nag_correg_ssqmat_to_corrmat (g02bw) calculates a matrix of Pearson product-moment correlation coefficients from sums of squares and cross-products of deviations about the mean.

Syntax

[r, ifail] = g02bw(m, r)

[r, ifail] = nag_correg_ssqmat_to_corrmat(m, r)

Description

nag_correg_ssqmat_to_corrmat (g02bw) calculates a matrix of Pearson product-moment correlation coefficients from sums of squares and cross-products about the mean for observations on

m

variables which can be computed by a single call to nag_correg_ssqmat (g02bu) or a series of calls to nag_correg_ssqmat_update (g02bt). The sums of squares and cross-products are stored in an array packed by column and are overwritten by the correlation coefficients.

Let

c_{j k}

be the cross-product of deviations from the mean, for

j = 1, 2, \dots, m

and

k = j, \dots, m

, then the product-moment correlation coefficient,

r_{j k}

is given by

r_{j k} = \frac{c_{j k}}{\sqrt{c_{j j} c_{k k}}} .

References

None.

Parameters

Compulsory Input Parameters

1: $m$ – int64int32nag_int scalar: $m$ , the number of variables.

Constraint: $m \geq 1$ .
2: $r ((m \times m + m) / 2)$ – double array: Contains the upper triangular part of the sums of squares and cross-products matrix of deviations from the mean. These are stored packed by column, i.e., the cross-product between variable $j$ and $k$ , $k \geq j$ , is stored in $r ((k \times (k - 1) / 2 + j))$ .

Optional Input Parameters

None.

Output Parameters

1: $r ((m \times m + m) / 2)$ – double array: The Pearson product-moment correlation coefficients.
These are stored packed by column corresponding to the input cross-products.
2: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Note: nag_correg_ssqmat_to_corrmat (g02bw) may return useful information for one or more of the following detected errors or warnings.

Errors or warnings detected by the function:

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

$ifail = 1$

On entry,

m < 1

W $ifail = 2$: A variable has a zero variance. All correlations involving the variable with zero variance will be returned as zero.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

The accuracy of nag_correg_ssqmat_to_corrmat (g02bw) is entirely dependent upon the accuracy of the elements of array r.

Further Comments

nag_correg_ssqmat_to_corrmat (g02bw) may also be used to calculate the correlations between parameter estimates from the variance-covariance matrix of the parameter estimates as is given by several functions in this chapter.

Example

A program to calculate the correlation matrix from raw data. The sum of squares and cross-products about the mean are calculated from the raw data by a call to nag_correg_ssqmat (g02bu). The correlation matrix is then calculated from these values.

Open in the MATLAB editor: g02bw_example

function g02bw_example


fprintf('g02bw example results\n\n');

wt = [  0.1300   1.3070   0.3700];
x  = [  9.1231   3.7011   4.5230;
        0.9310   0.0900   0.8870;
        0.0009   0.0099   0.0999];

[m, n] = size(x);
m      = int64(m);

% Calculate the sums of squares and cross-products matrix
[sw, wmean, c, ifail] = g02bu(x, 'wt', wt);

% Calculate the correlation matrix
[r, ifail] = g02bw(m, c);

mtitle = 'Correlation matrix:';
uplo   = 'Upper';
diag   = 'Non-unit';
[ifail] = x04cc( ...
                 uplo, diag, m, r, mtitle);

g02bw example results

 Correlation matrix:
          1       2       3
 1   1.0000  0.9908  0.9903
 2           1.0000  0.9624
 3                   1.0000

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox