# LDA and QDA Probabilistic (parametric) linear and quadratic discriminant analysis. UTF-8 ```r lda(X, y, prior = c("unif", "prop")) qda(X, y, prior = c("unif", "prop")) ## S3 method for class 'Lda' predict(object, X, ...) ## S3 method for class 'Qda' predict(object, X, ...) ``` ## Arguments - `X`: For the main functions: Training X-data ($n, p$). --- For the auxiliary functions: 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. - `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`). - `object`: For the auxiliary functions: A fitted model, output of a call to the main functions. - `...`: For the auxiliary functions: Optional arguments. Not used. ## Details For each observation to predict, the posterior probability to belong to a given class is estimated using the Bayes' formula, assuming priors (proportional or uniform) and a multivariate Normal distribution for the dependent variables $X$. The prediction is the class with the highest posterior probability. LDA assumes homogeneous $X-$covariance matrices for the classes while QDA assumes different covariance matrices. The functions use `dmnorm` for estimating the multivariate Normal densities. ## Returns For `lda` and `qda`: - **ct**: centers (column-wise means) for classes of observations. - **W**: unbiased within covariance matrices for classes of observations. - **wprior**: prior probabilities of the classes. - **lev**: y levels. - **ni**: number of observations by level of y. For `predict.Lda` and `predict.Qda`: - **pred**: predicted classes of observations. - **ds**: Prediction of the normal probability density. - **posterior**: posterior probabilities of the classes. ## References Saporta, G., 2011. Probabilités analyse des données et statistique. Editions Technip, Paris, France. Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer. ## Examples ```r ## EXAMPLE 1 data(iris) X <- iris[, 1:4] y <- iris[, 5] N <- nrow(X) nTest <- round(.25 * N) nTraining <- N - nTest s <- sample(1:N, nTest) Xtrain <- X[-s, ] ytrain <- y[-s] Xtest <- X[s, ] ytest <- y[s] prior <- "unif" fm <- lda(Xtrain, ytrain, prior = prior) res <- predict(fm, Xtest) names(res) headm(res$pred) headm(res$ds) headm(res$posterior) err(res$pred, ytest) ## EXAMPLE 2 data(iris) X <- iris[, 1:4] y <- iris[, 5] N <- nrow(X) nTest <- round(.25 * N) nTraining <- N - nTest s <- sample(1:N, nTest) Xtrain <- X[-s, ] ytrain <- y[-s] Xtest <- X[s, ] ytest <- y[s] prior <- "prop" fm <- lda(Xtrain, ytrain, prior = prior) res <- predict(fm, Xtest) names(res) headm(res$pred) headm(res$ds) headm(res$posterior) err(res$pred, ytest) ```

lda function