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#' Combine Model-based Recursive Partitioning with Multinomial Logistic Regression.
#'
#' This page lists all ingredients to combine Multinomial Regression with Model-Based Recursive Partitioning
#' (\code{\link[party]{mob}} from package \pkg{party}). See the example for how to do that.
#'
#' \code{multinomModel} is an object of class \code{\link[modeltools]{StatModel-class}} implemented in package \pkg{modeltools} that
#' provides an infra-structure for an unfitted \code{\link[nnet]{multinom}} model.
#'
#' Moreover, methods for \code{\link[nnet]{multinom}} and \code{multinomModel} objects for the generic functions
#' \code{\link[party]{reweight}}, \code{\link[stats]{deviance}}, \code{\link[sandwich]{estfun}}, and
#' \code{\link[stats]{predict}} are provided.
#'
#' @title Combine Model-based Recursive Partitioning with Multinomial Logistic Regression
#'
#' @param object An object of class "multinomModel" and "multinom", respectively.
#' @param x An object of class "multinom".
#' @param weights A vector of observation weights.
#' @param out Should class labels or posterior probabilities be returned?
#' @param \dots Further arguments.
#'
#' @return
#' \code{reweight}: The re-weighted fitted "multinomModel" object. \cr
#' \code{deviance}: The value of the deviance extracted from \code{object}. \cr
#' \code{estfun}: The empirical estimating (or score) function, i.e. the derivatives of the log-likelihood with respect
#' to the parameters, evaluated at the training data. \cr
#' \code{predict}: Either a vector of predicted class labels or a matrix of class posterior probabilities.
#'
#' @seealso \code{\link[party]{reweight}}, \code{\link[stats]{deviance}}, \code{\link[sandwich]{estfun}}, \code{\link[stats]{predict}}.
#'
#' @references
#' Zeileis, A., Hothorn, T. and Kornik, K. (2008), Model-based recursive partitioning.
#' \emph{Journal of Computational and Graphical Statistics}, \bold{17(2)} 492--514.
#'
#' @examples
#' library(locClassData)
#' library(party)
#'
#' data <- vData(500)
#' x <- seq(0,1,0.05)
#' grid <- expand.grid(x.1 = x, x.2 = x)
#'
#' fit <- mob(y ~ x.1 + x.2 | x.1 + x.2, data = data, model = multinomModel, trace = FALSE,
#' control = mob_control(objfun = deviance, minsplit = 200))
#'
#' ## predict posterior probabilities
#' pred <- predict(fit, newdata = grid, out = "posterior")
#' post <- do.call("rbind", pred)
#'
#' image(x, x, matrix(as.numeric(post[,1]), length(x)), xlab = "x.1", ylab = "x.2")
#' contour(x, x, matrix(as.numeric(post[,1]), length(x)), levels = 0.5, add = TRUE)
#' points(data$x, pch = as.character(data$y))
#'
#' ## predict node membership
#' splits <- predict(fit, newdata = grid, type = "node")
#' contour(x, x, matrix(splits, length(x)), levels = min(splits):max(splits), add = TRUE, lty = 2)
#'
#' @rdname multinomModel
#'
#' @import party
#' @export
multinomModel <- new("StatModel",
name = "multinomial logistic regression",
dpp = function(formula, data = list(), subset = NULL, na.action = NULL,
frame = NULL, enclos = sys.frame(sys.nframe()), other = list(),
designMatrix = TRUE, responseMatrix = TRUE, setHook = NULL, ...) {
mf <- match.call(expand.dots = FALSE)
m <- match(c("formula", "data", "subset", "na.action"), names(mf), 0)
mf <- mf[c(1, m)]
mf[[1]] <- as.name("model.frame")
mf$na.action <- stats::na.pass
#cat("mf\n")
#print(mf)
MEF <- new("ModelEnvFormula")
MEF@formula <- c(modeltools:::ParseFormula(formula, data = data)@formula,
other)
MEF@hooks$set <- setHook
if (is.null(frame))
frame <- parent.frame()
mf$subset <- try(subset)
if (inherits(mf$subset, "try-error"))
mf$subset <- NULL
MEF@get <- function(which, data = NULL, frame = parent.frame(),
envir = MEF@env) {
if (is.null(data))
RET <- get(which, envir = envir, inherits = FALSE)
else {
oldData <- get(which, envir = envir, inherits = FALSE)
if (!use.subset)
mf$subset <- NULL
mf$data <- data
mf$formula <- MEF@formula[[which]]
RET <- eval(mf, frame, enclos = enclos)
modeltools:::checkData(oldData, RET)
}
return(RET)
}
MEF@set <- function(which = NULL, data = NULL, frame = parent.frame(),
envir = MEF@env) {
if (is.null(which))
which <- names(MEF@formula)
if (any(duplicated(which)))
stop("Some model terms used more than once")
for (name in which) {
if (length(MEF@formula[[name]]) != 2)
stop("Invalid formula for ", sQuote(name))
mf$data <- data
mf$formula <- MEF@formula[[name]]
if (!use.subset)
mf$subset <- NULL
MF <- eval(mf, frame, enclos = enclos)
if (exists(name, envir = envir, inherits = FALSE))
modeltools:::checkData(get(name, envir = envir, inherits = FALSE),
MF)
assign(name, MF, envir = envir)
mt <- attr(MF, "terms")
if (name == "input" && designMatrix) {
#attr(mt, "intercept") <- 0 #???
