R/hcf.boot.R In Directional: A Collection of Functions for Directional Data Analysis

Documented in hcf.boot

```hcf.boot <- function(x1, x2, fc = TRUE, B = 999) {

n1 <- dim(x1)[1]    ;  n2 <- dim(x2)[1]
x <- rbind(x1, x2)
ina <- c( rep(1, n1), rep(2, n2) )
ni <- c(n1, n2)
p <- dim(x)[2]  ## dimensionality of the data
n <- n1 + n2  ## sample size of the data
S <- rowsum(x, ina)
m1 <- S[1, ]   ;   m2 <- S[2, ]
m1 <- m1 / sqrt( sum(m1^2) )
m2 <- m2 / sqrt( sum(m2^2) )
Ri <- sqrt( Rfast::rowsums(S^2) )  ## the resultant length of each group
S <- Rfast::colsums(x)
R <- sqrt( sum(S^2) )  ## the resultant length based on all the data
## Next we stimate the common concentration parameter kappa
m <- S / R
kapaa <- Directional::vmf.mle(x, fast = TRUE)\$kappa
## kapaa is the estimated concentration parameter based on all the data
Ft <- (n - 2) * ( sum(Ri) - R) / ( n - sum(Ri) )
if (fc) {  ## correction is used
if (p == 3) {
Ft <- kapaa * (1/kapaa - 1/(5 * kapaa^3)) * Ft
} else if (p > 3)  Ft <- kapaa * ( 1/kapaa - (p - 3)/(4 * kapaa^2) - (p - 3)/(4 * kapaa^3) ) * Ft
}

rot1 <- t( Directional::rotation(m1, m) )
rot2 <- t( Directional::rotation(m2, m) )
y1 <- x1 %*% rot1
y2 <- x2 %*% rot2
ftb <- numeric(B)

for (i in 1:B) {
b1 <- Rfast2::Sample.int(n1, n1, replace = TRUE)
b2 <- Rfast2::Sample.int(n2, n2, replace = TRUE)
yb <- rbind(y1[b1, ], y2[b2, ])
S <- rowsum(yb, ina)
Ri <- sqrt( Rfast::rowsums(S^2) )
S <- Rfast::colsums(yb)
R <- sqrt( sum(S^2) )
ftb[i] <- (n - 2) * ( sum(Ri) - R) / ( n - sum(Ri) )
if (fc) {  ## correction is used
kapa <- Directional::vmf.mle(yb, fast = TRUE)\$kappa
if (p == 3) {
ftb[i] <- kapa * (1/kapa - 1/(5 * kapa^3)) * ftb[i]
} else if (p > 3)  ftb[i] <- kapa * ( 1/kapa - (p - 3)/(4 * kappa^2) - (p - 3)/(4 * kapa^3) ) * ftb[i]
}
}

p.value <- ( sum(ftb > Ft) + 1 ) / (B + 1)
statistic <- Ft  ;   names(statistic) <- "Bootstrap hcf test statistic"
parameter <- "NA"     ;   names(parameter) <- "df"
alternative <- "The 2 directional mean vector differ"
method <- "Bootstrap ANOVA for 2 directional mean vectors using the high concentration test"
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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Directional documentation built on Oct. 12, 2023, 1:07 a.m.