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.
partial.r(m, x, y)
A data or correlation matrix
The variable numbers associated with the X set.
The variable numbers associated with the Y set
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.
To find the confidence intervals and "significance" of the correlations, use the
corr.p function with n = n - s where s is the numer of covariates.
The matrix of partial correlations.
Revelle, W. (in prep) An introduction to psychometric theory with applications in R. To be published by Springer. (working draft available at http://personality-project.org/r/book/
mat.regress for a similar application for regression
1 2 3 4 5
V1 V2 V3 V4 V5 V1 1.00 0.56 0.48 0.40 0.35 V2 0.56 1.00 0.42 0.35 0.30 V3 0.48 0.42 1.00 0.30 0.26 V4 0.40 0.35 0.30 1.00 0.42 V5 0.35 0.30 0.26 0.42 1.00 Call:corr.p(r = par.r, n = 98) Correlation matrix partial correlations V1 V3 V5 V1 1.00 0.29 0.14 V3 0.29 1.00 0.10 V5 0.14 0.10 1.00 Sample Size  98 Probability values (Entries above the diagonal are adjusted for multiple tests.) partial correlations V1 V3 V5 V1 0.00 0.01 0.31 V3 0.00 0.00 0.34 V5 0.16 0.34 0.00 To see confidence intervals of the correlations, print with the short=FALSE option Confidence intervals based upon normal theory. To get bootstrapped values, try cor.ci lower r upper p V1-V3 0.10 0.29 0.46 0.00 V1-V5 -0.06 0.14 0.33 0.16 V3-V5 -0.10 0.10 0.29 0.34
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