# multi-block PLSDA models Multi-block discrimination (DA) based on PLS. The training variable $y$ (univariate class membership) is firstly transformed to a dummy table containing $nclas$ columns, where $nclas$ is the number of classes present in $y$. Each column is a dummy variable (0/1). Then, a PLS2 is implemented on the $X-$data and the dummy table, returning latent variables (LVs) that are used as dependent variables in a DA model. - `mbplsrda`: Usual "PLSDA". A linear regression model predicts the Y-dummy table from the PLS2 LVs. This corresponds to the PLSR2 of the X-data and the Y-dummy table. For a given observation, the final prediction is the class corresponding to the dummy variable for which the prediction is the highest. - `mbplslda` and `mbplsqda`: Probabilistic LDA and QDA are run over the PLS2 LVs, respectively. latin1 ```r mbplsrda(Xlist, y, blockscaling = TRUE, weights = NULL, nlv, Xscaling = c("none", "pareto", "sd")[1], Yscaling = c("none", "pareto", "sd")[1]) mbplslda(Xlist, y, blockscaling = TRUE, weights = NULL, nlv, prior = c("unif", "prop"), Xscaling = c("none", "pareto", "sd")[1], Yscaling = c("none", "pareto", "sd")[1]) mbplsqda(Xlist, y, blockscaling = TRUE, weights = NULL, nlv, prior = c("unif", "prop"), Xscaling = c("none", "pareto", "sd")[1], Yscaling = c("none", "pareto", "sd")[1]) ## S3 method for class 'Mbplsrda' predict(object, X, ..., nlv = NULL) ## S3 method for class 'Mbplsprobda' predict(object, X, ..., nlv = NULL) ``` ## Arguments - `Xlist`: For the main functions: list of training X-data ($n$rows). - `X`: For the auxiliary functions: list of new X-data ($n$ rows), with the same variables than the training X-data. - `y`: Training class membership ($n$). Note: If `y` is a factor, it is replaced by a character vector. - `blockscaling`: logical. If TRUE, the scaling factor (computed on the training) is the "norm" of the block, i.e. the square root of the sum of the variances of each column of the block. - `weights`: Weights ($n$) to apply to the training observations for the PLS2. Internally, weights are "normalized" to sum to 1. Default to `NULL` (weights are set to $1 / n$). - `nlv`: The number(s) of LVs to calculate. - `prior`: The prior probabilities of the classes. Possible values are "unif" (default; probabilities are set equal for all the classes) or "prop" (probabilities are set equal to the observed proportions of the classes in `y`). - `Xscaling`: vector (of length Xlist) of variable scaling for each datablock, among "none" (mean-centering only), "pareto" (mean-centering and pareto scaling), "sd" (mean-centering and unit variance scaling). If "pareto" or "sd", uncorrected standard deviation is used. - `Yscaling`: character. variable scaling for the Y-block after binary transformation, among "none" (mean-centering only), "pareto" (mean-centering and pareto scaling), "sd" (mean-centering and unit variance scaling). If "pareto" or "sd", uncorrected standard deviation is used. - `object`: For the auxiliary functions: A fitted model, output of a call to the main functions. - `...