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## kwManyOneConoverTest.R
## Part of the R package: PMCMR
##
## Copyright (C) 2017, 2018 Thorsten Pohlert
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## A copy of the GNU General Public License is available at
## http://www.r-project.org/Licenses/
####
#### Requires package mvtnorm
#' @name kwManyOneConoverTest
#' @title Conover's Many-to-One Rank Comparison Test
#' @description
#' Performs Conover's non-parametric many-to-one comparison
#' test for Kruskal-type ranked data.
#'
#' @details
#' For many-to-one comparisons (pairwise comparisons with one control)
#' in an one-factorial layout with non-normally distributed
#' residuals Conover's non-parametric test can be performed.
#' Let there be \eqn{k} groups including the control,
#' then the number of treatment levels is \eqn{m = k - 1}.
#' Then \eqn{m} pairwise comparisons can be performed between
#' the \eqn{i}-th treatment level and the control.
#' H\eqn{_i: \theta_0 = \theta_i} is tested in the two-tailed case against
#' A\eqn{_i: \theta_0 \ne \theta_i, ~~ (1 \le i \le m)}.
#'
#' If \code{p.adjust.method == "single-step"} is selected,
#' the \eqn{p}-values will be computed
#' from the multivariate \eqn{t} distribution. Otherwise,
#' the \eqn{p}-values are computed from the \eqn{t}-distribution using
#' any of the \eqn{p}-adjustment methods as included in \code{\link{p.adjust}}.
#'
#' @inherit cuzickTest note
#'
#' @inherit kwAllPairsConoverTest references
#'
#' @template class-PMCMR
#'
#' @concept kruskalranks
#' @keywords nonparametric
#'
#' @seealso
#' \code{\link{pmvt}}, \code{\link{TDist}}, \code{\link{kruskalTest}},
#' \code{\link{kwManyOneDunnTest}}, \code{\link{kwManyOneNdwTest}}
#' @example examples/kwManyOneMC.R
#' @export
kwManyOneConoverTest <- function(x, ...) UseMethod("kwManyOneConoverTest")
#' @rdname kwManyOneConoverTest
#' @method kwManyOneConoverTest default
#' @aliases kwManyOneConoverTest.default
#' @template one-way-parms
#' @param alternative the alternative hypothesis. Defaults to \code{two.sided}.
#' @param p.adjust.method method for adjusting p values
#' (see \code{\link{p.adjust}}).
#' @importFrom stats pt
#' @importFrom stats p.adjust.methods
#' @importFrom stats p.adjust
#' @importFrom stats complete.cases
#' @importFrom mvtnorm pmvt
#' @export
kwManyOneConoverTest.default <-
function(x, g, alternative = c("two.sided", "greater", "less"), p.adjust.method = c("single-step" ,p.adjust.methods),...){
## taken from stats::kruskal.test
if (is.list(x)) {
if (length(x) < 2L)
stop("'x' must be a list with at least 2 elements")
DNAME <- deparse(substitute(x))
x <- lapply(x, function(u) u <- u[complete.cases(u)])
k <- length(x)
l <- sapply(x, "length")
if (any(l == 0))
stop("all groups must contain data")
g <- factor(rep(1 : k, l))
if (is.null(x$alternative)){
alternative <- "two.sided"
} else {
alternative <- x$alternative
}
if(is.null(x$p.adjust.method)){
p.adjust.method <- "single-step"
} else {
p.adjust.method <- x$p.adjust.method
}
x <- unlist(x)
}
else {
if (length(x) != length(g))
stop("'x' and 'g' must have the same length")
DNAME <- paste(deparse(substitute(x)), "and",
deparse(substitute(g)))
OK <- complete.cases(x, g)
x <- x[OK]
g <- g[OK]
if (!all(is.finite(g)))
stop("all group levels must be finite")
g <- factor(g)
k <- nlevels(g)
if (k < 2)
stop("all observations are in the same group")
}
alternative <- match.arg(alternative)
p.adjust.method <- match.arg(p.adjust.method)
## rank version
x.rank <- rank(x)
R.bar <- tapply(x.rank, g, mean, na.rm = TRUE)
R.n <- tapply(!is.na(x), g, length)
k <- nlevels(g)
n <- sum(R.n)
METHOD <- "Conover's many-to-one test"
## Kruskal-Wallis statistic
H <- HStat(x.rank, g)
C <- gettiesKruskal(x.rank)
H.cor <- H / C
if (C == 1) {
S2 <- n * (n + 1) / 12
} else {
warning("Ties are present. Quantiles were corrected for ties.")
S2 <- ( 1 / (n - 1)) * (sum(x.rank^2) - (n * (((n + 1)^2) / 4)))
}
compare.stats <- function(i) {
dif <- R.bar[i] - R.bar[1]
B <- (1 / R.n[i] + 1 / R.n[1])
D <- (n - 1 - H.cor) / (n - k)
tval <- dif / sqrt(S2 * B * D)
return(tval)
}
if (p.adjust.method != "single-step"){
df <- n - k
STATISTIC <- rep(NA, k - 1)
for (j in 2:k) {
STATISTIC[j-1] <- compare.stats(j)
}
PVAL <- switch(alternative,
"two.sided" =
2 * pt(abs(STATISTIC), df=df, lower.tail=FALSE),
"greater" =
pt(STATISTIC, df=df, lower.tail=FALSE),
"less" =
pt(STATISTIC, df=df)
)
PVAL <- p.adjust(PVAL, method = p.adjust.method)
PARMS <- c(df = df)
DIST <- "t"
} else {
## correlation matrix
n0 <- R.n[1]
nn <- R.n[2:k]
kk <- k - 1
corr <- matrix(0, nrow = kk, ncol = kk)
corr <- diag(kk)
for ( i in 1:(kk-1)){
for (j in (i+1):kk){
corr[i,j] <- ((nn[i] * nn[j]) /
((nn[i] + n0) * (nn[j] + n0)))^(1/2)
corr[j,i] <- corr[i, j]
}
}
df <- length(x) - k
STATISTIC <- rep(NA, k - 1)
## Get statistic values
for (j in 2:k) {
STATISTIC[j-1] <- compare.stats(j)
}
## Get p-values from multivariate t-distribution
if (alternative == "two.sided") {
PVAL <- sapply(STATISTIC,
function(x) 1 - pmvt(lower= -rep(abs(x),kk),
upper=rep(abs(x), kk), df=df,
corr=corr))
} else if (alternative == "greater"){
PVAL <- sapply(STATISTIC,
function(x) 1 - pmvt(lower= -Inf,
upper=rep(x, kk), df=df,
corr=corr))
} else {
PVAL <- sapply(STATISTIC,
function(x) 1 - pmvt(lower= rep(x, kk),
upper=Inf, df=df, corr=corr))
}
## Names
PARMS <- c(k = kk, df = df)
DIST <- "t"
}
LNAME <- levels(g)[2:k]
PSTAT <- matrix(data=STATISTIC, nrow = (k-1), ncol = 1,
dimnames = list(LNAME, levels(g)[1]))
PVAL <- matrix(data=PVAL, nrow = (k-1), ncol = 1,
dimnames = list(LNAME, levels(g)[1]))
MODEL <- data.frame(x, g)
ans <- list(method = METHOD, data.name = DNAME, p.value = PVAL,
statistic = PSTAT, p.adjust.method = p.adjust.method,
dist = DIST, model = MODEL, alternative = alternative,
parameter = PARMS)
class(ans) <- "PMCMR"
ans
}
#' @rdname kwManyOneConoverTest
#' @method kwManyOneConoverTest formula
#' @aliases kwManyOneConoverTest.formula
#' @template one-way-formula
#' @export
kwManyOneConoverTest.formula <-
function(formula, data, subset, na.action, alternative = c("two.sided", "greater", "less"), p.adjust.method = c("single-step" ,p.adjust.methods),...)
{
mf <- match.call(expand.dots=FALSE)
m <- match(c("formula", "data", "subset", "na.action"), names(mf), 0L)
mf <- mf[c(1L, m)]
mf[[1L]] <- quote(stats::model.frame)
if(missing(formula) || (length(formula) != 3L))
stop("'formula' missing or incorrect")
mf <- eval(mf, parent.frame())
if(length(mf) > 2L)
stop("'formula' should be of the form response ~ group")
DNAME <- paste(names(mf), collapse = " by ")
alternative <- match.arg(alternative)
p.adjust.method <- match.arg(p.adjust.method)
names(mf) <- NULL
y <- do.call("kwManyOneConoverTest", c(as.list(mf),
alternative = alternative,
p.adjust.method=p.adjust.method))
y$data.name <- DNAME
y
}
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