assign("designMatrix", model.matrix(mt, data = MF,
...), envir = envir)
}
if (name == "response" && responseMatrix) {
assign("responseMatrix", MF[,1:ncol(MF)], envir = envir)
#cat("MF[,1:ncol(MF)]")
#print(MF[,1:ncol(MF)])
}
}
MEapply(MEF, MEF@hooks$set, clone = FALSE)
}
use.subset <- TRUE
MEF@set(which = NULL, data = data, frame = frame)
use.subset <- FALSE
if (!is.null(na.action))
MEF <- na.action(MEF)
#cat("MEF\n")
#print(str(MEF))
MEF
},
##arguments subset, na.action, contrasts, Hess, model discarded
fit = function (object, weights = NULL, summ = 0, censored = FALSE, ...) {
class.ind <- function(cl) {
n <- length(cl)
x <- matrix(0, n, length(levels(cl)))
x[(1L:n) + n * (as.vector(unclass(cl)) - 1L)] <- 1
dimnames(x) <- list(names(cl), levels(cl))
x
}
summ2 <- function(X, Y) {
X <- as.matrix(X)
Y <- as.matrix(Y)
n <- nrow(X)
p <- ncol(X)
q <- ncol(Y)
Z <- t(cbind(X, Y))
storage.mode(Z) <- "double"
z <- .C("VR_summ2", as.integer(n), as.integer(p), as.integer(q),
Z = Z, na = integer(1L))
Za <- t(z$Z[, 1L:z$na, drop = FALSE])
list(X = Za[, 1L:p, drop = FALSE], Y = Za[, p + 1L:q])
}
Terms <- attr(object@get("input"), "terms")
X <- object@get("designMatrix")
cons <- attr(object@get("designMatrix"), "contrasts")
Xr <- qr(X)$rank
Y <- object@get("responseMatrix")
if (!is.matrix(Y))
Y <- as.factor(Y)
w <- weights
if (length(w) == 0L)
if (is.matrix(Y))
w <- rep(1, dim(Y)[1L])
else w <- rep(1, length(Y))
lev <- levels(Y)
if (is.factor(Y)) {
counts <- table(Y)
if (any(counts == 0L)) {
empty <- lev[counts == 0L]
warning(sprintf(ngettext(length(empty), "group %s is empty",
"groups %s are empty"), paste(sQuote(empty),
collapse = " ")), domain = NA)
Y <- factor(Y, levels = lev[counts > 0L])
lev <- lev[counts > 0L]
}
if (length(lev) < 2L)
stop("need two or more classes to fit a multinom model")
if (length(lev) == 2L)
Y <- as.vector(unclass(Y)) - 1
else Y <- class.ind(Y)
}
if (summ == 1) {
Z <- cbind(X, Y)
z1 <- cumprod(apply(Z, 2L, max) + 1)
Z1 <- apply(Z, 1L, function(x) sum(z1 * x))
oZ <- order(Z1)
Z2 <- !duplicated(Z1[oZ])
oX <- (seq_along(Z1)[oZ])[Z2]
X <- X[oX, , drop = FALSE]
Y <- if (is.matrix(Y))
Y[oX, , drop = FALSE]
else Y[oX]
w <- diff(c(0, cumsum(w))[c(Z2, TRUE)])
#print(dim(X))
}
if (summ == 2) {
Z <- summ2(cbind(X, Y), w)
X <- Z$X[, 1L:ncol(X)]
Y <- Z$X[, ncol(X) + 1L:ncol(Y), drop = FALSE]
w <- Z$Y
#print(dim(X))
}
if (summ == 3) {
Z <- summ2(X, Y * w)
X <- Z$X
Y <- Z$Y[, 1L:ncol(Y), drop = FALSE]
w <- rep(1, nrow(X))
#print(dim(X))
}
offset <- attr(object@get("designMatrix"), "offset")
r <- ncol(X)
if (is.matrix(Y)) {
p <- ncol(Y)
sY <- Y %*% rep(1, p)
if (any(sY == 0))
stop("some case has no observations")
if (!censored) {
Y <- Y/matrix(sY, nrow(Y), p)
w <- w * sY
}
if (length(offset) > 1L) {
if (ncol(offset) != p)
stop("ncol(offset) is wrong")
mask <- c(rep(FALSE, r + 1L + p), rep(c(FALSE, rep(TRUE,
r), rep(FALSE, p)), p - 1L))
X <- cbind(X, offset)
Wts <- as.vector(rbind(matrix(0, r + 1L, p), diag(p)))
# cat("mask1\n")
# print(mask)
z <- mynnet.default(X, Y, w, Wts = Wts, mask = mask,
size = 0, skip = TRUE, softmax = TRUE, censored = censored,
rang = 0, ...)
} else {
mask <- c(rep(FALSE, r + 1L), rep(c(FALSE, rep(TRUE,
r)), p - 1L))
# cat("mask2\n")
# print(mask)
z <- mynnet.default(X, Y, w, mask = mask, size = 0,
skip = TRUE, softmax = TRUE, censored = censored,
rang = 0, ...)
}
} else {
if (length(offset) <= 1L) {
mask <- c(FALSE, rep(TRUE, r))
# cat("mask3\n")
# print(mask)
z <- mynnet.default(X, Y, w, mask = mask, size = 0,
skip = TRUE, entropy = TRUE, rang = 0, ...)
} else {
mask <- c(FALSE, rep(TRUE, r), FALSE)
Wts <- c(rep(0, r + 1L), 1)
X <- cbind(X, offset)
# cat("mask4\n")
# print(mask)
z <- mynnet.default(X, Y, w, Wts = Wts, mask = mask,
size = 0, skip = TRUE, entropy = TRUE, rang = 0,
...)
}
}
z$formula <- as.vector(attr(Terms, "formula"))
z$terms <- Terms
#fit$call <- call
z$weights <- w
z$lev <- lev
z$deviance <- 2 * z$value
z$rank <- Xr
edf <- ifelse(length(lev) == 2L, 1, length(lev) - 1) * Xr
if (is.matrix(Y)) {
edf <- (ncol(Y) - 1) * Xr
if (length(dn <- colnames(Y)) > 0)
z$lab <- dn
else z$lab <- 1L:ncol(Y)
}
z$coefnames <- colnames(X)
z$vcoefnames <- z$coefnames[1L:r]
z$contrasts <- cons
z$xlevels <- attr(object@get("designMatrix"), "xlevels")
z$edf <- edf
z$AIC <- z$deviance + 2 * edf
# if (model)
# z$model <- m
# if (Hess)
# fit$Hessian <- multinomHess(fit, X)
class(z) <- c("multinomModel", "multinom", "nnet")
z$predict_response <- function(newdata = NULL) {#### prior als Argument für predict?
if (!is.null(newdata)) {
penv <- new.env()
object@set("input", data = newdata, env = penv)
dm <- get("designMatrix", envir = penv, inherits = FALSE)
} else {
dm <- object@get("designMatrix")
}
}
z$addargs <- list(...)
z$ModelEnv <- object
z$statmodel <- multinomModel
z
},
predict = function (object, newdata = NULL, ...) {
object$predict_response(newdata = newdata)
},
capabilities = new("StatModelCapabilities",
weights = TRUE,
subset = TRUE
)
)
#' @rdname multinomModel
#'
#' @method reweight multinomModel
#' @S3method reweight multinomModel
#' @import party
reweight.multinomModel <- function (object, weights, ...) {
fit <- multinomModel@fit
do.call("fit", c(list(object = object$ModelEnv, weights = weights), object$addargs))
}
#' @noRd
#'
#' @method model.matrix multinomModel
#' @S3method model.matrix multinomModel
#' @importFrom stats model.matrix
model.matrix.multinomModel <- function (object, ...)
object$ModelEnv@get("designMatrix")
#' @noRd
model.response.multinomModel <- function (object, ...)
object$ModelEnv@get("responseMatrix")
#' @rdname multinomModel
#'
#' @method deviance multinom
#' @S3method deviance multinom
#' @importFrom stats deviance
deviance.multinom <- function (object, ...) {
return(object$deviance)
}
#' @rdname multinomModel
#'
#' @method estfun multinom
#' @S3method estfun multinom
#' @importFrom sandwich estfun
estfun.multinom <- function(x, ...) {
#cat("gradient\n")
#print(x$gradient)
#print(colSums(x$gradient))
x$gradient
}
#' @import nnet
add.net <- nnet:::add.net
#' @rdname multinomModel
#'
#' @method predict multinomModel
#' @S3method predict multinomModel
predict.multinomModel <- function(object, out = c("class", "posterior"), ...) {
out <- match.arg(out)
pred <- switch(out,
class = {
cl <- NextMethod(object, type = "class", ...)
factor(cl, levels = object$lev)
},
posterior = {
post <- NextMethod(object, type = "probs", ...)
#print(str(post))
if (!is.matrix(post))
post = cbind(1 - post, post)
colnames(post) <- object$lev
lapply(seq_len(nrow(post)), function(i) post[i,, drop = FALSE])
})
return(pred)
}
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