GeDSboost-class: GeDSboost Class

Description

A fitted GeDSboost object returned by the function NGeDSboost, inheriting the methods for class "GeDSboost". Methods for functions coef, knots, plot, print, predict, visualize_boosting, and bl_imp are available.

Arguments

Slots

extcall: call to the NGeDSboost function.

formula

a formula object representing the model to be fitted.

args

a list containing the arguments passed to the NGeDSboost function. This list includes:

response: data.frame containing the response variable observations.
predictors: data.frame containing the observations corresponding to the predictor variables included in the model.
base_learners: description of model's base learners.
family: the statistical family; the possible options are
- mboost::Binomial(type = c("adaboost", "glm"), link = c("logit", "probit", "cloglog", "cauchit", "log"), ...)
- mboost::Gaussian()
- mboost::Poisson()
- mboost::GammaReg(nuirange = c(0, 100))
Other mboost families may be suitable; however, these have not yet been thoroughly tested and are therefore not recommended for use.
initial_learner: if TRUE a NGeDS or GGeDS fit was used as the initial learner; otherwise, the empirical risk minimizer corresponding to the selected family was employed.
int.knots_init: if initial_learner = TRUE, this corresponds to the maximum number of internal knots set in the NGeDS/GGeDS function before the initial learner fit.
shrinkage: shrinkage/step-length/learning rate utilized throughout the boosting iterations.
normalize_data: if TRUE, then response and predictors were standardized before running the FGB algorithm.
X_mean: mean of the predictor variables (only if normalize_data = TRUE, otherwise this is NULL).
X_sd: standard deviation of the predictors (only if normalize_data = TRUE, otherwise this is NULL).
Y_mean: mean of the response variable (only if normalize_data = TRUE, otherwise this is NULL).
Y_sd: standard deviation of the response variable (only if normalize_data = TRUE, otherwise this is NULL).

models

A list containing the 'model' generated at each boosting iteration. Each of these models includes:

best_bl: fit of the base learner that minimized the residual sum of squares (RSS) in fitting the gradient at the i-th boosting iteration.
Y_hat: model fitted values at the i-th boosting iteration.
base_learners: knots and polynomial coefficients for each of the base-learners at the i-th boosting iteration.

final_model

A list detailing the final GeDSboost model after the gradient descent algorithm is run:

model_name: the boosting iteration corresponding to the final model.
DEV: deviance of the final model.
Y_hat: fitted values.
base_learners: a list containing, for each base-learner, the intervals defined by the piecewise linear fit and its corresponding polynomial coefficients. It also includes the knots corresponding to each order fit, which result from computing the corresponding averaging knot location. See Kaishev et al. (2016) for details. If the number of internal knots of the final linear fit is less than $n-1$, the averaging knot location is not computed.
Linear.Fit/Quadratic.Fit/Cubic.Fit: final linear, quadratic and cubic fits in B-spline form. These include the same elements as Linear, Quadratic and Cubic in a GeDS-class object (see SplineReg for details).

predictions

a list containing the predicted values obtained for each of the fits (linear, quadratic and cubic).

internal_knots

a list detailing the internal knots obtained for each of the different order fits (linear, quadratic, and cubic).

References

Dimitrova, D. S., Kaishev, V. K., Lattuada, A. and Verrall, R. J. (2023). Geometrically designed variable knot splines in generalized (non-)linear models. Applied Mathematics and Computation, 436.
DOI: tools:::Rd_expr_doi("10.1016/j.amc.2022.127493")

Dimitrova, D. S., Guillen, E. S. and Kaishev, V. K. (2024). GeDS: An R Package for Regression, Generalized Additive Models and Functional Gradient Boosting, based on Geometrically Designed (GeD) Splines. Manuscript submitted for publication.