g02bh computes means and standard deviations, sums of squares and cross-products of deviations from means, and Pearson product-moment correlation 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

C#
public static void g02bh( int n, int m, double[,] x, int[] miss, double[] xmiss, int mistyp, int nvars, int[] kvar, double[] xbar, double[] std, double[,] ssp, double[,] r, out int ncases, out int ifail )

public static void g02bh(
	int n,
	int m,
	double[,] x,
	int[] miss,
	double[] xmiss,
	int mistyp,
	int nvars,
	int[] kvar,
	double[] xbar,
	double[] std,
	double[,] ssp,
	double[,] r,
	out int ncases,
	out int ifail
)

Visual Basic
Public Shared Sub g02bh ( _ n As Integer, _ m As Integer, _ x As Double(,), _ miss As Integer(), _ xmiss As Double(), _ mistyp As Integer, _ nvars As Integer, _ kvar As Integer(), _ xbar As Double(), _ std As Double(), _ ssp As Double(,), _ r As Double(,), _ <OutAttribute> ByRef ncases As Integer, _ <OutAttribute> ByRef ifail As Integer _ )

Visual Basic

Public Shared Sub g02bh ( _
	n As Integer, _
	m As Integer, _
	x As Double(,), _
	miss As Integer(), _
	xmiss As Double(), _
	mistyp As Integer, _
	nvars As Integer, _
	kvar As Integer(), _
	xbar As Double(), _
	std As Double(), _
	ssp As Double(,), _
	r As Double(,), _
	<OutAttribute> ByRef ncases As Integer, _
	<OutAttribute> ByRef ifail As Integer _
)

Visual C++
public: static void g02bh( int n, int m, array<double,2>^ x, array<int>^ miss, array<double>^ xmiss, int mistyp, int nvars, array<int>^ kvar, array<double>^ xbar, array<double>^ std, array<double,2>^ ssp, array<double,2>^ r, [OutAttribute] int% ncases, [OutAttribute] int% ifail )

Visual C++

public:
static void g02bh(
	int n, 
	int m, 
	array<double,2>^ x, 
	array<int>^ miss, 
	array<double>^ xmiss, 
	int mistyp, 
	int nvars, 
	array<int>^ kvar, 
	array<double>^ xbar, 
	array<double>^ std, 
	array<double,2>^ ssp, 
	array<double,2>^ r, 
	[OutAttribute] int% ncases, 
	[OutAttribute] int% ifail
)

F#
static member g02bh : n : int * m : int * x : float[,] * miss : int[] * xmiss : float[] * mistyp : int * nvars : int * kvar : int[] * xbar : float[] * std : float[] * ssp : float[,] * r : float[,] * ncases : int byref * ifail : int byref -> unit

static member g02bh : 
        n : int * 
        m : int * 
        x : float[,] * 
        miss : int[] * 
        xmiss : float[] * 
        mistyp : int * 
        nvars : int * 
        kvar : int[] * 
        xbar : float[] * 
        std : float[] * 
        ssp : float[,] * 
        r : float[,] * 
        ncases : int byref * 
        ifail : int byref -> unit

Parameters

n: Type: System..::..Int32
On entry: $n$ , the number of observations or cases.

Constraint: $n \geq 2$ .

m: Type: System..::..Int32
On entry: $m$ , the number of variables.

Constraint: $m \geq 2$ .

x: Type: array<System..::..Double,2>[,](,)[,][,]
An array of size [dim1, m]
Note: dim1 must satisfy the constraint: $dim1 \geq n$
On entry: $x [i - 1, j - 1]$ must be set to $x_{i j}$ , the value of the $i$ th observation on the $j$ th variable, for $i = 1, 2, \dots, n$ and $j = 1, 2, \dots, m$ .

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, $x m_{j}$ , is to be specified for the $j$ th 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.
On exit: the array miss is overwritten by the method, and the information it contained on entry is lost.

xmiss: Type: array<System..::..Double>[]()[][]
An array of size [m]
On entry: $xmiss [j - 1]$ must be set to the missing value, $x m_{j}$ , to be associated with the $j$ th variable in the array x, for those variables for which missing values are specified by means of the array miss (see [Accuracy]).
On exit: the array xmiss is overwritten by the method, and the information it contained on entry is lost.

mistyp

Type: System..::..Int32

On entry: 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 $1, 2, \dots, m$ .
$mistyp = 0$: A case is excluded if it contains a missing value for any of the $p (\leq m)$ variables specified in the array kvar.

nvars: Type: System..::..Int32
On entry: $p$ , the number of variables for which information is required.

Constraint: $2 \leq nvars \leq m$ .

kvar: Type: array<System..::..Int32>[]()[][]
An array of size [nvars]
On entry: $kvar [j]$ must be set to the column number in x of the $j$ th variable for which information is required, for $j = 0, 1, \dots, p - 1$ .

