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################################
#### ANOVA for hyper-spherical data (Heterogeneous case, kappas not equal)
#### Tsagris Michail 1/2015
#### mtsagris@yahoo.gr
#### References: Mardia Kanti V. and Jupp Peter E. (2000)
#### Directional statistics, page 228
################################
het.aov <- function(x, ina) {
## x contains all the data
## ina is an indicator variable of each sample
ina <- as.numeric(ina)
g <- max(ina) ## how many groups are there
p <- dim(x)[2] ## dimensionality of the data
ni <- tabulate(ina) ## group sample sizes
kapa <- numeric(g)
mi <- rowsum(x, ina) / ni
for (i in 1:g) kapa[i] <- Directional::vmf.mle( x[ina == i, ], fast = TRUE )$kappa
tw <- Rfast::colsums(kapa * ni * mi)
Tt <- 2 * ( sum( kapa * ni * sqrt( Rfast::rowsums(mi^2) ) ) - sqrt( sum(tw^2) ) )
p.value <- pchisq(Tt, (g - 1) * (p - 1), lower.tail = FALSE)
statistic <- Tt ; names(statistic) <- "chi-square test statistic"
parameter <- (g - 1) * (p - 1) ; names(parameter) <- "df"
alternative <- "At least one directional mean vector differs"
method <- "ANOVA for directional data using the heterogeneous approach"
data.name <- c("data ", " groups")
result <- list( statistic = statistic, parameter = parameter, p.value = p.value,
alternative = alternative, method = method, data.name = data.name )
class(result) <- "htest"
return(result)
}
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