nag_contab_binary_service (g11sb) is a service function which may be used prior to calling nag_contab_binary (g11sa) to calculate the frequency distribution of a set of dichotomous score patterns.

Syntax

[ns, x, irl, ifail] = g11sb(x, 'ip', ip, 'n', n)

[ns, x, irl, ifail] = nag_contab_binary_service(x, 'ip', ip, 'n', n)

Note: the interface to this routine has changed since earlier releases of the toolbox:

At Mark 22:

n was made optional

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. nag_contab_binary_service (g11sb) calculates the number of different score patterns,

s

, and the frequency with which each occurs. This information can then be passed to nag_contab_binary (g11sa).

References

None.

Parameters

Compulsory Input Parameters

1: $x (ldx, ip)$ – logical array: ldx, the first dimension of the array, must satisfy the constraint $ldx \geq n$ .
$x (i, j)$ 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 $j = 1, 2, \dots, p$ .

Optional Input Parameters

1: $ip$ – int64int32nag_int scalar: Default: the second dimension of the array x.
$p$ , the number of dichotomous variables.

Constraint: $ip \geq 3$ .
2: $n$ – int64int32nag_int scalar: Default: the first dimension of the array x.
$n$ , the number of individuals in the sample.

Constraint: $n \geq 7$ .

Output Parameters

1: $ns$ – int64int32nag_int scalar: The number of different score patterns, $s$ .
2: $x (ldx, ip)$ – logical array: The first $s$ rows of x contain the $s$ different score patterns.
3: $irl (n)$ – int64int32nag_int array: The frequency with which the $l$ th row of x occurs, for $l = 1, 2, \dots, s$ .
4: $ifail$ – 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,	$ip < 3$ ,
or	$n < 7$ ,
or	$ldx < n$ .

$ifail = - 99$: 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

Exact.

Further Comments

The time taken by nag_contab_binary_service (g11sb) is small and increases with

n

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

Open in the MATLAB editor: g11sb_example

function g11sb_example


fprintf('g11sb example results\n\n');

x = [false, false, false;
     false, true,  false;
     true,  true,  true;
     false, false, false;
     false, false, true;
     false, false, false;
     false, false, false;
     true,  true,  false;
     false, false, true;
     false, true,  true];

[ns, x, irl, ifail] = g11sb(x);

% Display results
fprintf('Frequency     Score pattern\n\n');
for i = 1:ns
  fprintf('%5d            ', irl(i));
  fprintf('%2d', x(i,:));
  fprintf('\n');
end

g11sb example results

Frequency     Score pattern

    4             0 0 0
    1             0 1 0
    1             1 1 1
    2             0 0 1
    1             1 1 0
    1             0 1 1

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox