cgam (version 1.8)

predict.cgam: Predict Method for CGAM Fits

Description

Predicted values based on a cgam object

Usage

# S3 method for cgam
predict(object, newData, interval = c("none", "confidence"), level = 0.95,...)

Arguments

object

A cgam object.

newData

A data frame in which to look for variables with which to predict. If omitted, the fitted values are used.

interval

Type of interval calculation.

level

Tolerance/confidence level.

…

Further arguments passed to the routine.

Value

fit

A vector of predictions.

lower

A vector of lower bound if interval is set to be "confidence".

upper

A vector of upper bound if interval is set to be "confidence".

Details

Constrained spline estimators can be characterized by projections onto a polyhedral convex cone. Point-wise confidence intervals for constrained splines are constructed by estimating the probabilities that the projection lands on each of the faces of the cone, and using a mixture of covariance matrices to estimate the standard error of the function estimator at any design point.

Note that currently predict.cgam only works when all components in a cgam formula are additive.

See references cited in this section for more details.

References

Meyer, M. C. (2008) Inference using shape-restricted regression splines. Annals of Applied Statistics 2(3), 1013--1033.

Meyer, M. C. (2012) Constrained penalized splines. Canadian Journal of Statistics 40(1), 190--206.

Meyer, M. C. (2017) Constrained partial linear regression splines. Statistical Sinica in press.

Meyer, M. C. (2017) Confidence intervals for regression functions using constrained splines with application to estimation of tree height

Examples

# NOT RUN {
	# generate data
	n <- 100
	set.seed(123)
	x <- runif(n)
	y <- 4*x^3 + rnorm(n)

	# regress y on x under the shape-restriction: "increasing-convex"
	fit <- cgam(y ~ s.incr.conv(x))
	
	# make a data frame 
	x0 <- seq(min(x), max(x), by = 0.05)
	new.Data <- data.frame(x = x0)

	# predict values in new.Data based on the cgam fit without a confidence interval
	pfit <- predict(fit, new.Data)
	
	# or 
	pfit <- predict(fit, new.Data, interval = "none")
	
	# make a plot to check the prediction
	plot(x, y, main = "Predict Method for CGAM")
	lines(sort(x), (fitted(fit)[order(x)]))
	points(x0, pfit$fit, col = 2, pch = 20)

	# predict values in new.Data based on the cgam fit with a confidence interval
	pfit <- predict(fit, new.Data, interval = "confidence")

	# make a plot to check the prediction
	plot(x, y, main = "Predict Method for CGAM with Confidence Bands")
	lines(sort(x), (fitted(fit)[order(x)]))
	lines(sort(x0), (pfit$lower)[order(x0)], col = 2, lty = 2)
	lines(sort(x0), (pfit$upper)[order(x0)], col = 2, lty = 2)
	points(x0, pfit$fit, col = 2, pch = 20)
# }