GeDSgam-class | R Documentation |
A fitted GeDSgam object returned by the function NGeDSgam
inheriting the methods from class "GeDSgam"
. Methods for functions
coef
, knots
, print
and predict
.
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
: internal knots and coefficients of the final
model for each of the base-learners.
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).
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: \Sexpr[results=rd]{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.
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