#' A Sparse and Structured Procedure to Identify Combined Effects of Functional Predictors
#' @details The main function of the package is the \code{\link{spicefp}} function. It directly
#' performs the three main steps of the SpiceFP approach, by using intermediate functions of the package. \cr
#' 1) At he first step, contingency tables are constructed by
#' defining joint modalities using class intervals or bins. Several candidate
#' partitions are then defined.
#' For each statistical individual \eqn{i} and each candidate partition (denoted \eqn{u} here), the 2 (resp. 3)
#' functional predictors are transformed into frequency bi(resp. tri)-variate histograms (or contingency tables),
#' stored as row vectors. The combination of these row vectors for all individuals enables the construction of a
#' candidate explanatory matrix indexed by \eqn{u} (denoted here \eqn{X^u}).
#' The function \code{\link{candidates}} is designed to build these candidate matrices. \cr
#' 2) At the second step, for each candidate explanatory matrix, an edge matrix is defined to
#' represent the contiguity constraints between modalities of the contingency table. \cr
#' 3) Finally at the last step, the best class intervals and related
#' regression coefficients are defined by: i) performing a Generalized Fused Lasso
#' using each candidate explanatory matrix. The SpiceFP model is the following
#' \deqn{y_i  = X_i^u \beta^u + \varepsilon_i,}
#' where \eqn{\beta^u} is the coefficient to be estimated on the 2D (resp. 3D) intervals.
#' The estimator of \eqn{\beta} is obtained as follows:
#' \deqn{ \hat{\beta}^{u,\gamma}(\lambda) = argmin \frac{1}{2} \|y - X^u \beta\|_2^2 + \lambda \|D ^{u,\gamma} \beta\|_1,}
#' where \eqn{\lambda} is a penalty parameter that controls the smoothness of the coefficients, and
#' \eqn{\gamma} is the ratio between the regularization parameters of parsimony and fusion.
#' ii) choosing the best candidate matrix
#' and selecting its variables using an information criterion and checking the
#' shutdown conditions to stop the approach. Indeed, SpiceFP  may be used in an iterative way. It
#' therefore allows to identify up to K best candidate matrices and related coefficients.

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SpiceFP documentation built on Sept. 15, 2021, 9:07 a.m.