PDF version (NAG web site
, 64-bit version, 64-bit version)
NAG Toolbox: nag_correg_coeffs_zero_miss_pair (g02bf)
Purpose
nag_correg_coeffs_zero_miss_pair (g02bf) computes means and standard deviations of variables, sums of squares and cross-products about zero and correlation-like coefficients for a set of data omitting cases with missing values from only those calculations involving the variables for which the values are missing.
Syntax
[
xbar,
std,
sspz,
rz,
ncases,
cnt,
ifail] = g02bf(
x,
miss,
xmiss, 'n',
n, 'm',
m)
[
xbar,
std,
sspz,
rz,
ncases,
cnt,
ifail] = nag_correg_coeffs_zero_miss_pair(
x,
miss,
xmiss, 'n',
n, 'm',
m)
Note: the interface to this routine has changed since earlier releases of the toolbox:
At Mark 22: |
n was made optional |
Description
The input data consists of
observations for each of
variables, given as an array
where
is the
th observation on the
th variable. In addition, each of the
variables may optionally have associated with it a value which is to be considered as representing a missing observation for that variable; the missing value for the
th variable is denoted by
. Missing values need not be specified for all variables.
Let
if the
th observation for the
th variable is a missing value, i.e., if a missing value,
, has been declared for the
th variable, and
(see also
Accuracy); and
otherwise, for
and
.
The quantities calculated are:
(a) |
Means:
|
(b) |
Standard deviations:
|
(c) |
Sums of squares and cross-products about zero:
|
(d) |
Correlation-like coefficients:
where and (i.e., the sums of squares about zero are based on the same set of observations as are used in the calculation of the numerator).
If or is zero, is set to zero. |
(e) |
The number of cases used in the calculation of each of the correlation-like coefficients:
(The diagonal terms, , for , also give the number of cases used in the calculation of the means and the standard deviations .) |
References
None.
Parameters
Compulsory Input Parameters
- 1:
– double array
-
ldx, the first dimension of the array, must satisfy the constraint
.
must be set to , the value of the th observation on the th variable, for and .
- 2:
– int64int32nag_int array
-
must be set equal to
if a missing value,
, is to be specified for the
th variable in the array
x, or set equal to
otherwise. Values of
miss must be given for all
variables in the array
x.
- 3:
– double array
-
must be set to the missing value,
, to be associated with the
th variable in the array
x, for those variables for which missing values are specified by means of the array
miss (see
Accuracy).
Optional Input Parameters
- 1:
– int64int32nag_int scalar
-
Default:
the first dimension of the array
x.
, the number of observations or cases.
Constraint:
.
- 2:
– int64int32nag_int scalar
-
Default:
the dimension of the arrays
miss,
xmiss and the second dimension of the array
x. (An error is raised if these dimensions are not equal.)
, the number of variables.
Constraint:
.
Output Parameters
- 1:
– double array
-
The mean value,
, of the th variable, for .
- 2:
– double array
-
The standard deviation,
, of the th variable, for .
- 3:
– double array
-
is the cross-product about zero, , for and .
- 4:
– double array
-
is the correlation-like coefficient, , between the th and th variables, for and .
- 5:
– int64int32nag_int scalar
-
The minimum number of cases used in the calculation of any of the sums of squares and cross-products and correlation-like coefficients (when cases involving missing values have been eliminated).
- 6:
– double array
-
is the number of cases, , actually used in the calculation of , and , the sum of cross-products and correlation-like coefficient for the th and th variables, for and .
- 7:
– int64int32nag_int scalar
unless the function detects an error (see
Error Indicators and Warnings).
Error Indicators and Warnings
Note: nag_correg_coeffs_zero_miss_pair (g02bf) 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.
-
-
-
-
-
-
On entry, | , |
or | , |
or | , |
or | . |
- W
-
After observations with missing values were omitted, fewer than two cases remained for at least one pair of variables. (The pairs of variables involved can be determined by examination of the contents of the array
cnt). All means, standard deviations, sums of squares and cross-products, and correlation-like coefficients based on two or more cases are returned by the function even if
.
-
An unexpected error has been triggered by this routine. Please
contact
NAG.
-
Your licence key may have expired or may not have been installed correctly.
-
Dynamic memory allocation failed.
Accuracy
nag_correg_coeffs_zero_miss_pair (g02bf) does not use additional precision arithmetic for the accumulation of scalar products, so there may be a loss of significant figures for large .
You are warned of the need to exercise extreme care in your selection of missing values.
nag_correg_coeffs_zero_miss_pair (g02bf) treats all values in the inclusive range
, where
is the missing value for variable
specified in
xmiss.
You must therefore ensure that the missing value chosen for each variable is sufficiently different from all valid values for that variable so that none of the valid values fall within the range indicated above.
Further Comments
The time taken by nag_correg_coeffs_zero_miss_pair (g02bf) depends on and , and the occurrence of missing values.
The function uses a two-pass algorithm.
Example
This example reads in a set of data consisting of five observations on each of three variables. Missing values of , and are declared for the first, second and third variables respectively. The means, standard deviations, sums of squares and cross-products about zero, and correlation-like coefficients for all three variables are then calculated and printed, omitting cases with missing values from only those calculations involving the variables for which the values are missing. The program therefore omits cases and in calculating the correlation between the first and second variables, and cases and for the first and third variables, etc.
Open in the MATLAB editor:
g02bf_example
function g02bf_example
fprintf('g02bf example results\n\n');
x = [ 2, 3, 3;
4, 6, 4;
9, 9, 0;
0, 12, 2;
12, -1, 5];
[n,m] = size(x);
fprintf('Number of variables (columns) = %d\n', m);
fprintf('Number of cases (rows) = %d\n\n', n);
disp('Data matrix is:-');
disp(x);
miss = [int64(1); 1; 1];
xmiss = [ 0; -1; 0];
[xbar, std, sspz, rz, ncases, count, ifail] = ...
g02bf(x, miss, xmiss);
fprintf('Variable Mean St. dev.\n');
fprintf('%5d%11.4f%11.4f\n',[[1:m]' xbar std]');
fprintf('\nSums of squares and cross-products about zero\n');
disp(sspz)
fprintf('Correlation-like coefficients\n');
disp(rz);
fprintf('Number of cases used for any pair of variables = %d\n', ncases);
fprintf('\nNumbers used for each pair are:\n');
disp(count);
g02bf example results
Number of variables (columns) = 3
Number of cases (rows) = 5
Data matrix is:-
2 3 3
4 6 4
9 9 0
0 12 2
12 -1 5
Variable Mean St. dev.
1 6.7500 4.5735
2 7.5000 3.8730
3 3.5000 1.2910
Sums of squares and cross-products about zero
245 111 82
111 270 57
82 57 54
Correlation-like coefficients
1.0000 0.9840 0.9055
0.9840 1.0000 0.7699
0.9055 0.7699 1.0000
Number of cases used for any pair of variables = 3
Numbers used for each pair are:
4 3 3
3 4 3
3 3 4
PDF version (NAG web site
, 64-bit version, 64-bit version)
© The Numerical Algorithms Group Ltd, Oxford, UK. 2009–2015