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Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_correg_coeffs_zero_miss_case (g02be)

 Contents

    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example

Purpose

nag_correg_coeffs_zero_miss_case (g02be) 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 completely any cases with a missing observation for any variable.

Syntax

[xbar, std, sspz, rz, ncases, ifail] = g02be(x, miss, xmiss, 'n', n, 'm', m)
[xbar, std, sspz, rz, ncases, ifail] = nag_correg_coeffs_zero_miss_case(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; miss and xmiss are no longer output parameters

Description

The input data consists of n observations for each of m variables, given as an array
xij,  i=1,2,,n n2,j=1,2,,mm2,  
where xij is the ith observation on the jth variable. In addition, each of the m 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 jth variable is denoted by xmj. Missing values need not be specified for all variables.
Let wi=0 if observation i contains a missing value for any of those variables for which missing values have been declared, i.e., if xij=xmj for any j for which an xmj has been assigned (see also Accuracy); and wi=1 otherwise, for i=1,2,,n.
The quantities calculated are:
(a) Means:
x-j=i=1nwixij i=1nwi ,  j=1,2,,m.  
(b) Standard deviations:
sj= i= 1nwi xij-x-j 2 i= 1nwi- 1 ,   j= 1,2,,m.  
(c) Sums of squares and cross-products about zero:
S~jk=i=1nwixijxik,  j,k=1,2,,m.  
(d) Correlation-like coefficients:
R~jk=S~jkS~jj S~kk ,   j,k= 1,2,,m.  
If S~jj or S~kk is zero, R~jk is set to zero.

References

None.

Parameters

Compulsory Input Parameters

1:     xldxm – double array
ldx, the first dimension of the array, must satisfy the constraint ldxn.
xij must be set to xij, the value of the ith observation on the jth variable, for i=1,2,,n and j=1,2,,m.
2:     missm int64int32nag_int array
missj must be set equal to 1 if a missing value, xmj, is to be specified for the jth variable in the array x, or set equal to 0 otherwise. Values of miss must be given for all m variables in the array x.
3:     xmissm – double array
xmissj must be set to the missing value, xmj, to be associated with the jth 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:     n int64int32nag_int scalar
Default: the first dimension of the array x.
n, the number of observations or cases.
Constraint: n2.
2:     m 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.)
m, the number of variables.
Constraint: m2.

Output Parameters

1:     xbarm – double array
The mean value, x-j, of the jth variable, for j=1,2,,m.
2:     stdm – double array
The standard deviation, sj, of the jth variable, for j=1,2,,m.
3:     sspzldsspzm – double array
sspzjk is the cross-product about zero, S~jk, for j=1,2,,m and k=1,2,,m.
4:     rzldrzm – double array
rzjk is the correlation-like coefficient, R~jk, between the jth and kth variables, for j=1,2,,m and k=1,2,,m.
5:     ncases int64int32nag_int scalar
The number of cases actually used in the calculations (when cases involving missing values have been eliminated).
6:     ifail int64int32nag_int scalar
ifail=0 unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:
   ifail=1
On entry,n<2.
   ifail=2
On entry,m<2.
   ifail=3
On entry,ldx<n,
orldsspz<m,
orldrz<m.
   ifail=4
After observations with missing values were omitted, no cases remained.
   ifail=5
After observations with missing values were omitted, only one case remained.
   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

nag_correg_coeffs_zero_miss_case (g02be) does not use additional precision arithmetic for the accumulation of scalar products, so there may be a loss of significant figures for large n.
You are warned of the need to exercise extreme care in your selection of missing values. nag_correg_coeffs_zero_miss_case (g02be) treats all values in the inclusive range 1±0.1x02be-2×xmj, where xmj is the missing value for variable j 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_case (g02be) depends on n and m, 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 0.0 are declared for the first and third variables; no missing value is specified for the second variable. 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 completely all cases containing missing values; cases 3 and 4 are therefore eliminated, leaving only three cases in the calculations.
function g02be_example


fprintf('g02be 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);  0;  1];
xmiss = [         0;  0;  0];
[xbar, std, sspz, rz, ncases, ifail] = ...
  g02be(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 actually used  = %d\n', ncases);



g02be 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     6.0000     5.2915
    2     2.6667     3.5119
    3     4.0000     1.0000

Sums of squares and cross-products about zero
   164    18    82
    18    46    28
    82    28    50

Correlation-like coefficients
    1.0000    0.2072    0.9055
    0.2072    1.0000    0.5838
    0.9055    0.5838    1.0000

Number of cases actually used  = 3

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