Learn R Programming
GeDS (version 0.3.1)

GeDSgam-class: GeDSgam Class

Description

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

Arguments

Slots

extcall

call to the NGeDSgam function.

formula

a formula object representing the model to be fitted.

args

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

  • response: data.frame containing the response variable observations.

  • predictors: data.frame containing the corresponding observations of the predictor variables included in the model.

  • base_learners: description of the model's base learners ('smooth functions').

  • family: the statistical family. The possible options are

    • binomial(link = "logit", "probit", "cauchit", "log", "cloglog")

    • gaussian(link = "identity", "log", "inverse")

    • Gamma(link = "inverse", "identity", "log")

    • inverse.gaussian(link = "1/mu^2", "inverse", "identity", "log")

    • poisson(link = "log", "identity", "sqrt")

    • quasi(link = "identity", variance = "constant")

    • quasibinomial(link = "logit", "probit", "cloglog", "identity", "inverse", "log", "1/mu^2", "sqrt")

    • quasipoisson(llink = "logit", "probit", "cloglog", "identity", "inverse", "log", "1/mu^2", "sqrt")

  • normalize_data: if TRUE, then response and predictors were standardized before running the local-scoring algorithm.

  • X_mean: mean of the predictor variables (only if normalize_data = TRUE).

  • X_sd: standard deviation of the predictors (only if normalize_data = TRUE, else is NULL).

  • Y_mean: mean of the response variable (only if normalize_data = TRUE, else is NULL).

  • Y_sd: standard deviation of the response variable (only if normalize_data = TRUE, else is NULL).

final_model

A list detailing the final GeDSgam model selected after running the local scoring algorithm. The chosen model minimizes deviance across all models generated by each local-scoring iteration. This list includes:

  • model_name: local-scoring iteration that yielded the "best" model. Note that when family = "gaussian", it will always correspond to iter1, as only one local-scoring iteration is conducted in this scenario. This occurs because, with family = "gaussian", the algorithm is tantamount to directly implementing backfitting.

  • DEV: the deviance for the fitted predictor model, defined as in Dimitrova et al. (2023), which for family = "gaussian" coincides with the Residual Sum of Squares.

  • Y_hat: fitted values.

    • eta: additive predictor.

    • mu: vector of means.

    • z: adjusted dependent variable.

  • base_learners: a list containing, for each base-learner, the corresponding linear fit piecewise polynomial coefficients. It includes the knots for each order fit, resulting from computing the averaging knot location. Although 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: final model linear fit in B-spline form. See SplineReg for details.

  • Quadratic.Fit: quadratic fit obtained via Schoenberg variation diminishing spline approximation. See SplineReg for details.

  • Cubic.Fit: cubic fit obtained via Schoenberg variation diminishing spline approximation. See SplineReg for details.

predictions

A list containing the predicted values obtained for each of the fits (linear, quadratic, and cubic). Each of the predictions contains both the additive predictor eta and the vector of means mu.

internal_knots

A list detailing the internal knots obtained for the fits of different order (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., Kaishev, V. K. and Saenz Guillen, E. L. (2025). GeDS: An R Package for Regression, Generalized Additive Models and Functional Gradient Boosting, based on Geometrically Designed (GeD) Splines. Manuscript submitted for publication.