Predictions from a bgam fit

Returns predictions from a fitted component-wise P-spline boosting model. New B-spline bases are constructed for newdata using the stored knot sequences; values outside the training range are extrapolated by the natural boundary behaviour of the de Boor recursion (polynomial extrapolation). For bagged fits (n.boot > 0), the bag mean across all surviving replicates is returned.

Usage

# S3 method for class 'bgam'
predict(
  object,
  newdata = NULL,
  type = c("response", "link", "terms"),
  se.fit = FALSE,
  level = 0.95,
  ...
)

Arguments

object

An object of class "bgam", as returned by bgam().

newdata

A numeric matrix or data frame of new predictor values with the same columns (in any order) as the training data. NULL (default) returns stored training predictions: $fitted.values for non-bagged fits, bag mean for bagged fits. Out-of-vocabulary factor levels in newdata cause an informative error.

type

Prediction scale:

"response"

(default) Fitted probabilities for family = "binomial"; fitted values (identical to link scale) for family = "gaussian".

"link"

The linear predictor (additive predictor on the link scale). Identical to "response" for gaussian.

"terms"

An nrow(newdata) x p numeric matrix of per- predictor component contributions. Column j holds B_new_j %*% beta_j. Column names match object$predictor_names. Row sums of all columns plus object$intercept_value equal the link-scale prediction.

se.fit

If TRUE, returns a list with elements $fit (predictions as described above) and $se.fit (plug-in standard errors summed across active base-learners). For predictor j active at observation i, the component variance is diag(B_j[i,,drop=FALSE] %*% solve(A_j) %*% t(B_j[i,,drop=FALSE])) * sigma2 where A_j = B_j'B_j + lambda_j * D_j'D_j. For binomial, delta-method SE on the response scale is applied: se_mu = se_eta * mu_hat * (1 - mu_hat). Default FALSE.

level

Unused; reserved for a future prediction-interval interface. Default 0.95.

...

Currently unused.

Value

se.fit = FALSE

A numeric vector of length nrow(newdata), or a numeric matrix of dimension nrow(newdata) x p when type = "terms".

se.fit = TRUE

A list with elements $fit (as above) and $se.fit (numeric vector of per-observation standard errors).

For bagged fits the bag mean is returned (se.fit is not available for bagged fits).

Examples

set.seed(1)
n <- 200
x <- matrix(rnorm(n * 3), n, 3)
y <- sin(x[, 1]) + 0.5 * x[, 2] + rnorm(n, sd = 0.5)
fit <- bgam(x, y, mstop = 50, autotune = FALSE)
predict(fit, x[1:5, ])
#> [1] -0.3366752  0.7512314 -0.1265925  0.7345903 -0.7901804

# Per-component contributions
terms_mat <- predict(fit, x, type = "terms")
head(terms_mat)
#>              V1         V2           V3
#> [1,] -0.5329743  0.2183459  0.003791868
#> [2,]  0.1482210  0.6084561  0.020393019
#> [3,] -0.6898030  0.5936835 -0.004634227
#> [4,]  0.9312412 -0.1562703 -0.014541880
#> [5,]  0.2519345 -1.0027555 -0.013520765
#> [6,] -0.6804948  0.7373870 -0.015122571

# Plug-in standard errors
p_se <- predict(fit, x[1:5, ], se.fit = TRUE)
p_se$se.fit
#> [1] 0.1301678 0.1169086 0.1519135 0.1167717 0.1240764