qrs.fast.bt {fastqrs} | R Documentation |
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)