GeDS (version 0.2.8)

predict.GeDSboost,gam: Predict method for GeDSboost, GeDSgam

Description

This method computes predictions from GeDSboost and GeDSgam objects. It is designed to be user-friendly and accommodate different orders of the GeDSboost or GeDSgam fits.

Usage

# S3 method for GeDSboost
predict(object, newdata, n = 3L, base_learner = NULL, ...)
# S3 method for GeDSgam
predict(object, newdata, n = 3L, base_learner = NULL, ...)

Value

Numeric vector of predictions (vector of means).

Arguments

object

the GeDSboost-class or GeDSgam-class object.

newdata

an optional data frame for prediction.

n

the order of the GeDS fit (2L for linear, 3L for quadratic, and 4L for cubic). Default is 3L.

base_learner

either NULL or a character string specifying the base-learner of the model for which predictions should be computed. Note that single base-learner predictions are provided on the linear predictor scale.

...

potentially further arguments.

References

Gu, C. and Wahba, G. (1991). Minimizing GCV/GML Scores with Multiple Smoothing Parameters via the Newton Method. SIAM J. Sci. Comput., 12, 383--398.

Examples

## Gu and Wahba 4 univariate term example ##
# Generate a data sample for the response variable
# y and the covariates x0, x1 and x2; include a noise predictor x3
set.seed(123)
N <- 400
f_x0x1x2 <- function(x0,x1,x2) {
  f0 <- function(x0) 2 * sin(pi * x0)
  f1 <- function(x1) exp(2 * x1)
  f2 <- function(x2) 0.2 * x2^11 * (10 * (1 - x2))^6 + 10 * (10 * x2)^3 * (1 - x2)^10
  f <- f0(x0) + f1(x1) + f2(x2)
  return(f)
}
x0 <- runif(N, 0, 1)
x1 <- runif(N, 0, 1)
x2 <- runif(N, 0, 1)
x3 <- runif(N, 0, 1)
# Specify a model for the mean of y
f <- f_x0x1x2(x0 = x0, x1 = x1, x2 = x2)
# Add (Normal) noise to the mean of y
y <- rnorm(N, mean = f, sd = 0.2)
data <- data.frame(y = y, x0 = x0, x1 = x1, x2 = x2, x3 = x3)

# Fit a GeDSgam model
Gmodgam <- NGeDSgam(y ~ f(x0) + f(x1) + f(x2) + f(x3), data = data)
# Check that the sum of the individual base-learner predictions equals the final
# model prediction

pred0 <- predict(Gmodgam, n = 2, newdata = data, base_learner = "f(x0)")
pred1 <- predict(Gmodgam, n = 2, newdata = data, base_learner = "f(x2)")
pred2 <- predict(Gmodgam, n = 2, newdata = data, base_learner = "f(x1)")
pred3 <- predict(Gmodgam, n = 2, newdata = data, base_learner = "f(x3)")
round(predict(Gmodgam, n = 2, newdata = data) -
(mean(predict(Gmodgam, n = 2, newdata = data)) + pred0 + pred1 + pred2 + pred3), 12)

pred0 <- predict(Gmodgam, n = 3, newdata = data, base_learner = "f(x0)")
pred1 <- predict(Gmodgam, n = 3, newdata = data, base_learner = "f(x2)")
pred2 <- predict(Gmodgam, n = 3, newdata = data, base_learner = "f(x1)")
pred3 <- predict(Gmodgam, n = 3, newdata = data, base_learner = "f(x3)")

round(predict(Gmodgam, n = 3, newdata = data) - (pred0 + pred1 + pred2 + pred3), 12)

pred0 <- predict(Gmodgam, n = 4, newdata = data, base_learner = "f(x0)")
pred1 <- predict(Gmodgam, n = 4, newdata = data, base_learner = "f(x2)")
pred2 <- predict(Gmodgam, n = 4, newdata = data, base_learner = "f(x1)")
pred3 <- predict(Gmodgam, n = 4, newdata = data, base_learner = "f(x3)")

round(predict(Gmodgam, n = 4, newdata = data) - (pred0 + pred1 + pred2 + pred3), 12)

# Plot GeDSgam partial fits to f(x0), f(x1), f(x2)
par(mfrow = c(1,3))
for (i in 1:3) {
  # Plot the base learner
  plot(Gmodgam, n = 3, base_learners = paste0("f(x", i-1, ")"), col = "seagreen",
       cex.lab = 1.5, cex.axis = 1.5)
  # Add legend
  if (i == 2) {
    position <- "topleft"
    } else if (i == 3) {
      position <- "topright"
      } else {
        position <- "bottom"
      }
  legend(position, legend = c("GAM-GeDS Quadratic", paste0("f(x", i-1, ")")),
         col = c("seagreen", "darkgray"),
         lwd = c(2, 2),
         bty = "n",
         cex = 1.5)
}