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####################################################################################################################################
### Filename: f2.R
### Description: Function for calculating the test statistic for one whole- and one subplot factor
###
###
###
####################################################################################################################################
#' Test for interaction of factor A and B
#'
#' @param X dataframe containing the data in the long table format
#' @param alpha alpha level used for the test
#' @param group column name of the data frame X specifying the groups
#' @param factor1 column name of the data frame X of the first factor variable
#' @param subject column name of the data frame X identifying the subjects
#' @param data column name of the response variable
#' @param H string specifying the hypothesis
#' @param text a string, which will be printed in the output
#' @return Returns a data frame consisting of the degrees of freedom, the test value, the critical value and the p-value
#' @keywords internal
hrm.1w.1f <- function(X, alpha, group , factor1, subject, data, H, text, nonparametric, ranked, varQGlobal, np.correction, tmpQ1g, tmpQ2g ){
stopifnot(is.data.frame(X),is.character(subject), is.character(group),is.character(factor1), alpha<=1, alpha>=0, is.logical(nonparametric))
f <- 0
f0 <- 0
crit <- 0
test <- 0
group <- as.character(group)
factor1 <- as.character(factor1)
subject <- as.character(subject)
X <- as.data.table(X)
setnames(X, c(data, group, factor1, subject), c("data", "group", "factor1", "subject"))
a <- nlevels(X[,group])
d <- nlevels(X[,factor1])
c <- 1
n <- table(X[,group])/d
if(nonparametric & is.null(ranked)) {
X[,data:= 1/(sum(n)*d)*(pseudorank(X[,data], X[, group]) - 1/2)]
}
X <- split(X, X[,group], drop=TRUE)
for(i in 1:a){
X[[i]] <- X[[i]][ order(subject, factor1), ]
X[[i]] <- X[[i]][,data]
X[[i]] <- matrix(X[[i]],ncol=d*c,byrow=TRUE)
n[i] <- dim(X[[i]])[1]
}
if(is.null(ranked)){
eval.parent(substitute(ranked<-X))
} else {
X <- data.table::copy(ranked)
}
# creating X_bar
X_bar <- as.matrix(vec(sapply(X, colMeans, na.rm=TRUE)))
eval.parent(substitute(means <- X_bar))
kdim <- 1
if(H=="A"){
K <- 1/d*J(d)
S <- diag(n)-1/sum(n)*tcrossprod(n,n)
} else if(H=="Au"){
K <- 1/d*J(d)
S <- P(a)
} else if(H=="B"){
K <- P(d)
S <- 1/a*J(a)
kdim <- d
} else if(H=="AB"){
K <- P(d)
S <- P(a)
kdim <- d
} else if(H=="A|B"){
K <- I(d)
S <- P(a)
kdim <- 1
}else if(H=="B|A"){
K <- P(d)
S <- I(a)
kdim <- d
}
# creating dual empirical covariance matrices
K_AB <- kronecker(S, K)
V <- lapply(X, DualEmpirical2, B=K)
##########################
### U statistics
#########################
Q <- data.frame(Q1 = rep(0,a), Q2 = rep(0,a))
if(nonparametric){
for(i in 1:a){
Q[i,] <- calcU(X,n,i,K)
}
}
eval.parent(substitute(correction <- np.correction))
if(is.na(np.correction)) {
eval.parent(substitute(correction <- (d >= max(n))))
np.correction <- (kdim >= max(n))
}
if(np.correction & nonparametric) {
if(H == "AB" | H == "B") {
