| Title: | Fast Algorithms for Quantile Regression with Selection |
| Version: | 1.0.0 |
| Description: | Fast estimation algorithms to implement the Quantile Regression with Selection estimator and the multiplicative Bootstrap for inference. This estimator can be used to estimate models that feature sample selection and heterogeneous effects in cross-sectional data. For more details, see Arellano and Bonhomme (2017) <doi:10.3982/ECTA14030> and Pereda-Fernández (2024) <doi:10.48550/arXiv.2402.16693>. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2 |
| Imports: | quantreg, copula, stats |
| Suggests: | knitr, rmarkdown, sampleSelection, ggplot2 |
| Depends: | R (≥ 2.10) |
| LazyData: | true |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2025-04-14 05:48:35 UTC; santi |
| Author: | Santiago Pereda-Fernandez
 [aut, cre] |
| Maintainer: | Santiago Pereda-Fernandez <santiagopereda@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2025-04-16 20:10:02 UTC |
bt.results
Description
Collects the bootstrap results and yields the bootstrapped mean, standard error, and confidence intervals
Usage
.bt.results(x, alpha)
Arguments
x |
= Vector with the bootstrap repetitions of an estimator |
alpha |
= Set of significance levels to be returned |
Value
m = Bootstrapped mean
se = Bootstrapped standard error
ub = Upper bound of the bootstrapped confidence interval
lb = Lower bound of the bootstrapped confidence interval
qrs.prop.fast
Description
Algorithm 3: algorithm with preprocessing and quantile grid reduction for Quantile Regression with Selection (QRS); propensity score estimated previously.
Usage
.qrs.prop.fast(y, x, prop, w = NULL, Q1, Q2, P = 10, family, gridtheta, m)
Arguments
y |
= Dependent variable (N x 1) |
x |
= Regressors matrix (N x K) |
prop |
= Propensity score (N x 1) |
w |
= Sample weights (N x 1) |
Q1 |
= Number of quantiles in reduced grid |
Q2 |
= Number of quantiles in large grid |
P |
= Number of evaluated values of parameter with large quantile grid |
family |
= Parametric copula family |
gridtheta |
= Grid of values for copula parameter (T x 1) |
m |
= Parameter to select interval of observations in top and bottom groups |
Value
beta = Estimated beta coefficients (K x Q2)
theta = Estimated copula parameter
objf_min = Value of objective function at the optimum
b1 = Estimated beta coefficients for the grid of values of the copula parameter with the reduced quantile grid (K x Q1 x T)
objf1 = Value of objective function for the grid of values of the copula parameter with the reduced quantile grid
gridtheta2 = Grid of values for copula parameter selected during the first part of the algorithm (P x 1)
b2 = Estimated beta coefficients for the grid of values of the copula parameter with large quantile grid (K x Q2 x P)
objf2 = Value of objective function for the grid of values of the copula parameter with large quantile grid (P x 1)
rqr.fast
Description
Algorithm 2: algorithm with preprocessing for Rotated Quantile Regression (RQR) for a grid of quantiles and the rotation obtained with a copula.
Usage
.rqr.fast(y, x, w = NULL, G, zeta, m, initq)
Arguments
y |
= Dependent variable (N x 1) |
x |
= Regressors matrix (N x K) |
w |
= Sample weights (N x 1) |
G |
= Copula conditional on participation (N x Q) |
zeta |
= Conservative estimate of standard error of residuals (N x 1) |
m |
= Parameter to select interval of observations in top and bottom groups |
initq |
= Initial quantile to estimate regularly and obtain preliminary values for remaining quantiles |
Value
b = Estimated beta coefficients (K x Q)
rqrb0.fast
Description
Algorithm with preprocessing for Rotated Quantile Regression (RQR) for a grid of quantiles, the rotation obtained with a copula and initial values of the beta coefficients (used by Algorithms 3-4).
Usage
.rqrb0.fast(y, x, w = NULL, G, zeta, m, b0)
Arguments
y |
= Dependent variable (N x 1) |
x |
= Regressors matrix (N x K) |
w |
= Sample weights |
G |
= Copula conditional on participation (N x Q) |
zeta |
= Conservative estimate of standard error of residuals |
m |
= Parameter to select interval of observations in top and bottom groups |
b0 |
= Initial values of the beta coefficients for all quantiles (K x Q) |
Value
b = Estimated beta coefficients (K x Q)
rqrtau.fast
Description
Algorithm 1: algorithm with preprocessing for Rotated Quantile Regression (RQR) with initial values of the beta coefficients for a single quantile tau
Usage
.rqrtau.fast(y, x, w = NULL, tau, zeta, m, b0)
Arguments
y |
= Dependent variable (N x 1) |
x |
= Regressors matrix (N x K) |
w |
= Sample weights (N x 1) |
tau |
= Quantile indexes rotated at individual level (N x 1) |
zeta |
= Conservative estimate of standard error of residuals (N x 1) |
m |
= Parameter to select interval of observations in top and bottom groups |
b0 |
= Initial values of the beta coefficients (K x 1) |
Value
b = Estimated beta coefficients (K x 1)
Mroz87: U.S. Women's Labor Force Participation (Example dataset)
Description
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), Appendix 1.
Usage
Mroz87
Format
A data frame with 753 observations on the following 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.
Source
Mroz, T. A. (1987) "The sensitivity of an empirical model of married women's hours of work to economic and statistical assumptions." Econometrica 55, 765–799. PSID Staff, The Panel Study of Income Dynamics, Institute for Social ResearchPanel Study of Income Dynamics, University of Michigan, (For more information, visit the PSID website.).
qrs.fast
Description
Estimation of Quantile Regression with Selection (QRS) using Algorithm 3 for the estimation of the quantile and copula coefficients.
