GeDSgam-class {GeDS} | R Documentation |
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.
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
: ifTRUE
, then response and predictors were standardized before running the local-scoring algorithm. -
X_mean
: mean of the predictor variables (only ifnormalize_data = TRUE
). -
X_sd
: standard deviation of the predictors (only ifnormalize_data = TRUE
, else isNULL
). -
Y_mean
: mean of the response variable (only ifnormalize_data = TRUE
, else isNULL
). -
Y_sd
: standard deviation of the response variable (only ifnormalize_data = TRUE
, else isNULL
).
-
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 whenfamily = "gaussian"
, it will always correspond toiter1
, as only one local-scoring iteration is conducted in this scenario. This occurs because, withfamily = "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 forfamily = "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. SeeSplineReg
for details. -
Quadratic.Fit
: quadratic fit obtained via Schoenberg variation diminishing spline approximation. SeeSplineReg
for details. -
Cubic.Fit
: cubic fit obtained via Schoenberg variation diminishing spline approximation. SeeSplineReg
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 meansmu
.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.