Constraint: $1 \leq kvar [j] \leq m$ , for $j = 0, 1, \dots, p - 1$ .

xbar: Type: array<System..::..Double>[]()[][]
An array of size [nvars]
On exit: the mean value, of ${\bar{x}}_{j}$ , of the variable specified in $kvar [j - 1]$ , for $j = 1, 2, \dots, p$ .

std: Type: array<System..::..Double>[]()[][]
An array of size [nvars]
On exit: the standard deviation, $s_{j}$ , of the variable specified in $kvar [j - 1]$ , for $j = 1, 2, \dots, p$ .

ssp: Type: array<System..::..Double,2>[,](,)[,][,]
An array of size [dim1, nvars]
Note: dim1 must satisfy the constraint: $dim1 \geq nvars$
On exit: $ssp [j - 1, k - 1]$ is the cross-product of deviations, $S_{j k}$ , for the variables specified in $kvar [j - 1]$ and $kvar [k - 1]$ , for $j = 1, 2, \dots, p$ and $k = 1, 2, \dots, p$ .

r: Type: array<System..::..Double,2>[,](,)[,][,]
An array of size [dim1, nvars]
Note: dim1 must satisfy the constraint: $dim1 \geq nvars$
On exit: $r [j - 1, k - 1]$ is the product-moment correlation coefficient, $R_{j k}$ , between the variables specified in $kvar [j - 1]$ and $kvar [k - 1]$ , for $j = 1, 2, \dots, p$ and $k = 1, 2, \dots, p$ .

ncases: Type: System..::..Int32%
On exit: the number of cases actually used in the calculations (when cases involving missing values have been eliminated).

ifail: Type: System..::..Int32%
On exit: $ifail = 0$ unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).

Description

The input data consists of

n

observations for each of

m

variables, given as an array

[x_{i j}], i = 1, 2, \dots, n (n \geq 2), j = 1, 2, \dots, m (m \geq 2),

where

x_{i j}

is the

i

th observation on the

j

th variable, together with the subset of these variables,

v_{1}, v_{2}, \dots, v_{p}

, 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

j

th variable is denoted by

{xm}_{j}

. 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

w_{i} = 0

if observation

i

contains a missing value for any of those variables in the set

1, 2, \dots, m

for which missing values have been declared, i.e., if

x_{i j} = {xm}_{j}

for any

j

(

j = 1, 2, \dots, m

) for which an

{xm}_{j}

has been assigned (see also [Accuracy]); and

w_{i} = 1

otherwise, for

i = 1, 2, \dots, n

Secondly, let

w_{i} = 0

if observation

i

contains a missing value for any of those variables in the selected subset

v_{1}, v_{2}, \dots, v_{p}

for which missing values have been declared, i.e., if

x_{i j} = {xm}_{j}

for any

j

(

j = v_{1}, v_{2}, \dots, v_{p}

) for which an

{xm}_{j}

has been assigned (see also [Accuracy]); and

w_{i} = 1

otherwise, for

i = 1, 2, \dots, n

The quantities calculated are:

(a)

Means:

{\bar{x}}_{j} = \frac{\sum_{i = 1}^{n} w_{i} x_{i j}}{\sum_{i = 1}^{n} w_{i}}, j = v_{1}, v_{2}, \dots, v_{p} .

(b)

Standard deviations:

s_{j} = \sqrt{\frac{\sum_{i = 1}^{n} w_{i} {(x_{i j} - {\bar{x}}_{j})}^{2}}{\sum_{i = 1}^{n} w_{i} - 1}}, j = v_{1}, v_{2}, \dots, v_{p} .

(c)

Sums of squares and cross-products of deviations from means:

S_{j k} = \sum_{i = 1}^{n} w_{i} (x_{i j} - {\bar{x}}_{j}) (x_{i k} - {\bar{x}}_{k}), j, k = v_{1}, v_{2}, \dots, v_{p} .

(d)

Pearson product-moment correlation coefficients:

R_{j k} = \frac{S_{j k}}{\sqrt{S_{j j} S_{k k}}}, j, k = v_{1}, v_{2}, \dots, v_{p} .

S_{j j}

S_{k k}

is zero,

R_{j k}

is set to zero.

References

None.

Error Indicators and Warnings

Errors or warnings detected by the method:

Some error messages may refer to parameters that are dropped from this interface (LDX, LDSSP, LDR) 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,	$nvars < 2$ ,
or	$nvars > m$ .

$ifail = 4$

On entry,	$kvar [j - 1] < 1$ ,
or	$kvar [j - 1] > m$ for some $j = 1, 2, \dots, nvars$ .

$ifail = 5$

On entry,

mistyp \neq 1

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.

$ifail = -9000$: An error occured, see message report.
$ifail = -6000$: Invalid Parameters $〈value〉$
$ifail = -4000$: Invalid dimension for array $〈value〉$
$ifail = -8000$: Negative dimension for array $〈value〉$
$ifail = -6000$: Invalid Parameters $〈value〉$

Accuracy

g02bh 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. g02bh treats all values in the inclusive range

(1 \pm {0.1}^{(x02be - 2)}) \times {x m}_{j}

, where

{xm}_{j}

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.

Parallelism and Performance

None.

Further Comments

The time taken by g02bh depends on

n

and

p

, and the occurrence of missing values.

The method 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 of deviations from means, and Pearson product-moment correlation 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.

Example program (C#): g02bhe.cs

Example program data: g02bhe.d

Example program results: g02bhe.r