for(gg in 1:a) {
# not yet calculated
if(is.null(tmpQ1g) & is.null(tmpQ2g)) {
tmp <- X[[gg]]%*%K
nr <- dim(tmp)[1]
if(nr%%2 == 1){
nr <- nr - 1
}
mm <- colMeans(tmp)
g <- rep(0,nr)
g2 <- vector("list", length = nr)
t2 <- matrix(rep(0,d^2), ncol = d)
for(i in 1:nr) {
g[i] <- t(tmp[i,] - mm) %*% (tmp[i,] - mm)
g2[[i]] <- (tmp[i,] - mm) %*% t(tmp[i,] - mm)
t2 <- t2 + g2[[i]]
}
reps <- min(150, choose(nr,nr/2))
#reps <- min(500, choose(nr,nr/2))
covs <- rep(0,reps)
g1 <- rep(0, nr/2)
g12 <- rep(0, nr/2)
for(i in 1:reps) {
grp <- sample(c(rep(1,nr/2), rep(2,nr/2)))
g1 <- g[grp == 1]
g12 <- g[grp == 2]
covs[i] <- cov(g1,g12)
}
t4 <- rep(0, nr*(nr - 1)/2)
k <- 1
#t2 <- matrix(rep(0,d^2), ncol = d)
for(i in 1:nr) {
j <- i + 1
while(j <= nr) {
t4[k] <- matrix.trace(g2[[i]]%*%g2[[j]])
k <- k + 1
j <- j + 1
}
}
# for(i in 1:(nr/2)) {
# t2 <- t2 + g2[[i]] + g2[[(nr/2) + i]]
# }
corr <- mean(covs)
corr2 <- mean(t4) - matrix.trace((1/nr*t2)*(1/nr*t2))
tmpQ1 <- Q[gg,1] - corr*(n[gg]^2*1/(n[gg]^2 - n[gg]))^2
tmpQ2 <- Q[gg,2] - corr2*(n[gg]^2*1/(n[gg]^2 - n[gg]))^2
eval.parent(substitute(tmpQ1g <- tmpQ1))
eval.parent(substitute(tmpQ2g <- tmpQ2))
}
# already calculated
if(!is.null(tmpQ1g) & !is.null(tmpQ2g)) {
tmpQ1 <- tmpQ1g
tmpQ2 <- tmpQ2g
}
if(tmpQ1 > 0) {
Q[gg,1] <- tmpQ1
}
if(tmpQ2 > 0) {
Q[gg,2] <- tmpQ2
}
}
}
}
#################################################################################################
# f
f_1 <- 0
f_2 <- 0
for(i in 1:a){
f_1 <- f_1 + (S[i,i]*1/n[i])^2*.E1(n,i,V[[i]],nonparametric,Q)
j <- i+1
while(j<=a){
f_1 <- f_1 + 2*(S[i,i]*1/n[i])*(S[j,j]*1/n[j])*.E3(V[[i]],V[[j]])
j <- j+1
}
}
for(i in 1:a){
f_2 <- f_2 + (S[i,i]*1/n[i])^2*.E2(n,i,V[[i]],nonparametric,Q)
j <- i+1
while(j<=a){
f_2 <- f_2 + 2*S[i,j]*S[j,i]*1/(n[i]*n[j])*.E4(1/(n[i]-1)*P(n[i])%*%X[[i]], 1/(n[j]-1)*K%*%t(X[[j]])%*%P(n[j])%*%X[[j]]%*%K%*%t(X[[i]])%*%P(n[i]))
j <- j+1
}
}
f <- f_1/f_2
##################################################################################################
#################################################################################################
# f0
f0_1 <- f_1
f0_2 <- 0
for(i in 1:a){
f0_2 <- f0_2 + (S[i,i]*1/n[i])^2*1/(n[i]-1)*.E2(n,i,V[[i]],nonparametric,Q)
}
f0 <- f0_1/f0_2
##################################################################################################
f <- abs(f)
# critical value
crit <- qf(1-alpha,f,f0)
# variance estimator
direct <- direct.sum(1/n[1]*var(X[[1]]),1/n[2]*var(X[[2]]))
if(a>2){
for(i in 3:a) {
direct <- direct.sum(direct, 1/n[i]*var(X[[i]]))
}
}
eval.parent(substitute(varQGlobal <- direct))
den_one <- rep(1, dim(K_AB)[1])
test <- crossprod(X_bar, crossprod(K_AB, X_bar))/(crossprod(den_one, crossprod(K_AB*direct, den_one)))
p.value <- 1-pf(test,f,f0)
output <- data.frame(hypothesis=text,df1=f,df2=f0, crit=crit, test=test, p.value=p.value, sign.code=.hrm.sigcode(p.value))
if(nonparametric) {
output$np.correction <- np.correction
}
return (output)
}
# End ------------------------------------------------------------
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