GeDS (version 0.3.1)

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,
  type = c("response", "link"),
  ...
)
# S3 method for GeDSgam
predict(
  object,
  newdata,
  n = 3L,
  base_learner = NULL,
  type = c("response", "link"),
  ...
)

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.

type

character string indicating the type of prediction required. By default it is equal to "response", i.e. the result is on the scale of the response variable. See details for the other options. Alternatively if one wants the predictions to be on the predictor scale, it is necessary to set type = "link".

...

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)
}