predict.piqr: Prediction After Penalized Quantile Regression Coefficients...
In gianluca-sottile/qrcmPen: Penalized Quantile Regression Coefficients Modeling

Description Usage Arguments Details Value Note Author(s) See Also Examples

Predictions from an object of class “piqr”, after selecting the best tuning parameter.

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## S3 method for class 'piqr'
predict(object, lambda, type=c("beta", "CDF", "QF", "sim"), newdata,
                       p, se=TRUE, ...)

`object`	an object of class “`piqr`”, the result of a call to `piqr`.
`lambda`	a value of lambda in the sequence of the object of class “`piqr`”. Could be the best after selecting the result of a call to `gof.piqr`
`type`	a character string specifying the type of prediction. See ‘Details’.
`newdata`	an optional data frame in which to look for variables with which to predict. If omitted, the data are used. For `type = "CDF"`, it must include the response variable. Ignored if `type = "beta"`.
`p`	a numeric vector indicating the order(s) of the quantile to predict. Only used if `type = "beta"` or `type = "QF"`.
`se`	logical. If TRUE (the default), standard errors of the prediction will be computed. Only used if type = "beta" or type = "QF".
`...`	for future methods.

If the best lambda or one value of lambda is chosen, the function call predict.iqr.

See details in predict.iqr

Prediction may generate quantile crossing if the support of the new covariates values supplied in newdata is different from that of the observed data.

Gianluca Sottile gianluca.sottile@unipa.it

piqr, for model fitting; gof.piqr, to find the best lambda value; summary.piqr and plot.piqr, for summarizing and plotting piqr objects.

# using simulated data

set.seed(1234)
n <- 1000
x1 <- rexp(n)
x2 <- runif(n, 0, 5)
x <- cbind(x1,x2)

b <- function(p){matrix(cbind(1, qnorm(p), slp(p, 2)), nrow=4, byrow=TRUE)}
theta <- matrix(0, nrow=3, ncol=4); theta[, 1] <- 1; theta[1,2] <- 1; theta[2:3,3] <- 2
qy <- function(p, theta, b, x){rowSums(x * t(theta %*% b(p)))}

y <- qy(runif(n), theta, b, cbind(1, x))

s <- matrix(1, nrow=3, ncol=4); s[1,3:4] <- 0
obj <- piqr(y ~ x1 + x2, formula.p = ~ I(qnorm(p)) + slp(p, 2), s=s)

best <- gof.piqr(obj, method="AIC", plot=FALSE)

# predict beta(0.25), beta(0.5), beta(0.75)
predict(obj, best$minLambda, type = "beta", p = c(0.25,0.5, 0.75))

# predict the CDF and the PDF at new values of x and y
predict(obj, best$minLambda, type = "CDF",
        newdata = data.frame(x1=rexp(3), x2=runif(3), y = c(1,2,3)))

# computes the quantile function at new x, for p = (0.25,0.5,0.75)
predict(obj, best$minLambda, type = "QF", p = c(0.25,0.5,0.75),
        newdata = data.frame(x1=rexp(3), x2=runif(3), y = c(1,2,3)))

# simulate data from the fitted model
ysim <- predict(obj, best$minLambda, type = "sim") # 'newdata' can be supplied

# if the model is correct, the distribution of y and that of ysim should be similar
qy <- quantile(y, prob = seq(.1,.9,.1))
qsim <- quantile(ysim, prob = seq(.1,.9,.1))
plot(qy, qsim); abline(0,1)