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#' PCA, PLS(-DA) and OPLS(-DA) for multivariate analysis and feature selection
#' of omics data
#'
#' Latent variable modeling with Principal Component Analysis (PCA) and Partial
#' Least Squares (PLS) are powerful methods for visualization, regression,
#' classification, and feature selection of omics data where the number of
#' variables exceeds the number of samples and with multicollinearity among
#' variables. Orthogonal Partial Least Squares (OPLS) enables to separately
#' model the variation correlated (predictive) to the factor of interest and
#' the uncorrelated (orthogonal) variation. While performing similarly to PLS,
#' OPLS facilitates interpretation. Successful applications of these
#' chemometrics techniques include spectroscopic data such as Raman
#' spectroscopy, nuclear magnetic resonance (NMR), mass spectrometry (MS) in
#' metabolomics and proteomics, but also transcriptomics data. In addition to
#' scores, loadings and weights plots, the package provides metrics and
#' graphics to determine the optimal number of components (e.g. with the R2 and
#' Q2 coefficients), check the validity of the model by permutation testing,
#' detect outliers, and perform feature selection (e.g. with Variable
#' Importance in Projection or regression coefficients). The package can be
#' accessed via a user interface on the Workflow4Metabolomics.org online
#' resource for computational metabolomics (built upon the Galaxy environment).
#'
#' @import Biobase methods
#' @importFrom grDevices dev.new dev.off pdf rainbow
#' @importFrom graphics abline axTicks axis barplot boxplot layout legend lines mtext par pie plot points rect text
#' @importFrom stats complete.cases cor cov median qchisq qf qnorm sd var
#' @importFrom utils head object.size read.table str tail write.table
#' @name ropls-package
#' @aliases ropls ropls-package
#' @docType package
#' @author E. Thevenot (CEA, LIST, MetaboHub)
#'
#' Maintainer: Etienne Thevenot <etienne.thevenot@@cea.fr>
#' @keywords package
#' @examples
#'
#' #### PCA
#'
#' data(foods) ## see Eriksson et al. (2001); presence of 3 missing values (NA)
#' head(foods)
#' foodMN <- as.matrix(foods[, colnames(foods) != "Country"])
#' rownames(foodMN) <- foods[, "Country"]
#' head(foodMN)
#' foo.pca <- opls(foodMN)
#'
#' #### PLS with a single response
#'
#' data(cornell) ## see Tenenhaus, 1998
#' head(cornell)
#' cornell.pls <- opls(as.matrix(cornell[, grep("x", colnames(cornell))]),
#' cornell[, "y"])
#'
#' ## Complementary graphics
#'
#' plot(cornell.pls, typeVc = c("outlier", "predict-train", "xy-score", "xy-weight"))
#'
#' #### PLS with multiple (quantitative) responses
#'
#' data(lowarp) ## see Eriksson et al. (2001); presence of NAs
#' head(lowarp)
#' lowarp.pls <- opls(as.matrix(lowarp[, c("glas", "crtp", "mica", "amtp")]),
#' as.matrix(lowarp[, grepl("^wrp", colnames(lowarp)) |
#' grepl("^st", colnames(lowarp))]))
#'
#' #### PLS-DA
#'
#' data(sacurine)
#' attach(sacurine)
#' sacurine.plsda <- opls(dataMatrix, sampleMetadata[, "gender"])
#' plot(sacurine.plsda, parPaletteVc = c("green4", "magenta"))
#'
#' #### OPLS-DA
#'
#' sacurine.oplsda <- opls(dataMatrix, sampleMetadata[, "gender"], predI = 1, orthoI = NA)
#'
#' #### Application to an ExpressionSet
#'
#' sacSet <- Biobase::ExpressionSet(assayData = t(dataMatrix),
#' phenoData = new("AnnotatedDataFrame",
#' data = sampleMetadata),
#' featureData = new("AnnotatedDataFrame",
#' data = variableMetadata),
#' experimentData = new("MIAME",
#' title = "sacurine"))
#'
#' sacPlsda <- opls(sacSet, "gender")
#' sacSet <- getEset(sacPlsda)
#' head(Biobase::pData(sacSet))
#' head(Biobase::fData(sacSet))
#'
#' detach(sacurine)
#'
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