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#############
# Fisher 23 #
#############
fisher23.model <- function() {
return(list(model=list(typ="Fisher 2-by-3")))
}
mutoss.fisher23.model <- function() { return(new(Class="MutossMethod",
label="Fisher's exact test in (2x3) tables",
callFunction="fisher23.model",
output=c("model"),
info="<h2></h2>
<p>(Marginal) Fisher's exact test in (2x3) tables</p>
<p></p>
<h3>Reference:</h3>
<ul>
<li>Fisher, R. A. (1922). \"<i>On the interpretation of Chi^2 from contingency tables, and the calculation of P.</i>\" Journal of the Royal Statistical Society, 85 (1):87-94.</li>
</ul>",
parameters=list(
)
)) }
fisher23.marginal <- function(data, model) {
#m <- dim(data)[3]
#result <- vector(mode="numeric",length=m)
result <- apply(data, 3, function(x) {fisher23_fast(x,2.0e-16)$rand_p} )
return(list(pValues=result))
}
fisher23_fast <- function(obs, epsilon){
# obs = observations = a 2x3 table
#build marginals = (n1., n2., n.1, n.2, n.3)
marginals <- c(sum(obs[1, ]), sum(obs[2, ]), sum(obs[, 1]), sum(obs[, 2]), sum(obs[, 3]))
n <- sum(marginals) / 2
x <- array(data=rep.int(0.0, 2*3*max(marginals)*max(marginals)), c(2, 3, max(marginals)*max(marginals)))
#build log nominator statistic
log_nom <- sum(log(gamma(marginals+1))) - log(gamma(n+1))
#build log denominator statistic
log_denom <- sum(log(gamma(obs+1)))
#compute probability of observed table
prob_table <- exp(log_nom - log_denom)
nonrand_p <- 0.0
rand_count <- 0
dim1 <- min(marginals[1], marginals[3])
#traverse all possible tables with given marginals
counter <- 0
for (k in 0:dim1)
{
for (l in max(0,marginals[1]-marginals[5]-k):min(marginals[1]-k, marginals[4]))
{
counter <- counter+1
x[1, 1, counter] <- k
x[1, 2, counter] <- l
x[1, 3, counter] <- marginals[1] - x[1, 1, counter] - x[1, 2, counter]
x[2, 1, counter] <- marginals[3] - x[1, 1, counter]
x[2, 2, counter] <- marginals[4] - x[1, 2, counter]
x[2, 3, counter] <- marginals[5] - x[1, 3, counter]
}
}
log_denom_iter <- rep.int(0.0, times=counter)
for (k in 1:counter)
{
log_denom_iter[k] <- sum(log(gamma(x[, , k]+1)))
}
prob_lauf <- exp(log_nom - log_denom_iter)
nonrand_p <- sum(prob_lauf[prob_lauf <= prob_table])
rand_count <- sum(abs(exp(prob_lauf) - exp(prob_table)) < epsilon)
u <- runif(1)
rand_p <- max(0.0, nonrand_p - u*rand_count*prob_table)
return(list(nonrand_p=nonrand_p, rand_p=rand_p, prob_table=prob_table))
}
#############
# Fisher 22 #
#############
fisher22.model <- function() {
return(list(model=list(typ="Fisher 2-by-2")))
}
mutoss.fisher22.model <- function() { return(new(Class="MutossMethod",
label="Fisher's exact test in (2x2) tables",
callFunction="fisher22.model",
output=c("model"),
info="<h2></h2>
<p>(Marginal) Fisher's exact test in (2x2) tables</p>
<p></p>
<h3>Reference:</h3>
<ul>
<li>Fisher, R. A. (1922). \"<i>On the interpretation of Chi^2 from contingency tables, and the calculation of P.</i>\" Journal of the Royal Statistical Society, 85 (1):87-94.</li>
</ul>",
parameters=list(
)
)) }
fisher22.marginal <- function(data, model) {
#m <- dim(data)[3]
#result <- vector(mode="numeric",length=m)
result <- apply(data, 3, function(x) {fisher22_fast(x,2.0e-16)$rand_p} )
return(list(pValues=result))
}
fisher22_fast <- function(obs, epsilon){
# obs = observations = a 2x2 table
#build marginals = (n1., n2., n.1, n.2)
marginals <- c(sum(obs[1, ]), sum(obs[2, ]), sum(obs[, 1]), sum(obs[, 2]))
n <- sum(obs)
x <- array(data=rep.int(0.0, 2*2*max(marginals)*max(marginals)), c(2, 2, max(marginals)*max(marginals)))
#build log nominator statistic
log_nom <- sum(log(gamma(marginals+1))) - log(gamma(n+1))
#build log denominator statistic
log_denom <- sum(log(gamma(obs+1)))
#compute probability of observed table
prob_table <- exp(log_nom - log_denom)
nonrand_p <- 0.0
rand_count <- 0
dim1 <- min(marginals[1], marginals[3])
#traverse all possible tables with given marginals
counter <- 0
for (k in (marginals[1]-marginals[4]):dim1)
{
counter <- counter+1
x[1, 1, counter] <- k
x[1, 2, counter] <- marginals[1] - k
x[2, 1, counter] <- marginals[3] - k
x[2, 2, counter] <- marginals[2] - x[2, 1, counter]
}
log_denom_iter <- rep.int(0.0, times=counter)
for (k in 1:counter)
{
log_denom_iter[k] <- sum(log(gamma(x[, , k]+1)))
}
prob_lauf <- exp(log_nom - log_denom_iter)
nonrand_p <- sum(prob_lauf[prob_lauf <= prob_table])
rand_count <- sum(abs(exp(prob_lauf) - exp(prob_table)) < epsilon)
u <- runif(1)
rand_p <- max(0.0, nonrand_p - u*rand_count*prob_table)
return(list(nonrand_p=nonrand_p, rand_p=rand_p, prob_table=prob_table))
}
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