circ_cor {BAMBI}

Sample circular correlation coefficients

Description

Sample circular correlation coefficients

Usage

circ_cor(
  x,
  type = "js",
  alternative = "two.sided",
  jackknife = FALSE,
  bootse = FALSE,
  n.boot = 100
)

Arguments

x

two column matrix. NA values are not allowed.

type

type of the circular correlation. Must be one of "fl", "js", "tau1" and "tau2". See details.

alternative

one of "two.sided", "less" or "greater" (defaults to "two.sided"). Hypothesis test is performed only when type is either "fl" or "js", in which case asymptotic standard error of the estimator is used to construct the test statistic.

jackknife

logical. Compute jackknifed estimate and standard error? Defaults to FALSE.

bootse

logical. Compute bootstrap standard error? Defaults to FALSE.

n.boot

number of bootstrapped samples to compute bootstrap standard error. Defaults to 100. Ignored if bootse if FALSE.

Details

circ_cor calculates the (sample) circular correlation between the columns of x. Two parametric (the Jammalamadaka-Sarma (1988, equation 2.6) form "js", and the Fisher-Lee (1983, Section 3) form "fl") and two non-parametric (two versions of Kendall's tau) correlation coefficients are considered. The first version of Kendall's tau ("tau1") is based on equation 2.1 in Fisher and Lee (1982), whereas the second version ("tau2") is computed using equations 6.7-6.8 in Zhan et al (2017).

The cost-complexity for "js", "fl", "tau2" and "tau1" are O(n), O(n^2), O(n^2) and O(n^3) respectively, where n denotes the number of rows in x. As such, for large n evaluation of "tau1" will be slow.

References

Fisher, N. I. and Lee, A. J. (1982). Nonparametric measures of angular-angular association. Biometrika, 69(2), 315-321.

Fisher, N. I. and Lee, A. J. (1983). A correlation coefficient for circular data. Biometrika, 70(2):327-332.

Jammalamadaka, S. R. and Sarma, Y. (1988). A correlation coefficient for angular variables. Statistical theory and data analysis II, pages 349-364.

Zhan, X., Ma, T., Liu, S., & Shimizu, K. (2017). On circular correlation for data on the torus. Statistical Papers, 1-21.

Examples

# generate data from vmsin model
set.seed(1)
dat <- rvmsin(100, 2,3,-0.8,0,0)

# now calculate circular correlation(s) between the 2 columns of dat
circ_cor(dat, type="js")
circ_cor(dat, type="fl")
circ_cor(dat, type="tau1")
circ_cor(dat, type="tau2")