Usage
qrs.fast(y, x, d, z, w = NULL, Q1, Q2, P = 10, link, family, gridtheta, m = 1)
Arguments
y |
= Dependent variable (N x 1) |
x |
= Regressors matrix (N x K) |
d |
= Participation variable (N x 1) |
z |
= Regressors and instruments matrix for the propensity score (N x Kz) |
w |
= Sample weights (N x 1) |
Q1 |
= Number of quantiles in reduced grid |
Q2 |
= Number of quantiles in large grid |
P |
= Number of evaluated values of parameter with large quantile grid |
link |
= Link function to compute the propensity score |
family |
= Parametric copula family |
gridtheta |
= Grid of values for copula parameter (T x 1) |
m |
= Parameter to select interval of observations in top and bottom groups |
Value
gamma = Estimated gamma coefficients (Kz x 1)
beta = Estimated beta coefficients (K x Q2)
theta = Estimated copula parameter
objf = Value of objective function at the optimum
b1 = Estimated beta coefficients for the grid of values of the copula parameter with the reduced quantile grid (K x Q1 x T)
Examples
set.seed(1)
N <- 100
x <- cbind(1, 2 + runif(N))
z <- cbind(x, runif(N))
cop <- copula::normalCopula(param = -0.5, dim = 2)
copu <- copula::rCopula(N, cop)
v <- copu[,1]
u <- copu[,2]
gamma <- c(-1.5, 0.05, 2)
beta <- cbind(qnorm(u), u^0.5)
prop <- exp(z %*% gamma) / (1 + exp(z %*% gamma))
d <- as.numeric(v <= prop)
y <- d * rowSums(x * beta)
w <- matrix(1, nrow = N, ncol = 1)
Q1 <- 9
Q2 <- 19
P <- 2
m <- 1
gridtheta <- seq(from = -1, to = 0, by = .1)
link <- "probit"
family <- "Gaussian"
result <- qrs.fast(y, x[,-1], d, z[,-1], w, Q1, Q2, P, link, family, gridtheta, m)
summary(result)
qrs.fast.bt
Description
Algorithm 4: bootstrap algorithm with preprocessing and quantile grid reduction for Quantile Regression with Selection (QRS).
Usage
qrs.fast.bt(
y,
x,
d,
z,
w0 = NULL,
Q1,
Q2,
P = 10,
link,
family,
gridtheta,
m,
b0,
reps,
alpha
)
Arguments
y |
= Dependent variable (N x 1) |
x |
= Regressors matrix (N x K) |
d |
= Participation variable (N x 1) |
z |
= Regressors and instruments matrix for the propensity score (N x Kz) |
w0 |
= Sample weights (N x 1) |
Q1 |
= Number of quantiles in reduced grid |
Q2 |
= Number of quantiles in large grid |
P |
= Number of evaluated values of parameter with large quantile grid |
link |
= Link function to compute the propensity score |
family |
= Parametric copula family |
gridtheta |
= Grid of values for copula parameter (T x 1) |
m |
= Parameter to select interval of observations in top and bottom groups |
b0 |
= Initial values of the beta coefficients for all quantiles in the reduced quantile grid (K x Q1) |
reps |
= Number of bootstrap repetitions |
alpha |
= Significance level |
Value
gammase = Bootstrapped standard error of gamma coefficients (Kz x 1)
gammaub = Bootstrapped upper bound of confidence interval of gamma coefficients (Kz x 1)
gammalb = Bootstrapped lower bound of confidence interval of gamma coefficients (Kz x 1)
betase = Bootstrapped standard error of beta coefficients (K x Q)
betaub = Bootstrapped upper bound of confidence interval of beta coefficients (K x Q)
betalb = Bootstrapped lower bound of confidence interval of beta coefficients (K x Q)
thetase = Bootstrapped standard error of theta coefficients (1 x 1)
thetaub = Bootstrapped upper bound of confidence interval of theta coefficients (1 x 1)
thetalb = Bootstrapped lower bound of confidence interval of theta coefficients (1 x 1)
gamma = Bootstrapped estimated theta coefficients (Kz x reps)
beta = Bootstrapped estimated beta coefficients (K x Q2 x reps)
theta = Bootstrapped estimated copula parameter (1 x reps)
objf = Bootstrapped value of objective function at the optimum (1 x reps)
Examples
set.seed(1)
N <- 100
x <- cbind(1, 2 + runif(N))
z <- cbind(x, runif(N))
cop <- copula::normalCopula(param = -0.5, dim = 2)
copu <- copula::rCopula(N, cop)
v <- copu[,1]
u <- copu[,2]
gamma <- c(-1.5, 0.05, 2)
beta <- cbind(qnorm(u), u^0.5)
prop <- exp(z %*% gamma) / (1 + exp(z %*% gamma))
d <- as.numeric(v <= prop)
y <- d * rowSums(x * beta)
w <- matrix(1, nrow = N, ncol = 1)
Q1 <- 9
Q2 <- 19
P <- 2
m <- 1
gridtheta <- seq(-1, 0, by = 0.1)
link <- "probit"
family <- "Gaussian"
reps <- 10
alpha <- 0.05
est <- qrs.fast(y, x[,-1], d, z[,-1], w, Q1, Q2, P, link, family, gridtheta, m)
bt <- qrs.fast.bt(y, x[,-1], d, z[,-1], w, Q1, Q2, P, link, family,
gridtheta, m, est$b1, reps, alpha)
summary(bt)