frame contains the following columns:
id: Individual identifier
age: Age
gender: Sex 1=male, 0=female
educ: Education is dichotomized into high school and above versus less than high school
race: categorical variable with five levels
income: Household income ($1000 per year) was reported as a range of values in dollar (e.g. 0–4999, 5000–9999, etc.) and had 10 interval categories.
Income: Household income ($1000 per year) was reported as a range of values in dollar (e.g. 0–4999, 5000–9999, etc.) and had 10 interval categories.
bmi: body mass index
sbp: systolic blood pressure
nhanesnhanes
An object of class data.frame with 9643 rows and 9 columns.
https://wwwn.cdc.gov/nchs/nhanes/ContinuousNhanes/Default.aspx?BeginYear=2003
Emmanuel O Ogundimu, Gary S Collins (2019). “A robust imputation method for missing responses and covariates in sample selection models.” Statistical methods in medical research, 28(1), 102–116.
Roderick J Little, Nanhua Zhang (2011). “Subsample ignorable likelihood for regression analysis with missing data.” Journal of the Royal Statistical Society: Series C (Applied Statistics), 60(4), 591–605.
Mikhail Zhelonkin, Marc G. Genton, Elvezio Ronchetti (2019). ssmrob: Robust Estimation and Inference in Sample Selection Models. R package version 0.7, https://CRAN.R-project.org/package=ssmrob.
Ott Toomet, Arne Henningsen (2008). “Sample Selection Models in R: Package sampleSelection.” Journal of Statistical Software, 27(7). https://www.jstatsoft.org/article/view/v027i07.
data("nhanes") attach(nhanes) hist(Income, prob= TRUE, breaks = seq(1, 99, 0.5), xlim = c(1,10), ylim = c(0,0.35), main = "Histogram of Income", xlab = "Category") data2 <- subset(nhanes, !is.na(sbp)) data3 <- subset(data2, !is.na(bmi)) attach(data3) data <- data3 data$YS <- ifelse(is.na(data$Income),0,1) data$educ <- ifelse(data$educ<=2,0,1) attach(data) selectionEq <- YS~age+gender+educ+race outcomeEq <- sbp~age+gender+educ+bmidata("nhanes") attach(nhanes) hist(Income, prob= TRUE, breaks = seq(1, 99, 0.5), xlim = c(1,10), ylim = c(0,0.35), main = "Histogram of Income", xlab = "Category") data2 <- subset(nhanes, !is.na(sbp)) data3 <- subset(data2, !is.na(bmi)) attach(data3) data <- data3 data$YS <- ifelse(is.na(data$Income),0,1) data$educ <- ifelse(data$educ<=2,0,1) attach(data) selectionEq <- YS~age+gender+educ+race outcomeEq <- sbp~age+gender+educ+bmi
The data come from the Panel Study of Income Dynamics, years 1981 to 1992 (also contains earnings data from 1980). The sample consists of 579 white females, who were followed over the considered period. In total, there are 6,948 observations over the 12-year period (1981-1992). This data frame contains the following columns:
id: Individual identifier
year: Survey year
age: Calculated age in years (based on year and month of birth)
educ: Years of schooling
children: Total number of children in family unit, ages 0-17
s: Participation dummy, =1 if worked (hours>0)
lnw: Log of real average hourly earnings
lnw80: Log earnings in 1980
agesq: Age squared
children_lag1: Number of children in t-1
children_lag2: Number of children in t-2
lnw2: Log of real average hourly earnings
Lnw: Log of real average hourly earnings
PSID2PSID2
An object of class data.frame with 6948 rows and 13 columns.
Anastasia Semykina, Jeffrey M Wooldridge (2013). “Estimation of dynamic panel data models with sample selection.” Journal of Applied Econometrics, 28(1), 47–61.
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.
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.
data(PSID2) attach(PSID2) hist(Lnw) selectEq <- s ~ educ+ age+ children+ year outcomeEq <- Lnw ~ educ+ age+ children HCinitial(selectEq,outcomeEq, data = PSID2) #Note that the estimated value of rho by the two-step #method is greater than 1 summary(HeckmanGe(selectEq,outcomeEq, 1, 1, data = PSID2))data(PSID2) attach(PSID2) hist(Lnw) selectEq <- s ~ educ+ age+ children+ year outcomeEq <- Lnw ~ educ+ age+ children HCinitial(selectEq,outcomeEq, data = PSID2) #Note that the estimated value of rho by the two-step #method is greater than 1 summary(HeckmanGe(selectEq,outcomeEq, 1, 1, data = PSID2))
'The RAND Health Insurance Experiment (RAND HIE) was a comprehensive study of health care cost, utilization and outcome in the United States. It is the only randomized study of health insurance, and the only study which can give definitive evidence as to the causal effects of different health insurance plans. For more information about the database visit: https://en.wikipedia.org/w/index.php?title=RAND_Health_Insurance_Experiment&oldid=110166949 accessed september 09, 2019). This data frame contains the following columns:
plan: HIE plan number.
site: Participant's place of residence when the participant was initially enrolled.
coins: Coinsurance rate.
