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##########################################################################################################
#
# pwrRasch: Statistical Power Simulation for Testing the Rasch Model
#
# Internal function: Computation of Three-Way ANOVA for balanced design
#
# Authors: Takuya Yanagida <takuya.yanagida@univie.ac.at>
# Jan Steinfeld <jan.steinfeld@univie.ac.at>
#
##########################################################################################################
aov.rasch.sim <- function(data) {
group <- data$group
person <- data$person
item <- data$item
response <- data$response
a <- length(unique(group))
b <- length(unique(person))
c <- length(unique(item))
###
SS.T <- (1/(a*b/a*c))*sum(response)^2
SS.A <- sum(rowsum(response, group)^2)*(1/(b/a*c))
SS.B <- sum(rowsum(response, person)^2)*(1/c)
SS.C <- sum(rowsum(response, item)^2)*(1/(a*b/a))
###
SS.interm. <- c(rowsum(response[group == 1], item[group == 1]), rowsum(response[group == 2], item[group == 2]))
SS.BC <- sum(SS.interm.)
SS.AC <- sum(SS.interm.^2)*(1/(b/a))
###
F.AC <- ((SS.AC - SS.A - SS.C + SS.T)/(c - 1)) / ((SS.BC - SS.B - SS.AC + SS.A)/(a*(b/a - 1)*(c - 1)))
p.AC <- pf(F.AC, c - 1, a*(b/a - 1)*(c - 1), lower.tail = FALSE)
return(p.AC)
}
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