void	nag_rand_subsamp_xyw (Integer nt, Integer n, Integer m, Nag_DataByObsOrVar sordx, double x[], Integer pdx, double y[], double w[], Integer state[], NagError *fail)

3

Description

Let

X_{o}

denote a matrix of

n

observations on

m

variables and

y_{o}

and

w_{o}

each denote a vector of length

n

. For example,

X_{o}

might represent a matrix of independent variables,

y_{o}

the dependent variable and

w_{o}

the associated weights in a weighted regression.

nag_rand_subsamp_xyw (g05pwc) generates a series of training datasets, denoted by the matrix, vector, vector triplet

(X_{t}, y_{t}, w_{t})

n_{t}

observations, and validation datasets, denoted

(X_{v}, y_{v}, w_{v})

with

n_{v}

observations. These training and validation datasets are generated by randomly assigning each observation to either the training dataset or the validation dataset.

The resulting datasets are suitable for use with repeated random sub-sampling validation.

One of the initialization functions nag_rand_init_repeatable (g05kfc) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeatable (g05kgc) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_subsamp_xyw (g05pwc).

4

References

None.

5

Arguments

1: $nt$ – IntegerInput

On entry:

n_{t}

, the number of observations in the training dataset.

Constraint:

1 \leq nt \leq n

2: $n$ – IntegerInput

On entry:

n

, the number of observations.

Constraint:

n \geq 1

3: $m$ – IntegerInput

On entry:

m

, the number of variables.

Constraint:

m \geq 1

4: $sordx$ – Nag_DataByObsOrVarInput

On entry: determines how variables are stored in x.

Constraint:

sordx = Nag_DataByVar

Nag_DataByObs

5: $x [\dim]$ – doubleInput/Output

Note: the dimension, dim, of the array x must be at least

$pdx \times m$ when $sordx = Nag_DataByVar$ ;
$pdx \times n$ when $sordx = Nag_DataByObs$ .

The way the data is stored in x is defined by sordx.

sordx = Nag_DataByVar

x [(j - 1) \times pdx + i - 1]

contains the

i

th observation for the

j

th variable, for

i = 1, 2, \dots, n

and

j = 1, 2, \dots, m

sordx = Nag_DataByObs

x [(i - 1) \times pdx + j - 1]

contains the

i

th observation for the

j

th variable, for

i = 1, 2, \dots, n

and

j = 1, 2, \dots, m

On entry: x must hold

X_{o}

, the values of

X

for the original dataset. This may be the same x as returned by a previous call to nag_rand_subsamp_xyw (g05pwc).

On exit: values of

X

for the training and validation datasets, with

X_{t}

held in observations

1

nt

and

X_{v}

in observations

nt + 1

n

6: $pdx$ – IntegerInput

On entry: the stride separating row elements in the two-dimensional data stored in the array x.

Constraints:

if $sordx = Nag_DataByObs$ , $pdx \geq m$ ;
otherwise $pdx \geq n$ .

7: $y [n]$ – doubleInput/Output

If the original dataset does not include

y_{o}

then y must be set to NULL.

On entry: y must hold

y_{o}

, the values of

y

for the original dataset. This may be the same y as returned by a previous call to nag_rand_subsamp_xyw (g05pwc).

On exit: values of

y

for the training and validation datasets, with

y_{t}

held in elements

1

nt

and

y_{v}

in elements

nt + 1

n

8: $w [n]$ – doubleInput/Output

If the original dataset does not include

w_{o}

then w must be set to NULL.

On entry: w must hold

w_{o}

, the values of

w

for the original dataset. This may be the same w as returned by a previous call to nag_rand_subsamp_xyw (g05pwc).

On exit: values of

w

for the training and validation datasets, with

w_{t}

held in elements

1

nt

and

w_{v}

in elements

nt + 1

n

9: $state [\dim]$ – IntegerCommunication Array

Note: the dimension,

\dim

, of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument state in the previous call to nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).

On entry: contains information on the selected base generator and its current state.

On exit: contains updated information on the state of the generator.

10: $fail$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
NE_ARRAY_SIZE: On entry, $pdx = 〈value〉$ and $m = 〈value〉$ .
Constraint: if $sordx = Nag_DataByObs$ , $pdx \geq m$ .

On entry, $pdx = 〈value〉$ and $n = 〈value〉$ .
Constraint: if $sordx = Nag_DataByVar$ , $pdx \geq n$ .
NE_BAD_PARAM: On entry, argument $〈value〉$ had an illegal value.
NE_INT: On entry, $m = 〈value〉$ .
Constraint: $m \geq 1$ .

On entry, $n = 〈value〉$ .
Constraint: $n \geq 1$ .
NE_INT_2: On entry, $nt = 〈value〉$ and $n = 〈value〉$ .
Constraint: $1 \leq nt \leq n$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_INVALID_STATE: On entry, state vector has been corrupted or not initialized.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

Not applicable.

8

Further Comments

nag_rand_subsamp_xyw (g05pwc) will be computationality more efficient if each observation in x is contiguous, that is

sordx = Nag_DataByObs

9

Example

This example uses nag_rand_subsamp_xyw (g05pwc) to facilitate repeated random sub-sampling cross-validation.

A set of simulated data is randomly split into a training and validation datasets. nag_glm_binomial (g02gbc) is used to fit a logistic regression model to each training dataset and then nag_glm_predict (g02gpc) is used to predict the response for the observations in the validation dataset. This process is repeated

10

times.

The counts of true and false positives and negatives along with the sensitivity and specificity is then reported.

NAG Library Function Document

nag_rand_subsamp_xyw (g05pwc)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

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

2

Specification

3

Description

4

References

5

Arguments

6

Error Indicators and Warnings

7

Accuracy

8

Further Comments

9

Example

9.1

Program Text

9.2

Program Data

9.3

Program Results