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#############################################################
# #
# Original Splus: Ulric Lund #
# E-mail: ulund@calpoly.edu #
# #
#############################################################
#############################################################
# #
# mle.vonmises.bootstrap.ci function #
# Author: Claudio Agostinelli #
# Email: claudio@unive.it #
# Date: November, 06, 2013 #
# Copyright (C) 2013 Claudio Agostinelli #
# #
# Version 0.3-3 #
#############################################################
mle.vonmises.bootstrap.ci <- function(x, mu=NULL, bias = FALSE, alpha = 0.05, reps = 1000, control.circular=list()) {
# Handling missing values
x <- na.omit(x)
if (length(x)==0) {
warning("No observations (at least after removing missing values)")
return(NULL)
}
if (is.circular(x)) {
datacircularp <- circularp(x)
} else
if (is.circular(mu)) {
datacircularp <- circularp(mu)
} else {
datacircularp <- list(type="angles", units="radians", template="none", modulo="asis", zero=0, rotation="counter")
}
dc <- control.circular
if (is.null(dc$type))
dc$type <- datacircularp$type
if (is.null(dc$units))
dc$units <- datacircularp$units
if (is.null(dc$template))
dc$template <- datacircularp$template
if (is.null(dc$modulo))
dc$modulo <- datacircularp$modulo
if (is.null(dc$zero))
dc$zero <- datacircularp$zero
if (is.null(dc$rotation))
dc$rotation <- datacircularp$rotation
x <- conversion.circular(x, units="radians", zero=0, rotation="counter", modulo="2pi")
attr(x, "class") <- attr(x, "circularp") <- NULL
if (is.null(mu)) {
sinr <- sum(sin(x))
cosr <- sum(cos(x))
mu <- atan2(sinr, cosr)
} else {
mu <- conversion.circular(mu, units="radians", zero=0, rotation="counter", modulo="2pi")
attr(mu, "class") <- attr(mu, "circularp") <- NULL
}
result <- MleVonmisesBootstrapCiRad(x, mu, bias, alpha, reps)
result$mu <- conversion.circular(circular(result$mu), dc$units, dc$type, dc$template, dc$modulo, dc$zero, dc$rotation)
result$mu.ci <- conversion.circular(circular(result$mu.ci), dc$units, dc$type, dc$template, dc$modulo, dc$zero, dc$rotation)
result$call <- match.call()
result$alpha <- alpha
class(result) <- "mle.vonmises.bootstrap.ci"
return(result)
}
MleVonmisesBootstrapCiRad <- function(x, mu, bias, alpha, reps) {
mean.bs <- boot(data = x, statistic = MleVonmisesMuRad, R = reps, stype="i")
mean.reps <- mean.bs$t
mean.reps <- sort(mean.reps %% (2 * pi))
spacings <- c(diff(mean.reps), mean.reps[1] - mean.reps[reps] + 2 * pi)
max.spacing <- (1:reps)[spacings == max(spacings)]
off.set <- 2 * pi - mean.reps[max.spacing + 1]
if (max.spacing != reps)
mean.reps2 <- mean.reps + off.set
else
mean.reps2 <- mean.reps
mean.reps2 <- sort(mean.reps2 %% (2 * pi))
mean.ci <- quantile(mean.reps2, c(alpha/2, 1 - alpha/2))
if (max.spacing != reps)
mean.ci <- mean.ci - off.set
kappa.bs <- boot(data = x, statistic = MleVonmisesKappaRad, R = reps, stype="i", mu=mu, bias = bias)
kappa.reps <- kappa.bs$t
kappa.ci <- quantile(kappa.reps, c(alpha/2, 1 - alpha/2))
result <- list()
result$mu.ci <- mean.ci
result$mu <- c(mean.reps)
result$kappa.ci <- kappa.ci
result$kappa <- c(kappa.reps)
return(result)
}
MleVonmisesMuRad <- function(x, i) {
sinr <- sum(sin(x[i]))
cosr <- sum(cos(x[i]))
mu <- atan2(sinr, cosr)
return(mu)
}
MleVonmisesKappaRad <- function(x, i, mu, bias) {
n <- length(x[i])
V <- mean(cos(x[i] - mu))
if (V > 0) {
kappa <- A1inv(V)
} else {
kappa <- 0
}
if (bias == TRUE) {
if (kappa < 2) {
kappa <- max(kappa - 2 * (n * kappa)^-1, 0)
} else {
kappa <- ((n - 1)^3 * kappa)/(n^3 + n)
}
}
return(kappa)
}
#############################################################
# #
# print.mle.vonmises.bootstrap.ci function #
# Author: Claudio Agostinelli #
# Email: claudio@unive.it #
# Date: September, 17, 2003 #
# Copyright (C) 2003 Claudio Agostinelli #
# #
# Version 0.1 #
#############################################################
print.mle.vonmises.bootstrap.ci <- function(x, ...) {
cat("Bootstrap Confidence Intervals for Mean Direction and Concentration", "\n")
cat("Confidence Level: ", round(100 * (1 - x$alpha),2), "%", "\n")
cat("Mean Direction: ", "Low =", round(x$mu.ci[1], 2), " High =", round(x$mu.ci[2], 2), "\n")
cat("Concentration Parameter: ", "Low =", round(x$kappa.ci[1], 2), " High =", round(x$kappa.ci[2], 2), "\n")
}
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