 Dataplot Vol 2 Vol 1

# PARTIAL CORRELATION MATRIX

Name:
PARTIAL CORRELATION MATRIX (LET)
Type:
Let Subcommand
Purpose:
Compute the partial correlation matrix of a matrix.
Description:
The partial correlation matrix computes the partial correlation coefficients of the columns of a matrix. That is, row i and column j of the partial correlation matrix is the partial correlation between column i and column j of the original matrix. This partial correlation between column i and column j is the correlation between these two columns after removing the effects of the remaining columns. Note that the diagonal elements of the partial correlation matrix will be 1 (since they are the partial correlation of a column with itself). The partial correlation matrix is also symmetric (since the partial correlation of column i with column j is the same as the partial correlation of column j with column i).

The algorithm for computing the partial correlations is:

1. Compute the standard correlation matrix.

2. Invert this correlation matrix.

3. Compute where rij is the (i,j)-th element of the inverted correlation matrix.

Alternatively, you can compute the CDF or the p-value for the partial correlation coefficients (i.e., to see if the partial correlation coefficient is significantly different than zero). The CDF value is

CDF = FCDF(VAL,1,N-NC)

where FCDF is the F cumulative distribution function with 1 and N - NC degrees of freedom (N is the number of observations and NC is the number of columns in the input matrix) and with r denoting the computed partial correlation. The pvalue is 1 - CDF.

Syntax 1:
LET <mat2> = PARTIAL CORRELATION MATRIX <mat1>
<SUBSET/EXCEPT/FOR qualification>
where <mat1> is a matrix for which the partial correlations are to be computed;
<mat2> is a matrix where the resulting partial correlations are saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional and rarely used in this context.
Syntax 2:
LET <mat2> = PARTIAL CORRELATION CDF MATRIX <mat1>
<SUBSET/EXCEPT/FOR qualification>
where <mat1> is a matrix for which the partial correlation CDF's are to be computed;
<mat2> is a matrix where the resulting partial correlation CDF's are saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional and rarely used in this context.

This syntax computes the CDF's of the partial correlation coefficients.

Syntax 3:
LET <mat2> = PARTIAL CORRELATION PVALUE MATRIX <mat1>
<SUBSET/EXCEPT/FOR qualification>
where <mat1> is a matrix for which the partial correlation p-value's are to be computed;
<mat2> is a matrix where the resulting partial correlation p-values's are saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional and rarely used in this context.

This syntax computes the p-values of the partial correlation coefficients.

Examples:
LET C = PARTIAL CORRELATION MATRIX A
Note:
By default, the partial correlation matrices are computed on the columns. That is, element (i,j) of the partial correlation matrix is the partial correlation between column i and column j of the input matrix.

To specify a partial correlation matrix based on rows rather than columns, enter the command

SET MATRIX CORRELATION DIRECTION ROW

To reset column based partial correlations, enter

SET MATRIX CORRELATION DIRECTION COLUMN
Note:
By default the Pearson correlation coefficient is computed. To specify a different type of correlation, enter the command

SET CORRELATION TYPE <DEFAULT/RANK/WINSORIZED/
BIWEIGHT MIDCORRELATION/PERCENTAGE BEND/
KENDALL TAU>

To see the definitions for these, enter

Note:
Matrices are created with either the READ MATRIX command or the MATRIX DEFINITION command. Enter HELP MATRIX DEFINITION and HELP READ MATRIX for details.
Note:
The columns of a matrix are accessible as variables by appending an index to the matrix name. For example, the 4x4 matrix C has columns C1, C2, C3, and C4. These columns can be operated on like any other DATAPLOT variable.
Note:
The maximum size matrix that DATAPLOT can handle is set when DATAPLOT is built on a particular site. The default maximums are 100 columns and 100 rows.
Default:
None
Synonyms:
None
Related Commands:
 PARTIAL CORRELATION = Compute the partial correlation of three variables. CORRELATION MATRIX = Generate the correlation matrix. CORRELATION = Compute the correlation of two variables. RANK CORRELATION = Compute the rank correlation of two variables. KENDALLS TAU = Compute the Kendall tau correlation of two variables. WINSORIZED CORRELATION = Compute the Winsorized correlation of two variables. BIWEIGHT MIDCORRELATION = Compute the biweight mid-correlation of two variables. PERCENTAGE BEND CORRELATION = Compute the percentage bend correlation of two variables. COVARIANCE = Compute the covariance of two variables.
Applications:
Linear Fitting
Implementation Date:
2012/06
Program:
```
.  This data is from page 202 of
.
.  Peavy, Bremer, Varner, Hogben (1986), "OMNITAB 80:
.  An Interpretive System for Statistical and Numerical
.  Data Analysis," NBS Special Publication 701.
.
.  Original source of the data is from
.  Draper and Smith (1981), "Applied Regression Analysis",
.  Wiley, p. 373.
.
dimension 40 columns
.
42.2  11.2  31.9  167.1
48.6  10.6  13.2  174.4
42.6  10.6  28.7  160.8
39.0  10.4  26.1  162.0
34.7   9.3  30.1  140.8
44.5  10.8   8.5  174.6
39.1  10.7  24.3  163.7
40.1  10.0  18.6  174.5
45.9  12.0  20.4  185.7
end of data
.
set write decimals 4
let pcorr = partial correlation matrix m
print pcorr
```
The following output is generated.
```        MATRIX PCORR   --            4 ROWS
--            4 COLUMNS

VARIABLES--PCORR1         PCORR2         PCORR3         PCORR4

1.0000         0.4317        -0.4566         0.1054
0.4317         1.0000         0.6972         0.7268
-0.4566         0.6972         1.0000        -0.6478
0.1054         0.7268        -0.6478         1.0000
```

Date created: 01/23/2013
Last updated: 01/23/2013