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NAG Toolbox

NAG Toolbox: nag_correg_coeffs_pearson_miss_case (g02bb)

Purpose

nag_correg_coeffs_pearson_miss_case (g02bb) computes means and standard deviations of variables, sums of squares and cross-products of deviations from means, and Pearson product-moment correlation coefficients for a set of data omitting completely any cases with a missing observation for any variable.

Syntax

[xbar, std, ssp, r, ncases, ifail] = g02bb(x, miss, xmiss, 'n', n, 'm', m)
[xbar, std, ssp, r, ncases, ifail] = nag_correg_coeffs_pearson_miss_case(x, miss, xmiss, 'n', n, 'm', m)
Note: the interface to this routine has changed since earlier releases of the toolbox:
Mark 22: n has been made optional; miss, xmiss no longer output
.

Description

The input data consist of nn observations for each of mm variables, given as an array
[xij],  i = 1,2,,n (n2),j = 1,2,,m(m2),
[xij],  i=1,2,,n (n2),j=1,2,,m(m2),
where xijxij is the iith observation on the jjth variable. In addition, each of the mm 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 jjth variable is denoted by xmjxmj. Missing values need not be specified for all variables.
Let wi = 0wi=0 if observation ii contains a missing value for any of those variables for which missing values have been declared, i.e., if xij = xmjxij=xmj for any jj for which an xmjxmj has been assigned (see also Section [Accuracy]); and wi = 1wi=1 otherwise, for i = 1,2,,ni=1,2,,n.
The quantities calculated are:
(a) Means:
xj = (i = 1nwixij)/(i = 1nwi),  j = 1,2,,m.
x-j=i=1nwixij i=1nwi ,  j=1,2,,m.
(b) Standard deviations:
sj = sqrt( (i = 1nwi(xijxj)2)/(i = 1nwi 1)),   j = 1,2,,m.
sj= i= 1nwi (xij-x-j) 2 i= 1nwi- 1 ,   j= 1,2,,m.
(c) Sums of squares and cross-products of deviations from means:
n
Sjk = wi(xijxj)(xikxk),  j,k = 1,2,,m.
i = 1
Sjk=i=1nwi(xij-x-j)(xik-x-k),  j,k=1,2,,m.
(d) Pearson product-moment correlation coefficients:
Rjk = (Sjk)/(sqrt(SjjSkk)),   j,k = 1,2,,m.
Rjk=SjkSjjSkk ,   j,k= 1,2,,m.
If SjjSjj or SkkSkk is zero, RjkRjk is set to zero.

References

None.

Parameters

Compulsory Input Parameters

1:     x(ldx,m) – double array
ldx, the first dimension of the array, must satisfy the constraint ldxnldxn.
x(i,j)xij must be set to xijxij, the value of the iith observation on the jjth variable, for i = 1,2,,ni=1,2,,n and j = 1,2,,mj=1,2,,m.
2:     miss(m) – int64int32nag_int array
m, the dimension of the array, must satisfy the constraint m2m2.
miss(j)missj must be set equal to 11 if a missing value, xmjxmj, is to be specified for the jjth variable in the array x, or set equal to 00 otherwise. Values of miss must be given for all mm variables in the array x.
3:     xmiss(m) – double array
m, the dimension of the array, must satisfy the constraint m2m2.
xmiss(j)xmissj must be set to the missing value, xmjxmj, to be associated with the jjth variable in the array x, for those variables for which missing values are specified by means of the array miss (see Section [Accuracy]).

Optional Input Parameters

1:     n – int64int32nag_int scalar
Default: The first dimension of the array x.
nn, the number of observations or cases.
Constraint: n2n2.
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.)
mm, the number of variables.
Constraint: m2m2.

Input Parameters Omitted from the MATLAB Interface

ldx ldssp ldr

Output Parameters

1:     xbar(m) – double array
The mean value, xjx-j, of the jjth variable, for j = 1,2,,mj=1,2,,m.
2:     std(m) – double array
The standard deviation, sjsj, of the jjth variable, for j = 1,2,,mj=1,2,,m.
3:     ssp(ldssp,m) – double array
ldsspmldsspm.
ssp(j,k)sspjk is the cross-product of deviations SjkSjk, for j = 1,2,,mj=1,2,,m and k = 1,2,,mk=1,2,,m.
4:     r(ldr,m) – double array
ldrmldrm.
r(j,k)rjk is the product-moment correlation coefficient RjkRjk between the jjth and kkth variables, for j = 1,2,,mj=1,2,,m and k = 1,2,,mk=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 = 0ifail=0 unless the function detects an error (see [Error Indicators and Warnings]).

Error Indicators and Warnings

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

Accuracy

nag_correg_coeffs_pearson_miss_case (g02bb) does not use additional precision arithmetic for the accumulation of scalar products, so there may be a loss of significant figures for large nn.
You are warned of the need to exercise extreme care in your selection of missing values. nag_correg_coeffs_pearson_miss_case (g02bb) treats all values in the inclusive range (1 ± 0.1(x02be2)) × xmj(1±0.1(x02be-2))×xmj, where xmjxmj is the missing value for variable jj 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_pearson_miss_case (g02bb) depends on nn and mm, and the occurrence of missing values.
The function uses a two-pass algorithm.

Example

function nag_correg_coeffs_pearson_miss_case_example
x = [2, 3, 3;
     4, 6, 4;
     9, 9, 0;
     0, 12, 2;
     12, -1, 5];
miss = [int64(1);0;1];
xmiss = [0;
     0;
     0];
[xbar, std, ssp, r, ncases, ifail] = nag_correg_coeffs_pearson_miss_case(x, miss, xmiss)
 

xbar =

    6.0000
    2.6667
    4.0000


std =

    5.2915
    3.5119
    1.0000


ssp =

   56.0000  -30.0000   10.0000
  -30.0000   24.6667   -4.0000
   10.0000   -4.0000    2.0000


r =

    1.0000   -0.8072    0.9449
   -0.8072    1.0000   -0.5695
    0.9449   -0.5695    1.0000


ncases =

                    3


ifail =

                    0


function g02bb_example
x = [2, 3, 3;
     4, 6, 4;
     9, 9, 0;
     0, 12, 2;
     12, -1, 5];
miss = [int64(1);0;1];
xmiss = [0;
     0;
     0];
[xbar, std, ssp, r, ncases, ifail] = g02bb(x, miss, xmiss)
 

xbar =

    6.0000
    2.6667
    4.0000


std =

    5.2915
    3.5119
    1.0000


ssp =

   56.0000  -30.0000   10.0000
  -30.0000   24.6667   -4.0000
   10.0000   -4.0000    2.0000


r =

    1.0000   -0.8072    0.9449
   -0.8072    1.0000   -0.5695
    0.9449   -0.5695    1.0000


ncases =

                    3


ifail =

                    0



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

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