# partial.r: Find the partial correlations for a set (x) of variables with... In psych: Procedures for Psychological, Psychometric, and Personality Research

## Description

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. If x and y are not specified, then the effect of all variables are partialled from all the other correlations.

## Usage

 `1` ```partial.r(data, x, y,use="pairwise",method="pearson") ```

## Arguments

 `data` A data or correlation matrix `x` The variable names or locations associated with the X set. `y` The variable names or locations associated with the Y set `use` How should we treat missing data? The default is pairwise complete. `method` Which method of correlation should we use, the default is pearson.

## Details

There are two ways to use `partial.r`. One is to find the complete partial correlation matrix (that is, partial all the other variables out of each variable). This may be done by simply specifying the raw data or correlation matrix. (In the case of raw data, correlations will be found according to use and method.) In this case, just specify the data matrix.

This is useful in the case of multiple regression. If we think of the data as an X matrix and a Y vector (D = X + Y) with correlations R. Then the partial correlations of the X predictors are just the last column of R^(-1). See the `Tal.Or` example below.

The second usage is to partial a set of variables(y) out of another set (x). 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.

Following a thoughtful request from Fransisco Wilheim, just find the correlations of the variables specified in the call (previously I had found the entire correlation matrix, which is a waste of time and breaks if some variables are non-numeric).)

In the case of non-positive definite matrices, find the Pinv (pseudo inverse) of the matrix.

## Value

The matrix of partial correlations.

William Revelle

## References

Revelle, W. (in prep) An introduction to psychometric theory with applications in R. To be published by Springer. (working draft available at https://personality-project.org/r/book/

`setCor` for a similar application for regression. `lowerMat` to neatly show a correlation matrix, and `corr.p` to find the confidence intervals of a correlation.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```jen <- make.hierarchical() #make up a correlation matrix lowerMat(jen[1:5,1:5]) par.r <- partial.r(jen,c(1,3,5),c(2,4)) lowerMat(par.r) cp <- corr.p(par.r,n=98) #assumes the jen data based upon n =100. print(cp,short=FALSE) #show the confidence intervals as well #partial all from all correlations. lowerMat(partial.r(jen)) #Consider the Tal.Or data set. lowerCor(Tal.Or) #partial gender and age from these relations (they hardly change) partial.r(Tal.Or,1:4,cs(gender,age)) #find the partial correlations between the first three variables and the DV (reaction) round(partial.r(Tal.Or[1:4])[4,1:3],2) #The partial correlations with the criterion ```