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NAG Toolbox: nag_correg_coeffs_zero_subset_miss_case (g02bl)

 Contents

    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example

Purpose

nag_correg_coeffs_zero_subset_miss_case (g02bl) computes means and standard deviations, sums of squares and cross-products about zero, and correlation-like coefficients for selected variables omitting completely any cases with a missing observation for any variable (either over all variables in the dataset or over only those variables in the selected subset).

Syntax

[xbar, std, sspz, rz, ncases, ifail] = g02bl(x, miss, xmiss, mistyp, kvar, 'n', n, 'm', m, 'nvars', nvars)
[xbar, std, sspz, rz, ncases, ifail] = nag_correg_coeffs_zero_subset_miss_case(x, miss, xmiss, mistyp, kvar, 'n', n, 'm', m, 'nvars', nvars)
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 consist of n observations for each of m variables, given as an array
xij ,   i=1,2,,nn2 ​ and ​ j=1,2,,mm2 ,  
where xij is the ith observation on the jth variable, together with the subset of these variables, v1,v2,,vp, for which information is required.
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.
The missing values can be utilized in two slightly different ways, you can indicate which scheme is required.
Firstly, let wi=0 if observation i contains a missing value for any of those variables in the set 1,2,,m for which missing values have been declared, i.e., if xij=xmj for any j (j=1,2,,m) for which an xmj has been assigned (see also Accuracy); and wi=1 otherwise, for i=1,2,,n.
Secondly, let wi=0 if observation i contains a missing value for any of those variables in the selected subset v1,v2,,vp for which missing values have been declared, i.e., if xij=xmj for any jj=v1,v2,,vp 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=v1,v2,,vp.  
(b) Standard deviations:
Sj=i= 1nwi xij-x-j 2 i= 1nwi- 1 ,   j=v1,v2,,vp.  
(c) Sums of squares and cross-products about zero:
S~jk=i=1nwixijxik,  j,k=v1,v2,,vp.  
(d) Correlation-like coefficients:
R~jk=S~jkS~jjS~kk ,   j,k=v1,v2,,vp.  
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).
4:     mistyp int64int32nag_int scalar
Indicates the manner in which missing observations are to be treated.
mistyp=1
A case is excluded if it contains a missing value for any of the variables 1,2,,m.
mistyp=0
A case is excluded if it contains a missing value for any of the pm variables specified in the array kvar.
5:     kvarnvars int64int32nag_int array
kvarj must be set to the column number in x of the jth variable for which information is required, for j=1,2,,p.
Constraint: 1kvarjm, for j=1,2,,p.

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.
3:     nvars int64int32nag_int scalar
Default: the dimension of the array kvar.
p, the number of variables for which information is required.
Constraint: 2nvarsm.

Output Parameters

1:     xbarnvars – double array
The mean value, x-j, of the variable specified in kvarj, for j=1,2,,p.
2:     stdnvars – double array
The standard deviation, sj, of the variable specified in kvarj, for j=1,2,,p.
3:     sspzldsspznvars – double array
sspzjk is the cross-product about zero, S~jk, for the variables specified in kvarj and kvark, for j=1,2,,p and k=1,2,,p.
4:     rzldrznvars – double array
rzjk is the correlation-like coefficient, R~jk, between the variables specified in kvarj and kvark, for j=1,2,,p and k=1,2,,p.
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,nvars<2,
ornvars>m.
   ifail=3
On entry,ldx<n,
orldsspz<nvars,
orldrz<nvars.
   ifail=4
On entry,kvarj<1,
orkvarj>m for some j=1,2,,nvars.
   ifail=5
On entry,mistyp1 or 0.
   ifail=6
After observations with missing values were omitted, no cases remained.
   ifail=7
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_subset_miss_case (g02bl) 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_subset_miss_case (g02bl) 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_subset_miss_case (g02bl) depends on n and p, 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 four variables. Missing values of 0.0 are declared for the second and fourth variables; no missing values are specified for the first and third variables. The means, standard deviations, sums of squares and cross-products about zero, and correlation-like coefficients for the fourth, first and second variables are then calculated and printed, omitting completely all cases containing missing values for these three selected variables; cases 3 and 4 are therefore eliminated, leaving only three cases in the calculations.
function g02bl_example


fprintf('g02bl example results\n\n');

x = [ 3,  3,  1,  2;
      6,  4, -1,  4;
      9,  0,  5,  9;
     12,  2,  0,  0;
     -1,  5,  4, 12];
[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(0); 1; 0; 1];
xmiss  = [        0;  0; 0; 0];
mistyp =  int64(0);
kvar   = [int64(4); 1; 2];
nvar   = size(kvar,1);

[xbar, std, sspz, rz, ncases, ifail] = ...
  g02bl( ...
         x, miss, xmiss, mistyp, kvar);

fprintf('Variable   Mean     St. dev.\n');
fprintf('%5d%11.4f%11.4f\n',[double(kvar) xbar(1:nvar) std(1:nvar)]');
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);


g02bl example results

Number of variables (columns) = 4
Number of cases     (rows)    = 5

Data matrix is:-
     3     3     1     2
     6     4    -1     4
     9     0     5     9
    12     2     0     0
    -1     5     4    12

Variable   Mean     St. dev.
    4     6.0000     5.2915
    1     2.6667     3.5119
    2     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

PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

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