qrnn (version 2.0.5)

composite.stack: Reformat data matrices for composite quantile regression

Description

Returns stacked x and y matrices and tau vector, which can be passed to qrnn.fit to fit composite quantile regression and composite QRNN models (Zou et al., 2008; Xu et al., 2017). In combination with the partial monotonicity constraints, stacking can be used to fit multiple non-crossing quantile functions (see mcqrnn). More details are provided in Cannon (2018).

Usage

composite.stack(x, y, tau)

Arguments

x

covariate matrix with number of rows equal to the number of samples and number of columns equal to the number of variables.

y

response column matrix with number of rows equal to the number of samples.

tau

vector of tau-quantiles.

References

Cannon, A.J., 2018. Non-crossing nonlinear regression quantiles by monotone composite quantile regression neural network, with application to rainfall extremes. Stochastic Environmental Research and Risk Assessment, 32(11): 3207-3225. doi:10.1007/s00477-018-1573-6

Xu, Q., K. Deng, C. Jiang, F. Sun, and X. Huang, 2017. Composite quantile regression neural network with applications. Expert Systems with Applications, 76, 129-139.

Zou, H. and M. Yuan, 2008. Composite quantile regression and the oracle model selection theory. The Annals of Statistics, 1108-1126.

See Also

qrnn.fit, mcqrnn

Examples

x <- as.matrix(iris[,"Petal.Length",drop=FALSE])
y <- as.matrix(iris[,"Petal.Width",drop=FALSE])

cases <- order(x)
x <- x[cases,,drop=FALSE]
y <- y[cases,,drop=FALSE]

tau <- seq(0.05, 0.95, by=0.05)
x.y.tau <- composite.stack(x, y, tau)
binary.tau <- dummy.code(as.factor(x.y.tau$tau))

set.seed(1)

# Composite QR
fit.cqr <- qrnn.fit(cbind(binary.tau, x.y.tau$x), x.y.tau$y,
                    tau=x.y.tau$tau, n.hidden=1, n.trials=1,
                    Th=linear, Th.prime=linear.prime)
pred.cqr <- matrix(qrnn.predict(cbind(binary.tau, x.y.tau$x), fit.cqr),
                   ncol=length(tau))
coef.cqr <- lm.fit(cbind(1, x), pred.cqr)$coef
colnames(coef.cqr) <- tau
print(coef.cqr)

# Composite QRNN
fit.cqrnn <- qrnn.fit(x.y.tau$x, x.y.tau$y, tau=x.y.tau$tau,
                      n.hidden=1, n.trials=1, Th=sigmoid,
                      Th.prime=sigmoid.prime)
pred.cqrnn <- qrnn.predict(x.y.tau$x, fit.cqrnn)
pred.cqrnn <- matrix(pred.cqrnn, ncol=length(tau), byrow=FALSE)

matplot(x, pred.cqrnn, col="red", type="l")
points(x, y, pch=20)