#' @rdname FLXMCL
# @aliases FLXMCLqda-class
#'
#' @family mixtures qda
#'
#' @import flexmix
#' @export
setClass("FLXMCLqda", contains = "FLXMCL")
#' @title Mixtures of Quadratic Discriminant Analysis Models
#'
#' @description This is a model driver for \code{\link[flexmix]{flexmix}} from package \pkg{flexmix} implementing mixtures of Quadratic Discriminant Analysis Models.
#'
#' @param formula A formula which is interpreted relative to the formula specified in the call to \code{\link[flexmix]{flexmix}} using \code{\link[stats]{update.formula}}.
#' Only the left-hand side (response) of the formula is used. Default is to use the original \code{\link[flexmix]{flexmix}} model formula.
# @param method Method for scaling the pooled weighted covariance matrix, either \code{"unbiased"} or maximum-likelihood (\code{"ML"}).
# Defaults to \code{"unbiased"}.
#' @param \dots Further arguments to and from other methods.
#'
#' @return Returns an object of class \code{FLXMCLqda} inheriting from \code{FLXMCL}.
#'
#' @note This method internally calls function \code{\link{wqda}}. \code{method = "ML"} is hard-coded.
#'
#' @rdname FLXMCLqda
#'
# @aliases FLXMCLqda
#'
#' @family mixtures qda
#'
#' @import flexmix
#'
#' @export
#'
#'
#' @examples
#' library(benchData)
#' data <- flashData(1000)
#' x1 <- seq(-6,6,0.2)
#' x2 <- seq(-4,4,0.2)
#' grid <- expand.grid(x.1 = x1, x.2 = x2)
#'
#' cluster <- kmeans(data$x, center = 2)$cluster
#' model <- FLXMCLqda()
#' fit <- flexmix(y ~ ., data = as.data.frame(data), model = model, cluster = cluster, control = list(verb = 1))
#'
#' ## prediction for single component models without aggregation
#' pred.grid <- predict(fit, newdata = grid)
#'
#' # joint density of predictors and class variable for class 1
#' image(x1, x2, matrix(pred.grid[[1]][,1], length(x1)))
#' contour(x1, x2, matrix(pred.grid[[1]][,1], length(x1)), add = TRUE)
#' points(data$x, pch = as.character(data$y))
#'
#' image(x1, x2, matrix(pred.grid[[2]][,1], length(x1)))
#' contour(x1, x2, matrix(pred.grid[[2]][,1], length(x1)), add = TRUE)
#' points(data$x, pch = as.character(data$y))
#'
#' # posterior probability of class 1
#' pred.grid <- lapply(pred.grid, function(x) x/rowSums(x))
#' image(x1, x2, matrix(pred.grid[[1]][,1], length(x1)))
#' contour(x1, x2, matrix(pred.grid[[1]][,1], length(x1)), add = TRUE)
#' points(data$x, pch = as.character(data$y))
#'
#' image(x1, x2, matrix(pred.grid[[2]][,1], length(x1)))
#' contour(x1, x2, matrix(pred.grid[[2]][,1], length(x1)), add = TRUE)
#' points(data$x, pch = as.character(data$y))
#'
#' ## prediction with aggregation depending on membership in mixture components
#' pred.grid <- mypredict(fit, newdata = grid, aggregate = TRUE)
#'
#' # joint density of predictors and class variable for class 1
#' image(x1, x2, matrix(pred.grid[[1]][,1], length(x1)))
#' contour(x1, x2, matrix(pred.grid[[1]][,1], length(x1)), add = TRUE)
#' points(data$x, pch = as.character(data$y))
#'
#' # posterior of class 1
#' pred.grid <- lapply(pred.grid, function(x) x/rowSums(x))
#' image(x1, x2, matrix(pred.grid[[1]][,1], length(x1)))
#' contour(x1, x2, matrix(pred.grid[[1]][,1], length(x1)), add = TRUE)
#' points(data$x, pch = as.character(data$y))
#'
#' ## local membership
#' grid <- cbind(y = flashBayesClass(grid), grid)
#' loc.grid <- posterior(fit, newdata = grid)
#' contour(x1, x2, matrix(loc.grid[,1], length(x1)), add = TRUE)
FLXMCLqda <- function(formula = . ~ ., ...) {
z <- new("FLXMCLqda", weighted = TRUE, formula = formula,
name = "Mixture of QDA models")
z@defineComponent <- expression({
predict <- function(x) {
## returns the joint density p(x,y), not posteriors !!!
ng <- length(attr(y, "lev"))
lev1 <- names(fit$prior)
post <- matrix(0, ncol = ng, nrow = nrow(x), dimnames = list(rownames(x), attr(y, "lev")))
post[,lev1] <- sapply(lev1, function(z) fit$prior[z] * dmvnorm(x, fit$means[z,], fit$cov[[z]]))
return(post)
}
logLik <- function(x, y) {
## unnormalized log posterior, joint log likelihood
ng <- length(attr(y, "lev"))
lev1 <- names(fit$prior)
post <- matrix(-10000, ncol = ng, nrow = nrow(x), dimnames = list(rownames(x), attr(y, "lev")))
post[,lev1] <- sapply(lev1, function(z) log(fit$prior[z]) + dmvnorm(x, fit$means[z,], fit$cov[[z]], log = TRUE))
#print(head(post))
ll <- post[cbind(rownames(post), as.character(y))]
#print(head(ll))
return(ll)
}
new("FLXcomponent", parameters = list(prior = fit$prior, means = fit$means, cov = fit$cov,
method = fit$method), logLik = logLik, predict = predict, df = fit$df)
})
z@preproc.y <- function(grouping) {
if (!is.factor(grouping))
warning("'grouping' was coerced to a factor")
g <- as.factor(grouping)
lev <- levels(g)
g <- as.matrix(g)
attr(g, "lev") <- lev
g
}
z@fit <- function(x, y, w) {
#print(attr(y, "lev"))
fit <- wqda(x, factor(y, levels = attr(y, "lev")), weights = w, method = "ML", ...)
K <- nrow(fit$means)
d <- ncol(fit$means)
fit$df <- K*d + K*d*(d-1)/2
with(fit, eval(z@defineComponent))
}
z
}
#' @rdname FLXMCLqda
# @aliases FLXgetModelmatrix,FLXMCLqda-method
#'
#' @family mixtures qda
#'
#' @import flexmix
#' @export
setMethod("FLXgetModelmatrix", signature(model = "FLXMCLqda"),
function (model, data, formula, lhs = TRUE, ...) {
formula <- flexmix:::RemoveGrouping(formula)
if (length(grep("\\|", deparse(model@formula))))
stop("no grouping variable allowed in the model")
if (is.null(model@formula))
model@formula = formula
model@fullformula = update(terms(formula, data = data),
model@formula)
if (lhs) {
mf <- if (is.null(model@terms))
model.frame(model@fullformula, data = data, na.action = NULL)
else model.frame(model@terms, data = data, na.action = NULL)
model@terms <- attr(mf, "terms")
modely <- model.response(mf)
model@y <- model@preproc.y(modely)
}
else {
mt1 <- if (is.null(model@terms))
terms(model@fullformula, data = data)
else model@terms
mf <- model.frame(delete.response(mt1), data = data,
na.action = NULL)
model@terms <- attr(mf, "terms")
}
attr(model@terms, "intercept") <- 0 ## intercept removed
X <- model.matrix(model@terms, data = mf)
model@contrasts <- attr(X, "contrasts")
model@x <- X
model@x <- model@preproc.x(model@x)
model@xlevels <- .getXlevels(model@terms, mf)
model
})
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