# Block dimension reduction by SO-PLS Function `soplsr` implements dimension reductions of pre-selected blocks of variables (= set of columns) of a reference (= training) matrix, by sequential orthogonalization-PLS (said "SO-PLS"). Function `soplsrcv` perfoms repeteated cross-validation of an SO-PLS model in order to choose the optimal lv combination from the different blocks. SO-PLS is described for instance in Menichelli et al. (2014), Biancolillo et al. (2015) and Biancolillo (2016). The block reduction consists in calculating latent variables (= scores) for each block, each block being sequentially orthogonalized to the information computed from the previous blocks. The function allows giving a priori weights to the rows of the reference matrix in the calculations. Auxiliary functions `transform` Calculates the LVs for any new matrices list $Xlist$ from the model. `predict` Calculates the predictions for any new matrices list $Xlist$ from the model. UTF-8 ```r soplsr(Xlist, Y, Xscaling = c("none", "pareto", "sd")[1], Yscaling = c("none", "pareto", "sd")[1], weights = NULL, nlv) soplsrcv(Xlist, Y, Xscaling = c("none", "pareto", "sd")[1], Yscaling = c("none", "pareto", "sd")[1], weights = NULL, nlvlist = list(), nbrep = 30, cvmethod = "kfolds", seed = 123, samplingk = NULL, nfolds = 7, optimisation = c("global","sequential")[1], selection = c("localmin","globalmin","1std")[1], majorityvote = FALSE) ## S3 method for class 'Soplsr' transform(object, X, ...) ## S3 method for class 'Soplsr' predict(object, X, ...) ``` ## Arguments - `Xlist`: A list of matrices or data frames of reference (= training) observations. - `X`: For the auxiliary functions: list of new X-data, with the same variables than the training X-data. - `Y`: A $n x q$ matrix or data frame, or a vector of length $n$, of reference (= training) responses. - `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`: variable scaling for the Y-block, 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. - `weights`: a priori weights to the rows of the reference matrix in the calculations. - `nlv`: A vector of same length as the number of blocks defining the number of scores to calculate for each block, or a single number. In this last case, the same number of scores is used for all the blocks. - `nlvlist`: A list of same length as the number of X-blocks. Each component of the list gives the number of PLS components of the corresponding X-block to test. - `nbrep`: An integer, setting the number of CV repetitions. Default value is 30. - `cvmethod`: "kfolds" for k-folds cross-validation, or "loo" for leave-one-out. - `seed`: a numeric. Seed used for the repeated resampling, and if cvmethod is "kfolds" and samplingk is not NULL. - `samplingk`: A vector of length n. The elements are the values of a qualitative variable used for stratified partition creation. If NULL, the first observation is set in the first fold, the second observation in the second fold, etc... - `nfolds`: An integer, setting the number of partitions to create. Default value is 7. - `optimisation`: "global" or "sequential" optimisation of the number of components. If "sequential", the optimal lv number is found for the first X-block, then for the 2nd one, etc... - `selection`: a character indicating the selection method to use to choose the optimal combination of components, among "localmin","globalmin","1std". If "localmin": the optimal combination corresponds to the first local minimum of the mean CV rmse. If "globalmin" : the optimal combination corresponds to the minimum mean CV rmse. If "1std" (one standard errror rule): it corresponds to the first combination after which the mean cross-validated rmse does not decrease significantly. - `majorityvote`: only if optimisation is "global" or one X-block. If majorityvote is TRUE, the optimal combination is chosen for each Y variable, with the chosen selection, before a majority vote. If majorityvote is "FALSE, the optimal combination is simply chosen with the chosen selection. - `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 `soplsr`: - **fm**: A list of the plsr models. - **T**: A matrix with the concatenated scores calculated from the X-blocks. - **pred**: A matrice $n x q$ with the calculated fitted values. - **xmeans**: list of vectors of X-mean values. - **ymeans**: vector of Y-mean values. - **xscales**: list of vectors of X-scaling values. - **yscales**: vector of Y-scaling values. - **b**: A list of X-loading weights, used in the orthogonalization step. - **weights**: Weights applied to the training observations. - **nlv**: vector of numbers of latent variables from each X-block. For `transform.Soplsr`: the LVs calculated for the new matrices list $Xlist$ from the model. For `predict.Soplsr`: predicted values for each observation For `soplsrcv`: - **lvcombi**: matrix or list of matrices, of tested component combinations. - **optimcombi**: the number of PLS components of each X-block allowing the optimisation of the mean rmseCV. - **rmseCV_byY**: matrix or list of matrices of mean and sd of cross-validated RMSE in the model for each combination and each response variable. - **ExplVarCV_byY**: matrix or list of matrices of mean and sd of cross-validated explained variances in the model for each combination and each response variable. - **rmseCV**: matrix or list of matrices of mean and sd of cross-validated RMSE in the model for each combination and response variables. - **ExplVarCV**: matrix or list of matrices of mean and sd of cross-validated explained variances in the model for each combination and response variables. ## References - Biancolillo et al. , 2015. Combining SO-PLS and linear discriminant analysis for multi-block classification. Chemometrics and Intelligent Laboratory Systems, 141, 58-67. - Biancolillo, A. 2016. Method development in the area of multi-block analysis focused on food analysis. PhD. University of copenhagen. - Menichelli et al., 2014. SO-PLS as an exploratory tool for path modelling. Food Quality and Preference, 36, 122-134. - Tenenhaus, M., 1998. La régression PLS: théorie et pratique. Editions Technip, Paris, France. ## See Also `soplsr_soplsda_allsteps` function to help determine the optimal number of latent variables, perform a permutation test, calculate model parameters and predict new observations. ## Examples ```r N <- 10 ; p <- 12 set.seed(1) X <- matrix(rnorm(N * p, mean = 10), ncol = p, byrow = TRUE) Y <- matrix(rnorm(N * 2, mean = 10), ncol = 2, byrow = TRUE) colnames(X) <- paste("varx", 1:ncol(X), sep = "") colnames(Y) <- paste("vary", 1:ncol(Y), sep = "") rownames(X) <- rownames(Y) <- paste("obs", 1:nrow(X), sep = "") set.seed(NULL) X Y n <- nrow(X) X_list <- list(X[,1:4], X[,5:7], X[,9:ncol(X)]) X_list_2 <- list(X[1:2,1:4], X[1:2,5:7], X[1:2,9:ncol(X)]) soplsrcv(X_list, Y, Xscaling = c("none", "pareto", "sd")[1], Yscaling = c("none", "pareto", "sd")[1], weights = NULL, nlvlist=list(0:1, 1:2, 0:1), nbrep=1, cvmethod="loo", seed = 123, samplingk=NULL, optimisation="global", selection="localmin", majorityvote=FALSE) ncomp <- 2 fm <- soplsr(X_list, Y, nlv = ncomp) transform(fm, X_list_2) predict(fm, X_list_2) mse(predict(fm, X_list), Y) # VIP calculation based on the proportion of Y-variance explained by the components vip(fm$fm[[1]], X_list[[1]], Y = NULL, nlv = ncomp) vip(fm$fm[[2]], X_list[[2]], Y = NULL, nlv = ncomp) vip(fm$fm[[3]], X_list[[3]], Y = NULL, nlv = ncomp) ncomp <- c(2, 0, 3) fm <- soplsr(X_list, Y, nlv = ncomp) transform(fm, X_list_2) predict(fm, X_list_2) mse(predict(fm, X_list), Y) ncomp <- 0 fm <- soplsr(X_list, Y, nlv = ncomp) transform(fm, X_list_2) predict(fm, X_list_2) ncomp <- 2 weights <- rep(1 / n, n) #w <- 1:n fm <- soplsr(X_list, Y, Xscaling = c("sd","pareto","none"), nlv = ncomp, weights = weights) transform(fm, X_list_2) predict(fm, X_list_2) ```

soplsr function