NAG Library Function Document

nag_pls_orth_scores_pred (g02ldc)

nag_pls_orth_scores_pred (Nag_OrderType order, Integer ip, Integer my, Nag_EstimatesOption orig, const double xbar[], const double ybar[], Nag_ScalePredictor iscale, const double xstd[], const double ystd[], const double b[], Integer pdb, Integer n, Integer mz, const Integer isz[], const double z[], Integer pdz, double yhat[], Integer pdyhat, NagError *fail)

3 Description

nag_pls_orth_scores_pred (g02ldc) calculates the predictions

\hat{Y}

of a PLS model given a set

Z

of test data and a set

B

of parameter estimates as returned by nag_pls_orth_scores_fit (g02lcc).

If nag_pls_orth_scores_fit (g02lcc) returns parameter estimates for the original data scale, no further information is required.

If nag_pls_orth_scores_fit (g02lcc) returns parameter estimates for the centred, and possibly scaled, data, further information is required. The means of variables in the fitted model must be supplied. In the case of a PLS model fitted by using scaled data, the means and standard deviations of variables in the fitted model must also be supplied. These means and standard deviations are those returned by either nag_pls_orth_scores_svd (g02lac) and nag_pls_orth_scores_wold (g02lbc).

4 References

None.

5 Arguments

1: order – Nag_OrderTypeInput

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by

order = Nag_RowMajor

. See Section 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

Constraint:

order = Nag_RowMajor

Nag_ColMajor

2: ip – IntegerInput

On entry: the number of predictor variables in the fitted model. ip must take the same value as that supplied to nag_pls_orth_scores_svd (g02lac) or nag_pls_orth_scores_wold (g02lbc) to fit the model.

Constraint:

ip > 1

3: my – IntegerInput

On entry: the number of response variables in the fitted model. my must take the same value as that supplied to nag_pls_orth_scores_svd (g02lac) or nag_pls_orth_scores_wold (g02lbc) to fit the model.

Constraint:

my \geq 1

4: orig – Nag_EstimatesOptionInput

On entry: indicates how parameter estimates are supplied.

$orig = Nag_EstimatesOrig$: Parameter estimates are for the original data.
$orig = Nag_EstimatesStand$: Parameter estimates are for the centred, and possibly scaled, data.

Constraint:

orig = Nag_EstimatesStand

Nag_EstimatesOrig

5: xbar[ip] – const doubleInput

On entry: if

orig = Nag_EstimatesStand

, xbar must contain mean values of predictor variables in the model; otherwise xbar is not referenced.

6: ybar[my] – const doubleInput

On entry: if

orig = Nag_EstimatesStand

, ybar must contain the mean value of each response variable in the model; otherwise ybar is not referenced.

7: iscale – Nag_ScalePredictorInput

On entry: if

orig = Nag_EstimatesStand

, iscale must take the value supplied to either nag_pls_orth_scores_svd (g02lac) or nag_pls_orth_scores_wold (g02lbc); otherwise iscale is not referenced.

Constraint: if

orig = Nag_EstimatesStand

iscale = Nag_PredNoScale

Nag_PredStdScale

Nag_PredUserScale

8: xstd[ip] – const doubleInput

On entry: if

orig = Nag_EstimatesStand

and

iscale \neq Nag_PredNoScale

, xstd must contain the scalings of predictor variables in the model as returned from either nag_pls_orth_scores_svd (g02lac) or nag_pls_orth_scores_wold (g02lbc); otherwise xstd is not referenced.

9: ystd[my] – const doubleInput

On entry: if

orig = Nag_EstimatesStand

and

iscale \neq Nag_PredNoScale

, ystd must contain the scalings of response variables as returned from either nag_pls_orth_scores_svd (g02lac) or nag_pls_orth_scores_wold (g02lbc); otherwise ystd is not referenced.

10: b[ $\dim$ ] – const doubleInput

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

$\max (1, pdb \times my)$ when $order = Nag_ColMajor$ ;
$\max (1, ip \times pdb)$ when $order = Nag_RowMajor$ and $orig = Nag_EstimatesStand$ ;
$\max (1, 1 + ip \times pdb)$ when $order = Nag_RowMajor$ and $orig = Nag_EstimatesOrig$ .

The

(i, j)

th element of the matrix

B

is stored in

$b [(j - 1) \times pdb + i - 1]$ when $order = Nag_ColMajor$ ;
$b [(i - 1) \times pdb + j - 1]$ when $order = Nag_RowMajor$ .

On entry: if

orig = Nag_EstimatesStand

, b must contain the parameter estimate for the centred, and possibly scaled, data as returned by nag_pls_orth_scores_fit (g02lcc); otherwise b must contain the parameter estimates for the original data as returned by nag_pls_orth_scores_fit (g02lcc).

11: pdb – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array b.

Constraints:

if order=Nag_ColMajor,
- if $orig = Nag_EstimatesStand$ , $pdb \geq ip$ ;
- if $orig = Nag_EstimatesOrig$ , $pdb \geq 1 + ip$ ;
if $order = Nag_RowMajor$ , $pdb \geq my$ .

12: n – IntegerInput

On entry:

n

, the number of observations in the test data

Z

Constraint:

n \geq 1

13: mz – IntegerInput

On entry: the number of available predictor variables in the test data.

