# RR-DA models Discrimination (DA) based on ridge regression (RR). latin1 ```r rrda(X, y, weights = NULL, lb = 1e-5) ## S3 method for class 'Rrda' predict(object, X, ..., lb = NULL) ``` ## Arguments For `rrda` : - `X`: For the main function: Training X-data ($n, p$). --- For the auxiliary function: New X-data ($m, p$) to consider. - `y`: Training class membership ($n$). Note: If `y` is a factor, it is replaced by a character vector. - `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 $1 / n$). - `lb`: A value of regularization parameter $lambda$. If `lb = 0`, a pseudo-inverse is used in the RR. - `object`: For the auxiliary function: A fitted model, output of a call to the main functions. - `...`: For the auxiliary function: Optional arguments. Not used. ## Details The training variable $y$ (univariate class membership) is 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 ridge regression (RR) is run on the $X-$data and the dummy table, returning predictions of the dummy variables. For a given observation, the final prediction is the class corresponding to the dummy variable for which the prediction is the highest. ## Returns For `rrda`: - **fm**: List with the outputs of the RR ((`V`): eigenvector matrix of the correlation matrix (n,n); (`TtDY`): intermediate output; (`sv`): singular values of the matrix $(1,n)$; (`lb`): value of regularization parameter $lambda$; (`xmeans`): the centering vector of X $(p,1)$; (`ymeans`): the centering vector of Y $(q,1)$ ; (`weights`): the weights vector of X-variables $(p,1)$. - **lev**: classes - **ni**: number of observations in each class For `predict.Rrda`: - **pred**: matrix or list of matrices (if lb is a vector), with predicted class for each observation - **posterior**: matrix or list of matrices (if lb is a vector), calculated probability of belonging to a class for each observation ## Examples ```r n <- 50 ; p <- 8 Xtrain <- matrix(rnorm(n * p), ncol = p) ytrain <- sample(c(1, 4, 10), size = n, replace = TRUE) m <- 5 Xtest <- Xtrain[1:m, ] ; ytest <- ytrain[1:m] lb <- 1 fm <- rrda(Xtrain, ytrain, lb = lb) predict(fm, Xtest) pred <- predict(fm, Xtest)$pred err(pred, ytest) predict(fm, Xtest, lb = 0:2) predict(fm, Xtest, lb = 0) ```

rrda function