multid (version 1.0.2)

qcc: Quantile correlation coefficient

Description

For computation of tail dependence as correlations estimated at different variable quantiles (Choi & Shin, 2022; Lee et al., 2022) summarized across two quantile regression models where x and y switch roles as independent/dependent variables.

Usage

qcc(
  x,
  y,
  tau = c(0.1, 0.5, 0.9),
  data,
  method = "br",
  boot_n = NULL,
  ci_level = 0.95
)

Value

r

Pearson's correlation estimate for comparison.

rho_tau

Correlations at different tau values (quantiles).

r_boot_est

Pearson's correlation bootstrap estimates.

rho_tau_boot_est

Bootstrap estimates for correlations at different tau values (quantiles).

Arguments

x

Name of x variable. Character string.

y

Name of y variable. Character string.

tau

The quantile(s) to be estimated. A vector of values between 0 and 1, default c(.1,.5,.9). @seealso rq

data

Data frame.

method

The algorithmic method used to compute the fit (default "br"). @seealso rq

boot_n

Number of bootstrap redraws (default NULL = no bootstrap inference).

ci_level

Level for percentile bootstrap confidence interval. Numeric values between 0 and 1. Default .95.

Details

Note that when quantile regression coefficients for y on x and x on y have a different sign, the quantile correlation is defined as zero (see Choi & Shin, 2022, p. 1080).

References

Choi, J.-E., & Shin, D. W. (2022). Quantile correlation coefficient: A new tail dependence measure. Statistical Papers, 63(4), 1075–1104. https://doi.org/10.1007/s00362-021-01268-7

Lee, J. A., Bardi, A., Gerrans, P., Sneddon, J., van Herk, H., Evers, U., & Schwartz, S. (2022). Are value–behavior relations stronger than previously thought? It depends on value importance. European Journal of Personality, 36(2), 133–148. https://doi.org/10.1177/08902070211002965

Examples

set.seed(2321)
d <- data.frame(x = rnorm(2000))
d$y <- 0.10 * d$x + (0.20) * d$x^2 + 0.40 * d$x^3 + (-0.20) * d$x^4 + rnorm(2000)
qcc_boot <- qcc(x = "x", y = "y", data = d, tau = 1:9 / 10, boot_n = 50)
qcc_boot$rho_tau