QRStepwise: Stepwise procedure

In QRegVCM: Quantile Regression in Varying-Coefficient Models

Description

The etimation of conditional quantile curves step-by-step involving the non-crossing constraints.

Usage

QRStepwise(VecX, tau, times, subj, X, y, d, kn, degree, lambda, gam)

Arguments

VecX	The representative values for each covariate used to estimate the desired conditional quantile curves.
tau	The quantiles of interest.
times	The vector of the time variable.
subj	The vector of subjects/individuals.
X	The covariate matrix containing 1 as its first column (including intercept in the model).
y	The response vector.
d	The order of the differencing operator for each covariate.
kn	The number of knots for each covariate.
degree	The degree of the B-spline basis function for each covariate.
lambda	The grid for the smoothing parameter to control the trade of between fidelity and penalty term (use a fine grid of lambda).
gam	The power used in estimating the smooting parameter for each covariate (e.g. gam=1 or gam=0.5).

Value

alpha	The estimators of the coefficient vector of the basis B-splines.
hat_bt	The varying-coefficient estimators.
W	The weight for each subject corresponding to the length of its repeated measurement
qhat	The conditional quantile curves estimator.

Note

Some warning messages are related to the function rq.fit.sfn.

Author(s)

Yudhie Andriyana

References

Andriyana, Y., Gijbels, I., and Verhasselt, A. P-splines quantile regression estimation in varying coefficient models. Test 23, 1 (2014a),153–194.

Andriyana, Y., Gijbels, I. and Verhasselt, A. (2014b). Quantile regression in varying coefficient models: non-crossingness and heteroscedasticity. Manuscript.

Wu, Y. and Liu, Y. Stepwise multiple quantile regression estimation using non-crossing constraints. Statistics and Its Interface 2, (2009), 299–310.

See Also

rq.fit.sfn as.matrix.csr truncSP

Examples

data(PM10)

PM10 = PM10[order(PM10$day,PM10$hour,decreasing=FALSE),]

y = PM10$PM10[1:200]
time_ub = PM10$hour[1:200]
subj = PM10$day[1:200]
dim = length(y)
x0 = rep(1,200)
x1 = PM10$cars[1:200]
x2 = PM10$wind.speed[1:200]

X = cbind(x0, x1, x2)

VecX = c(1, max(x1), max(x2))

##########################
#### Input parameters ####
##########################
kn = c(10, 10, 10)
degree = c(3, 3, 3)
taus = seq(0.1,0.9,0.1)
lambdas = c(1,1.5,2)
d = c(1, 1, 1)
gam = 1
##########################


Step = QRStepwise(VecX=VecX, tau=taus, time_ub, subj, X, y, d, kn, degree,
       lambda=lambdas, gam=gam)

qhat = Step$qhat

qhat1 = qhat[,1]
qhat2 = qhat[,2]
qhat3 = qhat[,3]
qhat4 = qhat[,4]
qhat5 = qhat[,5]
qhat6 = qhat[,6]
qhat7 = qhat[,7]
qhat8 = qhat[,8]
qhat9 = qhat[,9]


i = order(time_ub, y, qhat1, qhat2, qhat3, qhat4, qhat5, qhat6, qhat7,
    qhat8, qhat9);

time_ub = time_ub[i]; y = y[i]; qhat1 = qhat1[i]; qhat2=qhat2[i];
qhat3=qhat3[i]; qhat4=qhat4[i]; qhat5=qhat5[i]; qhat6=qhat6[i];
qhat7=qhat7[i]; qhat8=qhat8[i]; qhat9=qhat9[i];

ylim = range(qhat1, qhat9)
ylim = c(-4, 6)
plot(qhat1~time_ub, col="magenta", cex=0.2, lty=5, lwd=2, type="l", ylim=ylim,
    xlab="hour", ylab="PM10");
lines(qhat2~time_ub, col="aquamarine4", cex=0.2, lty=4, lwd=2);
lines(qhat3~time_ub, col="blue", cex=0.2, lty=3, lwd=3);
lines(qhat4~time_ub, col="brown", cex=0.2, lty=2, lwd=2);
lines(qhat5~time_ub, col="black", cex=0.2, lty=1, lwd=2);
lines(qhat6~time_ub, col="orange", cex=0.2, lty=2, lwd=2)
lines(qhat7~time_ub, col="darkcyan", cex=0.2, lty=3, lwd=3);
lines(qhat8~time_ub, col="green", cex=0.2, lty=4, lwd=2);
lines(qhat9~time_ub, col="red", cex=0.2, lty=5, lwd=3)

legend("bottom", c(expression(tau==0.9), expression(tau==0.8),
    expression(tau==0.7), expression(tau==0.6), expression(tau==0.5),
    expression(tau==0.4), expression(tau==0.3), expression(tau==0.2),
    expression(tau==0.1)), ncol=1, col=c("red","green","darkcyan",
    "orange","black","brown","blue","aquamarine4","magenta"),
    lwd=c(2,2,3,2,2,2,3,2,2), lty=c(5,4,3,2,1,2,3,4,5))

QRegVCM documentation built on May 1, 2019, 9:11 p.m.