cor_cyl {cylcop}

Estimate a Rank-Based Circular-Linear Correlation Coefficient

Description

The code is based on Mardia (1976), Solow et al. (1988) and Tu (2015). The function returns a numeric value between 0 and 1, not -1 and 1, positive and negative correlation cannot be discerned. Note also that the correlation coefficient is independent of the marginal distributions.

Usage

cor_cyl(theta, x)

Arguments

theta

numeric vector of angles (measurements of a circular variable).

x

numeric vector of step lengths (measurements of a linear variable).

Value

A numeric value between 0 and 1, the circular-linear correlation coefficient.

References

Mardia KV (1976). “Linear-Circular Correlation Coefficients and Rhythmometry.” Biometrika, 63(2), 403–405. ISSN 00063444, doi:10.2307/2335637.

Solow AR, Bullister JL, Nevison C (1988). “An application of circular-linear correlation analysis to the relationship between Freon concentration and wind direction in Woods Hole, Massachusetts.” Environmental Monitoring and Assessment, 10(3), 219–228. ISSN 1573-2959, doi:10.1007/BF00395081, https://doi.org/10.1007/BF00395081.

Tu R (2015). “A Study of the Parametric and Nonparametric Linear-Circular Correlation Coefficient.” California Polytechnic State University, San Luis Obispo, 1–24. https://digitalcommons.calpoly.edu/statsp/51/.

Hodel FH, Fieberg JR (2021). “Cylcop: An R Package for Circular-Linear Copulae with Angular Symmetry.” bioRxiv. doi:10.1101/2021.07.14.452253, https://www.biorxiv.org/content/10.1101/2021.07.14.452253v3/.

See Also

mi_cyl(), fit_cylcop_cor().

Examples

set.seed(123)

cop <- cyl_quadsec(0.1)

#draw samples and calculate the correlation coefficient
sample <- rcylcop(100, cop)
cor_cyl(theta = sample[,1], x = sample[,2])

#the correlation coefficient is independent of the marginal distribution.
sample <- traj_sim(100,
  cop,
  marginal_circ = list(name = "vonmises", coef  = list(0, 1)),
  marginal_lin = list(name = "weibull", coef = list(shape = 2))
)
cor_cyl(theta = sample$angle, x = sample$steplength)
cor_cyl(theta = sample$cop_u, x = sample$cop_v)

# Estimate correlation of samples drawn from circular-linear copulas with
# perfect correlation
cop <- cyl_rect_combine(copula::normalCopula(1))
sample <- rcylcop(100, cop)
cor_cyl(theta = sample[,1], x = sample[,2])