Find the Correlations for a Set x of Variables With Set y Removed

A straightforward application of matrix algebra to remove the effect of the variables in the y set from the x set. Input may be either a data matrix or a correlation matrix. Variables in x and y are specified by location.

CorPart(m, x, y)

Arguments

m

a data or correlation matrix.

x

the variable numbers associated with the X set.

y

the variable numbers associated with the Y set.

Details

It is sometimes convenient to partial the effect of a number of variables (e.g., sex, age, education) out of the correlations of another set of variables. This could be done laboriously by finding the residuals of various multiple correlations, and then correlating these residuals. The matrix algebra alternative is to do it directly.

Value

The matrix of partial correlations.

References

Revelle, W. An introduction to psychometric theory with applications in R Springer.
(working draft available at http://personality-project.org/r/book/

Author

William Revelle

See also

cor

Examples

# example from Bortz, J. (1993) Statistik fuer Sozialwissenschaftler, Springer, pp. 413

abstr <- c(9,11,13,13,14,9,10,11,10,8,13,7,9,13,14)
coord <- c(8,12,14,13,14,8,9,12,8,9,14,7,10,12,12)
age <- c(6,8,9,9,10,7,8,9,8,7,10,6,10,10,9)

# calculate the correlation of abstr and coord, after without the effect of the age
CorPart(cbind(abstr, coord, age), 1:2, 3)
#>           abstr     coord
#> abstr 1.0000000 0.7220272
#> coord 0.7220272 1.0000000

# by correlation matrix m
m <- cor(cbind(abstr, coord, age))
CorPart(m, 1:2, 3)
#>           abstr     coord
#> abstr 1.0000000 0.7220272
#> coord 0.7220272 1.0000000

# ... which would be the same as:
lm1 <- lm(abstr ~ age)
lm2 <- lm(coord ~ age)

cor(resid(lm1), resid(lm2))
#> [1] 0.7220272