tookphys: Took baseline physical.
year: Study year.
zper: Person identifier.
black: 1 if race of household head is black.
income: Family income.
xage: Age in years.
female: 1 if person is female.
educdec: Education of household head in years.
time: Time eligible during the year.
outpdol: Outpatient expenses: all covered outpatient medical services excluding dental care, outpatient psychotherapy, outpatient drugs or supplies.
drugdol: Drug expenses: all covered outpatient and dental drugs.
suppdol: Supply expenses: all covered outpatient supplies including dental.
mentdol: Psychotherapy expenses: all covered outpatient psychotherapy services including injections excluding charges for visits in excess of 52 per year, prescription drugs, and inpatient care.
inpdol: Inpatient expenses: all covered inpatient expenses in a hospital, mental hospital, or nursing home, excluding outpatient care and renal dialysis.
meddol: Medical expenses: all covered inpatient and outpatient services, including drugs, supplies, and inpatient costs of newborns excluding dental care and outpatient psychotherapy.
totadm: Hospital admissions: annual number of covered hospitalizations.
inpmis: Incomplete Hospital Records: missing inpatient records.
mentvis: Psychotherapy visits: indicates the annual number of outpatient visits for psychotherapy. It includes billed visits only. The limit was 52 covered visits per person per year. The count includes an initial visit to a psychiatrist or psychologist.
mdvis: Face-to-Face visits to physicians: annual covered outpatient visits with physician providers (excludes dental, psychotherapy, and radiology/anesthesiology/pathology-only visits).
notmdvis: Face-to-Face visits to nonphysicians: annual covered outpatient visits with nonphysician providers such as speech and physical therapists, chiropractors, podiatrists, acupuncturists, Christian Science etc. (excludes dental, healers, psychotherapy, and radiology/anesthesiology/pathology-only visits).
num: Family size.
mhi: Mental health index.
disea: Number of chronic diseases.
physlm: Physical limitations.
ghindx: General health index.
mdeoff: Maximum expenditure offer.
pioff: Participation incentive payment.
child: 1 if age is less than 18 years.
fchild: female * child.
lfam: log of num (family size).
lpi: log of pioff (participation incentive payment).
idp: 1 if individual deductible plan.
logc: log(coins+1).
fmde: 0 if idp=1,
ln(max(1,mdeoff/(0.01*coins))) otherwise.
hlthg: 1 if self-rated health is good – baseline is excellent self-rated health.
hlthf: 1 if self-rated health is fair – baseline is excellent self-rated health.
hlthp: 1 if self-rated health is poor – baseline is excellent self-rated health.
xghindx: ghindx (general healt index)
with imputations of missing values.
linc: log of income (family income).
lnum: log of num (family size).
lnmeddol: log of meddol (medical expenses).
binexp: 1 if meddol > 0.
RandHIERandHIE
An object of class data.frame with 20190 rows and 45 columns.
http://cameron.econ.ucdavis.edu/mmabook/mmadata.html
A Colin Cameron, Pravin K Trivedi (2005). Microeconometrics: methods and applications. Cambridge university press.
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.
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.
Wikipedia contributors (2019). “RAND Health Insurance Experiment — Wikipedia, The Free Encyclopedia.” https://en.wikipedia.org/w/index.php?title=RAND_Health_Insurance_Experiment&oldid=909771077. [Online; accessed 9-September-2019].
##Cameron and Trivedi (2005): Section 16.6 data(RandHIE) subsample <- RandHIE$year == 2 & !is.na( RandHIE$educdec ) selectEq <- binexp ~ logc + idp + lpi + fmde + physlm + disea + hlthg + hlthf + hlthp + linc + lfam + educdec + xage + female + child + fchild + black outcomeEq <- lnmeddol ~ logc + idp + lpi + fmde + physlm + disea + hlthg + hlthf + hlthp + linc + lfam + educdec + xage + female + child + fchild + black cameron <- HeckmanCL(selectEq, outcomeEq, data = RandHIE[subsample, ]) summary(cameron)##Cameron and Trivedi (2005): Section 16.6 data(RandHIE) subsample <- RandHIE$year == 2 & !is.na( RandHIE$educdec ) selectEq <- binexp ~ logc + idp + lpi + fmde + physlm + disea + hlthg + hlthf + hlthp + linc + lfam + educdec + xage + female + child + fchild + black outcomeEq <- lnmeddol ~ logc + idp + lpi + fmde + physlm + disea + hlthg + hlthf + hlthp + linc + lfam + educdec + xage + female + child + fchild + black cameron <- HeckmanCL(selectEq, outcomeEq, data = RandHIE[subsample, ]) summary(cameron)
Package that provides models to fit data with sample selection bias problems. Includes:
Heckman's classic model fit function. Sample selection usually arises in practice as a result of partial observability of the result of interest in a study. In the presence of sample selection, the observed data do not represent a random sample of the population, even after controlling for explanatory variables. That is, data is missing randomly. Thus, standard analysis using only complete cases will lead to biased results. Heckman introduced a sample selection model to analyze this data and proposed a complete likelihood estimation method under the assumption of normality. Such model was called Heckman model or Tobit 2 model.
