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################################
#### Cicrular correlation for cicular data II
#### Tsagris Michail 3/2014
#### mtsagris@yahoo.gr
#### References: Mardia Kanti V. and Jupp Peter E. (2000)
#### Directional statistics
################################
circ.cors2 <- function(theta, phi, rads = FALSE) {
## theta and phi are angular data in degrees or radians
## by default they are in degrees
n <- length(theta) ## sample size
## if the data are in degrees we transform them into radians
if ( !rads ) {
theta <- theta * pi/180
phi <- phi * pi/180
}
costheta <- cos(theta)
cosphi <- cos(phi)
sintheta <- sin(theta)
sinphi<- sin(phi)
rcc <- cor(costheta, cosphi)
rcs <- cor(costheta, sinphi)
rss <- cor(sintheta, sinphi)
rsc <- cor(sintheta, cosphi)
r1 <- cor(costheta, sintheta)
r2 <- Rfast::corpairs(cosphi, sinphi)
up <- rcc^2 + rcs^2 + rsc^2 + rss^2 + 2 * (rcc * rss + rcs * rsc) * r1 * r2 -
2 * (rcc * rcs + rsc * rss) * r2 - 2 * (rcc * rsc + rcs * rss) * r1
down <- (1 - r1^2) * (1 - r2^2)
rho <- up/down
test <- n * rho^2
pvalue <- pchisq(test, 4, lower.tail = FALSE)
res <- c(rho, pvalue)
names(res) <- c("rho", "p-value")
res
}
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