GeDSgam-class {GeDS}

GeDSgam Class

Description

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

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 observations of the response variable.

• predictors: data.frame containing observations of the vector of 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).

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

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

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 equivalent to simply 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 piecewise linear fit 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 for details SplineReg.

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

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

predictions

A list containing the predicted values obtained (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: 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.