Circular-linear correlation

Implementation of the circular-linear correlation measure introduced by Mardia (1976) and Johnson and Wehrly (1977) as cited in Jammalamadaka & Sengupta (2001).

Usage

circ_lin_corr(circ_x, lin_x, na.rm = FALSE)

Arguments

circ_x

circular variable

lin_x

linear variable

na.rm

a logical value indicating whether NA values should be removed before the computation proceeds

Value

circular-linear correlation measure

Details

This measure is computed as \[r^2 = (r_{xc}^2+r_{xs}^2-2 r_{xc} r_{xs}r_{cs})/(1-r_{cs}^2)\] where \(r_{xc} = corr(x, cos(\alpha))\), \(r_{xs} = corr(x, sin(\alpha))\), \(r_{cs} = corr(cos(\alpha), sin(\alpha))\), and \(\alpha\) and \(x\) are the circular and linear variables, respectively.

References

Jammalamadaka, S. R., & SenGupta, A. (2001). Topics in Circular Statistics. WORLD SCIENTIFIC. doi:10.1142/4031

Examples

set.seed(1)
x <- rnorm(50)
a <- rnorm(50, sd = 0.4)
circ_lin_corr(x + a, x)
#> [1] 0.864586