# Predict Method for CGAM Fits Predicted values based on a cgam object ```r ## S3 method for class 'cgam' predict(object, newdata, interval = c("none", "confidence", "prediction"), type = c("response", "link"), level = 0.95, n.mix = 500,...) ``` ## 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. A prediction interval is only implemented for Gaussian response for now. - `type`: If the response is Gaussian, type = "response" gives the predicted mean; if the response is binomial, type = "response" gives the predicted probabilities, and type = "link" gives the predicted systematic component. - `level`: Tolerance/confidence level. - `n.mix`: Number of simulations to get the mixture distribution. The default is n.mix = 500. - ``...``: Further arguments passed to the routine. ## 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. ## Returns - **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". ## References 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 Meyer, M. C. (2012) Constrained penalized splines. **Canadian Journal of Statistics 40(1)**, 190--206. Meyer, M. C. (2008) Inference using shape-restricted regression splines. **Annals of Applied Statistics 2(3)**, 1013--1033. ## Author(s) Mary C. Meyer and Xiyue Liao ## Examples ```r # Example 1. # 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) # predict values in new.Data based on the cgam fit without a confidence interval pfit <- predict(fit, newdata = data.frame(x = x0)) # 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$fit, col = 2, pch = 20) # predict values in newdata based on the cgam fit with a 95 percent confidence interval pfit <- predict(fit, newdata = data.frame(x = x0), interval = "confidence", level = 0.95) # make a plot to check the prediction plot(x, y, main = "Pointwise Confidence Bands (Gaussian Response)") lines(sort(x), (fitted(fit)[order(x)])) lines(sort(x0), (pfit$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) # Example 2. binomial response n <- 200 x <- seq(0, 1, length = n) eta <- 4*x^2 - 2 mu <- exp(eta)/(1+exp(eta)) set.seed(123) y <- 1:n*0 y[runif(n)

predict.cgam function