Partial and Semi-partial correlation

Source: R/partial.cor.R

Calculates a partial or semi-partial correlation with parametric and nonparametric options

partial.cor(
  x,
  y,
  z,
  method = c("partial", "semipartial"),
  statistic = c("kendall", "pearson", "spearman")
)

Arguments

x

A vector, data.frame or matrix with 3 columns
y

A vector same length as x
z

A vector same length as x
method

Type of correlation: "partial" or "semipartial"
statistic

Correlation statistic, options are: "kendall", "pearson", "spearman"

Value

data.frame containing:

  • correlation correlation coefficient

  • p.value p-value of correlation

  • test.statistic test statistic

  • n sample size

  • Method indicating partial or semipartial correlation

  • Statistic the correlation statistic used

Details

Partial and semipartial correlations show the association between two variables when one or more peripheral variables are controlled to hold them constant.

Suppose we have three variables, X, Y, and Z. Partial correlation holds constant one variable when computing the relations two others. Suppose we want to know the correlation between X and Y holding Z constant for both X and Y. That would be the partial correlation between X and Y controlling for Z. Semipartial correlation holds Z constant for either X or Y, but not both, so if we wanted to control X for Z, we could compute the semipartial correlation between X and Y holding Z constant for X.

Author

Jeffrey S. Evans <jeffrey_evans@tnc.org>

Examples

air.flow = stackloss[,1]
water.temperature = stackloss[,2]
acid = stackloss[,3]

# Partial using Kendall (nonparametric) correlation
partial.cor(air.flow, water.temperature, acid)

#>   correlation      p.value test.statistic  n  Method Statistic
#> 1   0.5528912 0.0006538091        3.40825 21 partial   kendall

scholar <- data.frame(
  HSGPA=c(3.0, 3.2, 2.8, 2.5, 3.2, 3.8, 3.9, 3.8, 3.5, 3.1), 
   FGPA=c(2.8, 3.0, 2.8, 2.2, 3.3, 3.3, 3.5, 3.7, 3.4, 2.9),
  SATV =c(500, 550, 450, 400, 600, 650, 700, 550, 650, 550)) 

# Standard Pearson's correlations between HSGPA and FGPA  
cor(scholar[,1], scholar[,2])

#> [1] 0.9226187

# Partial correlation using Pearson (parametric) between HSGPA 
#   and FGPA, controlling for SATV
partial.cor(scholar, statistic="pearson")

#>   correlation    p.value test.statistic  n  Method Statistic
#> 1   0.7475739 0.02057438       2.977956 10 partial   pearson

# Semipartial using Pearson (parametric) correlation 
partial.cor(x=scholar[,2], y=scholar[,1], z=scholar[,3], 
            method="semipartial", statistic="pearson")

#>   correlation   p.value test.statistic  n      Method Statistic
#> 1   0.4337853 0.2434054        1.27377 10 semipartial   pearson