Heckman-t model adjustment function. The Heckman-t model maintains the original parametric structure of the Classic Heckman model, but considers a bivariate Student's t distribution as the underlying joint distribution of the selection and primary regression variable and estimates the parameters by maximum likelihood.
Heckman-SK model adjustment function. The Heckman-sk model maintains the original parametric structure of the Classic Heckman model, but considers a bivariate Skew-Normal distribution as the underlying joint distribution of the selection and primary regression variable and estimates the parameters by maximum likelihood.
Heckman-BS model adjustment function. The Heckman-BS model maintains the original parametric structure of the Classic Heckman model, but considers a bivariate Birnbaum-Saunders distribution as the underlying joint distribution of the selection and primary regression variable and estimates the parameters by maximum likelihood.
Function for adjustment of Generalized Heckman model. The Generalized Heckman Model generalize the Classic Heckman model by adding covariables to the dispersion and correlation parameters, which allows to identify the covariates responsible for the presence of selection bias and the presence of heteroscedasticity.
selection |
Selection equation. |
outcome |
Primary Regression Equation. |
outcomeS |
Matrix with Covariables for fit of the Dispersion Parameter. |
outcomeC |
Matrix with Covariates for Adjusting the Correlation Parameter. |
df |
Initial value to the degree of freedom of Heckman-t model. |
lambda |
Initial value for asymmetry parameter. |
start |
initial values. |
data |
Database. |
Applying any package function returns a list of results that include estimates of the fit model parameters, hessian matrix, number of observations, and more. If the initial value is not included in the function argument, an initial value is estimated from the Heckman two-step method setting.
Fernando de Souza Bastos, Wagner Barreto de Souza
Estimate model parameters via two-step method
step2(YS, XS, YO, XO)step2(YS, XS, YO, XO)
YS |
Selection vector. |
XS |
Selection Matrix. |
YO |
Interest vector. |
XO |
Matrix of the equation of interest. |
Returns a numerical vector with the parameter estimates of the Classical Heckman model via a two-step method. For more information see Heckman (1979)
James J Heckman (1979). “Sample selection bias as a specification error.” Econometrica: Journal of the econometric society, 153–161.
data(MEPS2001) attach(MEPS2001) YS <- dambexp XS <- cbind(age, female, educ, blhisp, totchr, ins) YO <- lnambx XO <- cbind(age, female, educ, blhisp, totchr, ins, income) step2(YS, XS, YO, XO)data(MEPS2001) attach(MEPS2001) YS <- dambexp XS <- cbind(age, female, educ, blhisp, totchr, ins) YO <- lnambx XO <- cbind(age, female, educ, blhisp, totchr, ins, income) step2(YS, XS, YO, XO)
Summary of Birnbaum-Saunders Heckman Model
## S3 method for class 'HeckmanBS' summary(object, ...)## S3 method for class 'HeckmanBS' summary(object, ...)
object |
HeckmanBS class object. |
... |
others functions. |
Print estimates of the parameters of the Heckman-BS model
Summary of Classic Heckman Model
## S3 method for class 'HeckmanCL' summary(object, ...)## S3 method for class 'HeckmanCL' summary(object, ...)
object |
HeckmanCL class object. |
... |
others functions. |
Print estimates of the parameters of the Classic Heckman model
Summary of Generalized Heckman Model
## S3 method for class 'HeckmanGe' summary(object, ...)## S3 method for class 'HeckmanGe' summary(object, ...)
object |
HeckmanGe class object. |
... |
others functions. |
Print estimates of the parameters of the Generalized Heckman model
Summary of Skew-Normal Heckman Model
## S3 method for class 'HeckmanSK' summary(object, ...)## S3 method for class 'HeckmanSK' summary(object, ...)
object |
HeckmanSK class object. |
... |
others functions. |
Print estimates of the parameters of the Heckman-SK model
Summary of Heckman-ts Model
## S3 method for class 'HeckmantS' summary(object, ...)## S3 method for class 'HeckmantS' summary(object, ...)
object |
HeckmantS class object. |
... |
others functions. |
Print estimates of the parameters of the Heckman-ts model
Estimate model parameters via two-step method
twostep(selection, outcome, data = sys.frame(sys.parent()))twostep(selection, outcome, data = sys.frame(sys.parent()))
selection |
Selection equation. |
outcome |
Primary Regression Equation. |
data |
Database. |
Returns a numerical vector with the parameter estimates of the Classical Heckman model via a two-step method. For more information see Heckman (1979)
James J Heckman (1979). “Sample selection bias as a specification error.” Econometrica: Journal of the econometric society, 153–161.
data(MEPS2001) attach(MEPS2001) selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income outcomeEq <- lnambx ~ age + female + educ + blhisp + totchr + ins twostep(selectEq, outcomeEq)data(MEPS2001) attach(MEPS2001) selectEq <- dambexp ~ age + female + educ + blhisp + totchr + ins + income outcomeEq <- lnambx ~ age + female + educ + blhisp + totchr + ins twostep(selectEq, outcomeEq)