MultiKink (version 0.2.0)

mkqr.fit: Fit the multi-kink quantile regression conditional on a given or pre-specified number of change points.

Description

Fit the multi-kink quantile regression conditional on a given or pre-specified number of change points.

Usage

mkqr.fit(
  y,
  thre.x,
  cont.z,
  id,
  tau = 0.5,
  k,
  psi = NULL,
  bandwidth_type = "Hall-Sheather",
  control = fit.control(),
  est.type = "WI",
  wi.type = "general",
  wc.type = "cs"
)

Value

A list containing the estimated regression coefficients with intercept (bet.est), the estimated standard error of the regression coefficients (bet.se), the estimated change points (psi.est), the estimated standard errors of threshold parameters (psi.se), and the fitted quantile objective value (rho).

Arguments

y

A numeric vector of response.

thre.x

A numeric vector of scalar covariate with threshold effect.

cont.z

A numeric matrix of design with constant slopes.

id

A numeric vector of index used for longitudinal data; can be missing or NULL for iid data.

tau

The quantile level that belongs to (0,1).

k

The pre-specified number of change points.

psi

Numeric vector to indicate the starting values for the change points. When psi=NULL (default), k quantiles are assumed.

bandwidth_type

The bandwidth type. Specify one from "Hall-Sheather", "Bofinger", and "Chamberlain". Default is "Hall-Sheather".

control

A list returned by fit.control.

est.type

The estimation type for the longitudinal data. Specify one from "WI", "WC", corresponding to the working independence (WI) estimator and working correlation (WC) estimator. Default is "WI".

wi.type

If est.type = "WI", then set the error structure of the variance-covariance matrix estimation. Specify one from "Compound", "AR" and "general".

wc.type

If est.type = "WC", then set the correlation structure within subject. Specify one from "ar" and "cs". Default is "cs".

Examples

if (FALSE) {
# Simple examples for iid data type
n <- 500
Z1 <- rexp(n, 1)
Z2 <- rbinom(n, 1, 0.5)
Z <- cbind(Z1, Z2)
epsilon <- rnorm(n, 0, 1)
X <- runif(n, -2, 1)
psi <- c(-1, 0)
k <- length(psi)
Y <- XR %*% bet + epsilon
result_iid <- mkqr.fit(Y, X, Z, tau = 0.5, k = k)

# Simple examples for longitudinal data
N <- 200
T <- 5
subject <- rep(1:N, each = T)
NT <- N * T
Z1 <- rexp(NT, 1)
Z2 <- rbinom(NT, 1, 0.5)
Z <- cbind(Z1, Z2)
epsilon <- rnorm(NT, 0, 1)
X <- runif(NT, -2, 1)
psi <- c(-1, 0)
k <- length(psi)
PSI <- matrix(rep(psi, rep(NT, k)), ncol = k)
a <- rnorm(N, 0, 1)
A <- rep(a, each = T)
XP <- matrix(rep(X, k), nrow = NT)
XR <- cbind(1, X, pmax((XP - PSI), 0), Z)
bet <- c(1, -1, 3, -3, sqrt(3), -sqrt(3))
Y <- XR %*% bet + A + epsilon
tau = 0.5
k = 2

# Example 1: the working independence estimator; the error structure is "general"
est.type = "WI";
wi.type = "Compound"
result_WI_Compound <- mkqr.fit(y = Y, thre.x = X, cont.z = Z, id = subject, tau = tau,
                               k = k, est.type = est.type, wi.type = wi.type)

# Example 2: the working correlated estimator; the correlation structure is "cs"
est.type = "WC";
wc.type = "cs"
result_WC_cs <- mkqr.fit(y = Y, thre.x = X, cont.z = Z, id = subject, tau = tau,
                         k = k, est.type = est.type, wc.type = wc.type)

}