g02bc Method
関数リスト一覧 　　NagLibrary Namespaceへ　　ライブラリイントロダクション　　本ヘルプドキュメントのchm形式版

g02bc 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 cases with missing values from only those calculations involving the variables for which the values are missing.

Syntax

C#
public static void g02bc(
	int n,
	int m,
	double[,] x,
	int[] miss,
	double[] xmiss,
	double[] xbar,
	double[] std,
	double[,] ssp,
	double[,] r,
	out int ncases,
	double[,] cnt,
	out int ifail
)
Visual Basic (Declaration)
Public Shared Sub g02bc ( _
	n As Integer, _
	m As Integer, _
	x As Double(,), _
	miss As Integer(), _
	xmiss As Double(), _
	xbar As Double(), _
	std As Double(), _
	ssp As Double(,), _
	r As Double(,), _
	<OutAttribute> ByRef ncases As Integer, _
	cnt As Double(,), _
	<OutAttribute> ByRef ifail As Integer _
)
Visual C++
public:
static void g02bc(
	int n, 
	int m, 
	array<double,2>^ x, 
	array<int>^ miss, 
	array<double>^ xmiss, 
	array<double>^ xbar, 
	array<double>^ std, 
	array<double,2>^ ssp, 
	array<double,2>^ r, 
	[OutAttribute] int% ncases, 
	array<double,2>^ cnt, 
	[OutAttribute] int% ifail
)
F#
static member g02bc : 
        n:int * 
        m:int * 
        x:float[,] * 
        miss:int[] * 
        xmiss:float[] * 
        xbar:float[] * 
        std:float[] * 
        ssp:float[,] * 
        r:float[,] * 
        ncases:int byref * 
        cnt:float[,] * 
        ifail:int byref -> unit

Parameters

n
Type: System..::.Int32
On entry: n, the number of observations or cases.
Constraint: n≥2.
m
Type: System..::.Int32
On entry: m, the number of variables.
Constraint: m≥2.
x
Type: array< System..::.Double ,2>[,](,)[,]
An array of size [ldx, m]
Note: ldx must satisfy the constraint: ldx≥n
On entry: x[i-1,j-1] 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.
miss
Type: array< System..::.Int32 >[]()[]
An array of size [m]
On entry: miss[j-1] 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.
xmiss
Type: array< System..::.Double >[]()[]
An array of size [m]
On entry: xmiss[j-1] 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]).
xbar
Type: array< System..::.Double >[]()[]
An array of size [m]
On exit: the mean value, x-j, of the jth variable, for j=1,2,…,m.
std
Type: array< System..::.Double >[]()[]
An array of size [m]
On exit: the standard deviation, sj, of the jth variable, for j=1,2,…,m.
ssp
Type: array< System..::.Double ,2>[,](,)[,]
An array of size [ldssp, m]
Note: ldssp must satisfy the constraint: ldssp≥m
On exit: ssp[j-1,k-1] is the cross-product of deviations, Sjk, for j,k=1,2,…,m.
r
Type: array< System..::.Double ,2>[,](,)[,]
An array of size [ldr, m]
Note: ldr must satisfy the constraint: ldr≥m
On exit: r[j-1,k-1] is the product-moment correlation coefficient, Rjk, between the jth and kth variables, for j,k,=1,2,…,m.
ncases
Type: System..::.Int32 %
On exit: the minimum number of cases used in the calculation of any of the sums of squares and cross-products and correlation coefficients (when cases involving missing values have been eliminated).
cnt
Type: array< System..::.Double ,2>[,](,)[,]
An array of size [ldcnt, m]
Note: ldcnt must satisfy the constraint: ldcnt≥m
On exit: cnt[j-1,k-1] is the number of cases, cjk, actually used in the calculation of Sjk, and Rjk, the sum of cross-products and correlation coefficient for the jth and kth variables, for j,k=1,2,…,m.
ifail
Type: System..::.Int32 %
On exit: ifail=0 unless the method detects an error (see [Error Indicators and Warnings]).

Description

The input data consist of n observations for each of m variables, given as an array
xij,  i=1,2,…,nn≥2,j=1,2,…,mm≥2,
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 wij=0 if the ith observation for the jth variable is a missing value, i.e., if a missing value, xmj, has been declared for the jth variable, and xij=xmj (see also [Accuracy]); and wij=1 otherwise, for i=1,2,…,n and j=1,2,…,m.
The quantities calculated are:
(a) Means:
x-j=∑i=1nwijxij ∑i=1nwij ,  j=1,2,…,m.
(b) Standard deviations:
sj=∑i= 1nwij xij-x-j 2 ∑i= 1nwij- 1 ,   j= 1,2,…,m.
(c) Sums of squares and cross-products of deviations from means:
Sjk=∑i=1nwijwikxij-x-jkxik-x-kj,  j,k=1,2,…,m,
where
x-jk=∑i= 1nwijwikxij ∑i= 1nwijwik   and   x-kj=∑i= 1nwikwijxik ∑i= 1nwikwij ,
(i.e., the means used in the calculation of the sums of squares and cross-products of deviations are based on the same set of observations as are the cross-products.)
(d) Pearson product-moment correlation coefficients:
Rjk=SjkSjjkSkkj ,  j,k,=1,2,…,m,
where Sjjk=∑i=1nwijwikxij-x-jk2 and Skkj=∑i=1nwikwijxik-x-kj2 and x-jk and x-kj are as defined in (c) above
(i.e., the sums of squares of deviations used in the denominator are based on the same set of observations as are used in the calculation of the numerator).
If Sjjk or Skkj is zero, Rjk is set to zero.
(e) The number of cases used in the calculation of each of the correlation coefficients:
cjk=∑i=1nwijwik,  j,k=1,2,…,m.
(The diagonal terms, cjj, for j=1,2,…,m, also give the number of cases used in the calculation of the means, x-j, and the standard deviations, sj.)

References

Error Indicators and Warnings

Note: g02bc may return useful information for one or more of the following detected errors or warnings.
Errors or warnings detected by the method:
Some error messages may refer to parameters that are dropped from this interface (ldx, ldssp, ldr, ldcnt) In these cases, an error in another parameter has usually caused an incorrect value to be inferred.
ifail=1
On entry,n<2.
ifail=2
On entry,m<2.
ifail=4
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 coefficients based on two or more cases are returned by the method even if ifail=4.
ifail=-4000
Invalid dimension for array value
ifail=-8000
Negative dimension for array value
ifail=-6000
Invalid Parameters value

Accuracy

g02bc 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. g02bc 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 g02bc depends on n and m, and the occurrence of missing values.
The method uses a two-pass algorithm.

Example

See Also