Performs a forward variable selection for iterative bias reduction using kernel, thin plate splines or low rank splines. Missing values are not allowed.
forward(formula,data,subset,criterion="gcv",df=1.5,Kmin=1,Kmax=1e+06,
smoother="k",kernel="g",rank=NULL,control.par=list(),cv.options=list(),
varcrit=criterion)Returns an object of class forwardibr which is a matrix
with p columns. In the first row, each entry j contains
the value of the chosen criterion for the univariate smoother using
the jth explanatory variable. The variable which realize the minimum
of the first row is included in the model. All the column of this
variable will be Inf except the first row. In the second row,
each entry j contains the bivariate smoother using the jth
explanatory variable and the variable already included. The variable
which realize the minimum of the second row is included in the
model. All the column of this variable will be Inf except the
two first row. This forward selection process continue until the
chosen criterion increases.
An object of class "formula" (or one that
can be coerced to that class): a symbolic description of the
model to be fitted.
An optional data frame, list or environment (or object
coercible by as.data.frame to a data frame) containing
the variables in the model. If not found in data, the
variables are taken from environment(formula),
typically the environment from which forward is called.
An optional vector specifying a subset of observations to be used in the fitting process.
Character string. If the number of iterations
(iter) is missing or
NULL the number of iterations is chosen using
criterion. The criteria available are GCV (default, "gcv"),
AIC ("aic"), corrected AIC ("aicc"), BIC
("bic"), gMDL ("gmdl"), map ("map") or rmse
("rmse"). The last two are designed for cross-validation.
A numeric vector of either length 1 or length equal to the
number of columns of x. If smoother="k", it indicates
the desired degree of
freedom (trace) of the smoothing matrix for
each variable or for the initial smoother (see contr.sp$dftotal); df is repeated when the length of vector
df is 1. If smoother="tps", the minimum df of thin
plate splines is multiplied by df. This argument is useless if
bandwidth is supplied (non null).
The minimum number of bias correction iterations of the search grid considered by the model selection procedure for selecting the optimal number of iterations.
The maximum number of bias correction iterations of the search grid considered by the model selection procedure for selecting the optimal number of iterations.
Character string which allows to choose between thine plate
splines "tps" or kernel ("k").
Character string which allows to choose between gaussian kernel
("g"), Epanechnikov ("e"), uniform ("u"),
quartic ("q"). The default (gaussian kernel) is strongly advised.
Numeric value that control the rank of low rank splines
(denoted as k in mgcv package ; see also choose.k
for further details or gam for another smoothing approach with
reduced rank smoother.
a named list that control optional parameters. The
components are bandwidth (default to NULL), iter
(default to NULL), really.big (default to FALSE),
dftobwitmax (default to 1000), exhaustive (default to
FALSE),m (default to NULL), dftotal (default to
FALSE), accuracy (default to 0.01), ddlmaxi
(default to 2n/3) and fraction (default to c(100, 200, 500, 1000, 5000,10^4,5e+04,1e+05,5e+05,1e+06)).
bandwidth: a vector of either length 1 or length equal to the
number of columns of x. If smoother="k",
it indicates the bandwidth used for
each variable, bandwidth is repeated when the length of vector
bandwidth is 1. If smoother="tps", it indicates the
amount of penalty (coefficient lambda).
The default (missing) indicates, for smoother="k", that
bandwidth for each variable is
chosen such that each univariate kernel
smoother (for each explanatory variable) has df degrees of
freedom and for smoother="tps" that lambda is chosen such that
the df of the smoothing matrix is df times the minimum df.
iter: the number of iterations. If null or missing, an optimal number of
iterations is chosen from
the search grid (integer from Kmin to Kmax) to minimize the criterion.
really.big: a boolean: if TRUE it overides the limitation
at 500 observations. Expect long computation times if TRUE.
dftobwitmax: When bandwidth is chosen by specifying the degree
of freedom (see df) a search is done by
uniroot. This argument specifies the maximum number of iterations transmitted to uniroot function.
exhaustive: boolean, if TRUE an exhaustive search of
optimal number of iteration on the
grid Kmin:Kmax is performed. If FALSE the minimum of
criterion is searched using optimize between Kmin
and Kmax.
m: the order of thin plate splines. This integer m must verifies
2m/d>1, where d is the number of explanatory
variables. The missing default to choose the order m as the first integer
such that 2m/d>1, where d is the number of
explanatory variables (same for NULL).
dftotal: a boolean wich indicates when FAlSE that the
argument df is the objective df for each univariate kernel (the
default) calculated for each explanatory variable or for the overall
(product) kernel, that is the base smoother (when TRUE).
accuracy: tolerance when searching bandwidths which lead to a
chosen overall intial df.
dfmaxi: the maximum degree of freedom allowed for iterated
biased reduction smoother.
fraction: the subdivistion of interval Kmin,Kmax
if non exhaustive search is performed (see also iterchoiceA or iterchoiceS1).
A named list which controls the way to do cross
validation with component bwchange,
ntest, ntrain, Kfold, type,
seed, method and npermut. bwchange is a boolean (default to FALSE)
which indicates if bandwidth have to be recomputed each
time. ntest is the number of observations in test set and
ntrain is the number of observations in training set. Actually,
only one of these is needed the other can be NULL or missing. Kfold a boolean or an integer. If
Kfold is TRUE then the number of fold is deduced from
ntest (or ntrain). type is a character string in
random,timeseries,consecutive, interleaved
and give the type of segments. seed controls the seed of
random generator. method is either "inmemory" or
"outmemory"; "inmemory" induces some calculations outside
the loop saving computational time but leading to an increase of the required
memory. npermut is the number of random draws. If
cv.options is list(), then component ntest is set to
floor(nrow(x)/10), type is random, npermut is 20
and method is "inmemory", and the other components are
NULL
Character string. Criterion used for variable
selection. The criteria available are GCV,
AIC ("aic"), corrected AIC ("aicc"), BIC
("bic") and gMDL ("gmdl").
Pierre-Andre Cornillon, Nicolas Hengartner and Eric Matzner-Lober.
Cornillon, P.-A.; Hengartner, N.; Jegou, N. and Matzner-Lober, E. (2012) Iterative bias reduction: a comparative study. Statistics and Computing, 23, 777-791.
Cornillon, P.-A.; Hengartner, N. and Matzner-Lober, E. (2013) Recursive bias estimation for multivariate regression smoothers Recursive bias estimation for multivariate regression smoothers. ESAIM: Probability and Statistics, 18, 483-502.
Cornillon, P.-A.; Hengartner, N. and Matzner-Lober, E. (2017) Iterative Bias Reduction Multivariate Smoothing in R: The ibr Package. Journal of Statistical Software, 77, 1--26.
ibr, plot.forwardibr
if (FALSE) {
data(ozone, package = "ibr")
res.ibr <- forward(ozone[,-1],ozone[,1],df=1.2)
apply(res.ibr,1,which.min)
}
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