`: For the auxiliary functions: Optional arguments. Not used. ## Returns For `mbplsrda`: - **fm**: list with the MB-PLS model: (`T`): X-scores matrix; (`P`): X-loading matrix;(`R`): The PLS projection matrix (p,nlv); (`W`): X-loading weights matrix ;(`C`): The Y-loading weights matrix; (`TT`): the X-score normalization factor; (`xmeans`): the centering vector of X (p,1); (`ymeans`): the centering vector of Y (q,1); (`weights`): vector of observation weights; (`blockscaling`): block scaling; (`Xnorms`): "norm" of each block; (`U`): intermediate output. - **lev**: classes - **ni**: number of observations in each class For `mbplslda`, `mbplsqda`: - **fm**: list with [[1]] the MB-PLS model: (`T`): X-scores matrix; (`P`): X-loading matrix;(`R`): The PLS projection matrix (p,nlv); (`W`): X-loading weights matrix ;(`C`): The Y-loading weights matrix; (`TT`): the X-score normalization factor; (`xmeans`): the centering vectors of X; (`ymeans`): the centering vector of Y (q,1); (`xscales`): the scaling vector of X (p,1); (`yscales`): the scaling vector of Y (q,1); (`weights`): vector of observation weights; (`blockscaling`): block scaling; (`Xnorms`): "norm" of each block; (`U`): intermediate output. [[2]] lda or qda models. - **lev**: classes - **ni**: number of observations in each class For `predict.Mbplsrda`, `predict.Mbplsprobda`: - **pred**: predicted class for each observation - **posterior**: calculated probability of belonging to a class for each observation ## See Also `mbplsr_mbplsda_allsteps` function to help determine the optimal number of latent variables, perform a permutation test, calculate model parameters and predict new observations. ## Note The first example concerns MB-PLSDA, and the second one concerns MB-PLS LDA. `fm` are PLS1 models, and `zfm` are PLS2 models. ## Examples ```r ## EXAMPLE OF MB-PLSDA n <- 50 ; p <- 8 Xtrain <- matrix(rnorm(n * p), ncol = p) Xtrainlist <- list(Xtrain[,1:3], Xtrain[,4:8]) ytrain <- sample(c(1, 4, 10), size = n, replace = TRUE) Xtest <- Xtrain[1:5, ] ; ytest <- ytrain[1:5] Xtestlist <- list(Xtest[,1:3], Xtest[,4:8]) nlv <- 5 fm <- mbplsrda(Xtrainlist, ytrain, Xscaling = "sd", nlv = nlv) names(fm) predict(fm, Xtestlist) predict(fm, Xtestlist, nlv = 0:2)$pred pred <- predict(fm, Xtestlist)$pred err(pred, ytest) zfm <- fm$fm transform(zfm, Xtestlist) transform(zfm, Xtestlist, nlv = 1) summary(zfm, Xtrainlist) coef(zfm) coef(zfm, nlv = 0) coef(zfm, nlv = 2) ## EXAMPLE OF MB-PLS LDA n <- 50 ; p <- 8 Xtrain <- matrix(rnorm(n * p), ncol = p) Xtrainlist <- list(Xtrain[,1:3], Xtrain[,4:8]) ytrain <- sample(c(1, 4, 10), size = n, replace = TRUE) Xtest <- Xtrain[1:5, ] ; ytest <- ytrain[1:5] Xtestlist <- list(Xtest[,1:3], Xtest[,4:8]) nlv <- 5 fm <- mbplslda(Xtrainlist, ytrain, Xscaling = "none", nlv = nlv) predict(fm, Xtestlist) predict(fm, Xtestlist, nlv = 1:2)$pred zfm <- fm[[1]][[1]] class(zfm) names(zfm) summary(zfm, Xtrainlist) transform(zfm, Xtestlist) coef(zfm) ## EXAMPLE OF MB-PLS QDA n <- 50 ; p <- 8 Xtrain <- matrix(rnorm(n * p), ncol = p) Xtrainlist <- list(Xtrain[,1:3], Xtrain[,4:8]) ytrain <- sample(c(1, 4, 10), size = n, replace = TRUE) Xtest <- Xtrain[1:5, ] ; ytest <- ytrain[1:5] Xtestlist <- list(Xtest[,1:3], Xtest[,4:8]) nlv <- 5 fm <- mbplsqda(Xtrainlist, ytrain, Xscaling = "none", nlv = nlv) predict(fm, Xtestlist) predict(fm, Xtestlist, nlv = 1:2)$pred zfm <- fm[[1]][[1]] class(zfm) names(zfm) summary(zfm, Xtrainlist) transform(zfm, Xtestlist) coef(zfm) ```

mbplsda function