pzcor: Test for Equal Zero Order and (Semi) Partial Correlation

Description

Compute a bootstrap test to determine whether zero order correlation is equal to partial or semi-partial correlation.

Usage

pzcor(x, y, z, semi = FALSE, k = 1000, method = "pearson",
  test = "eq")

Arguments

a numeric vector.

a numeric vector (data.frame, matrix, etc.)

semi

logical. If TRUE, then the semi-partial correlation between x and y given z is used. If FALSE (default), then the partial correlation between x given z and y given z is used.

the number of bootstrap samples taken (default is 1000).

method

a character string indicating which correlation coefficient is to be computed. One of "pearson" (default), "kendall", or "spearman" can be abbreviated.

test

character string denoting the null hypothesis to be tested. Can be one of the three:

'eq' tests \(\rho.xy - \rho.xy.z = 0\) (default)
'gt' tests \(\rho.xy - \rho.xy.z \ge 0\)
'lt' tests \(\rho.xy - \rho.xy.z \le 0\)

Value

acceleration

the acceleration used for the BCa method.

alpha

the proportion of the bootstrapped distribution below zero.

bias

the bias used for the BCa method.

call

shows the function call.

difference

calculated from the data. Same as p.xy - p.xy.z.

distribution

the estimated distribution of the difference as determined through bootstrapping.

k_eff

the number of successful bootstrap samples. Less than or equal to k.

method

the method of correlation used.

p.value

significance level of the test.

p.xy

Zero order correlation between x and y.

p.xy.z

(semi) partial correlation between x and y while accounting for z.

semi

logical. If TRUE, p.xy.z is the semi-partial correlation. Otherwise p.xy.z is the partial correlation.

test

shows the type of test performed.

Details

Uses the bias-corrected and accelerated (BCa) bootstrap method to test if the difference \(\rho.xy - \rho.xy.z\) is equal to, above, or below zero where \(\rho.xy\) is the zero order correlation between variables \(x\) and \(y\), and \(\rho.xy.z\) is the (semi) partial correlation between the respective variables after partialing out variables represented by \(z\).

If the bootstrap distribution of \(\rho.xy - \rho.xy.z\) is strictly above or below zero, then the p-value provided is the most extreme value that can be determined by the test. In the case of highly correlated variables, the covariance matrix may be singular which will lead to k_eff being less than k (as \(\rho.xy - \rho.xy.z\) would not be computed).

Examples

Run this code

# NOT RUN {
require(graphics)
require(MASS)
# data
set.seed(1111)
mu <- rep(0,4)
Sigma <- matrix(.2, nrow=4, ncol=4) + diag(4)*.8
data <- mvrnorm(n=100, mu=mu, Sigma=Sigma)

# p.(1,2) = p.(1,2)|(3,4) test
test <- pzcor(data[,1], data[,2], data[,c(3,4)], k = 1000, semi = FALSE,
              test = 'eq')
hist(test$distribution)
test
# }