NAG Library Routine Document

G11SBF

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

+− 9 Example

9.1 Program Text

9.2 Program Data

9.3 Program Results

1 Purpose

G11SBF is a service routine which may be used prior to calling G11SAF to calculate the frequency distribution of a set of dichotomous score patterns.

2 Specification

SUBROUTINE G11SBF (

IP, N, NS, X, LDX, IRL, IFAIL)

INTEGER	IP, N, NS, LDX, IRL(N), IFAIL
LOGICAL	X(LDX,IP)

3 Description

When each of

n

individuals responds to each of

p

dichotomous variables the data assumes the form of the matrix

X

defined below

X = [\begin{array}{l} x_{11} & x_{12} & \dots & x_{1 p} \\ x_{21} & x_{22} & \dots & x_{2 p} \\ ⋮ & ⋮ & ⋮ \\ x_{n 1} & x_{n 2} & \dots & x_{n p} \end{array}] = [\begin{array}{l} {\underset{̲}{x}}_{1} \\ {\underset{̲}{x}}_{2} \\ ⋮ \\ {\underset{̲}{x}}_{n} \end{array}],

where the

x

take the value of

0

1

and

{\underset{̲}{x}}_{l} = (x_{l 1}, x_{l 2}, \dots, x_{l p})

, for

l = 1, 2, \dots, n

, denotes the score pattern of the

l

th individual. G11SBF calculates the number of different score patterns,

s

, and the frequency with which each occurs. This information can then be passed to G11SAF.

4 References

None.

5 Parameters

1: IP – INTEGERInput: On entry: $p$ , the number of dichotomous variables.

Constraint: $IP \geq 3$ .
2: N – INTEGERInput: On entry: $n$ , the number of individuals in the sample.

Constraint: $N \geq 7$ .
3: NS – INTEGEROutput: On exit: the number of different score patterns, $s$ .
4: X(LDX,IP) – LOGICAL arrayInput/Output: On entry: $X (i, j)$ must be set equal to .TRUE. if $x_{i j} = 1$ , and .FALSE. if $x_{i j} = 0$ , for $i = 1, 2, \dots, n$ and $j = 1, 2, \dots, p$ .

On exit: the first $s$ rows of X contain the $s$ different score patterns.
5: LDX – INTEGERInput: On entry: the first dimension of the array X as declared in the (sub)program from which G11SBF is called.
Constraint: $LDX \geq N$ .
6: IRL(N) – INTEGER arrayOutput: On exit: the frequency with which the $l$ th row of X occurs, for $l = 1, 2, \dots, s$ .
7: IFAIL – INTEGERInput/Output: On entry: IFAIL must be set to $0$ , $- 1 or 1$ . If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $- 1 or 1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$ . When the value $- 1 or 1$ is used it is essential to test the value of IFAIL on exit.

On exit: $IFAIL = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

IFAIL = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by X04AAF).

Errors or warnings detected by the routine:

$IFAIL = 1$

On entry,	$IP < 3$ ,
or	$N < 7$ ,
or	$LDX < N$ .

7 Accuracy

Exact.

8 Further Comments

The time taken by G11SBF is small and increases with

n

9 Example

This example counts the frequencies of different score patterns in the following list:

Score Patterns
000
010
111
000
001
000
000
110
001
011

NAG Library Routine DocumentG11SBF