Constraint:

mz \geq ip

14: isz[mz] – const IntegerInput

On entry: indicates which predictor variables are to be included in the model. Predictor variables included from z must be in the same order as those included in the fitted model.

isz [j - 1] = 1

, the

j

th predictor variable is included in the model, for

j = 1, 2, \dots, mz

, otherwise

isz [j - 1] = 0

Constraints:

$isz [j - 1] = 0 or 1$ , for $j = 1, 2, \dots, mz$ ;
$\sum_{j} isz [j - 1] = ip$ .

15: z[ $\dim$ ] – const doubleInput

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

$\max (1, pdz \times mz)$ when $order = Nag_ColMajor$ ;
$\max (1, n \times pdz)$ when $order = Nag_RowMajor$ .

Where

Z (i, j)

appears in this document, it refers to the array element

$z [(j - 1) \times pdz + i - 1]$ when $order = Nag_ColMajor$ ;
$z [(i - 1) \times pdz + j - 1]$ when $order = Nag_RowMajor$ .

On entry:

Z (i, j)

contains the

i

th observation on the

j

th available predictor variable, for

i = 1, 2, \dots, n

and

j = 1, 2, \dots, mz

16: pdz – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array z.

Constraints:

if $order = Nag_ColMajor$ , $pdz \geq n$ ;
if $order = Nag_RowMajor$ , $pdz \geq mz$ .

17: yhat[ $\dim$ ] – doubleOutput

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

$\max (1, pdyhat \times my)$ when $order = Nag_ColMajor$ ;
$\max (1, n \times pdyhat)$ when $order = Nag_RowMajor$ .

Where

YHAT (i, j)

appears in this document, it refers to the array element

$yhat [(j - 1) \times pdyhat + i - 1]$ when $order = Nag_ColMajor$ ;
$yhat [(i - 1) \times pdyhat + j - 1]$ when $order = Nag_RowMajor$ .

On exit:

YHAT (i, j)

contains the

i

th predicted value of the

j

y

-variable in the model.

18: pdyhat – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array yhat.

Constraints:

if $order = Nag_ColMajor$ , $pdyhat \geq n$ ;
if $order = Nag_RowMajor$ , $pdyhat \geq my$ .

19: fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
NE_BAD_PARAM: On entry, argument $⟨value⟩$ had an illegal value.
NE_ENUM_CHARACTER: On entry, $iscale = ⟨value⟩$ .
Constraint: if $orig = Nag_EstimatesStand$ , $iscale = Nag_PredNoScale$ , $Nag_PredStdScale$ or $Nag_PredUserScale$ .
NE_INT: On entry, $ip = ⟨value⟩$ .
Constraint: $ip > 1$ .
On entry, $my = ⟨value⟩$ .
Constraint: $my \geq 1$ .
On entry, $n = ⟨value⟩$ .
Constraint: $n \geq 1$ .
On entry, $pdb = ⟨value⟩$ .
Constraint: $pdb > 0$ .
On entry, $pdyhat = ⟨value⟩$ .
Constraint: $pdyhat > 0$ .
On entry, $pdz = ⟨value⟩$ .
Constraint: $pdz > 0$ .
NE_INT_2: On entry, $mz = ⟨value⟩$ and $ip = ⟨value⟩$ .
Constraint: $mz \geq ip$ .
On entry, $pdb = ⟨value⟩$ and $ip + 1 = ⟨value⟩$ .
Constraint: if $orig = Nag_EstimatesOrig$ , $pdb \geq 1 + ip$ .
On entry, $pdb = ⟨value⟩$ and $ip = ⟨value⟩$ .
Constraint: if $orig = Nag_EstimatesStand$ , $pdb \geq ip$ .
On entry, $pdb = ⟨value⟩$ and $my = ⟨value⟩$ .
Constraint: $pdb \geq my$ .
On entry, $pdyhat = ⟨value⟩$ and $my = ⟨value⟩$ .
Constraint: $pdyhat \geq my$ .
On entry, $pdyhat = ⟨value⟩$ and $n = ⟨value⟩$ .
Constraint: $pdyhat \geq n$ .
On entry, $pdz = ⟨value⟩$ and $mz = ⟨value⟩$ .
Constraint: $pdz \geq mz$ .
On entry, $pdz = ⟨value⟩$ and $n = ⟨value⟩$ .
Constraint: $pdz \geq n$ .
NE_INT_ARG_CONS: On entry, the number of elements of isz equal to $1$ is not ip.
NE_INT_ARRAY_VAL_1_OR_2: On entry, $isz [j - 1] = ⟨value⟩$ , $j = ⟨value⟩$ .
Constraint: $isz [j - 1] = 0 or 1$ .
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.

7 Accuracy

Not applicable.

8 Parallelism and Performance

nag_pls_orth_scores_pred (g02ldc) is not threaded by NAG in any implementation.

nag_pls_orth_scores_pred (g02ldc) makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.

Please consult the Users' Note for your implementation for any additional implementation-specific information.

9 Further Comments

nag_pls_orth_scores_pred (g02ldc) allocates internally

3 \times ip + my

elements of double storage.

10 Example

This example reads in parameter estimates for a fitted PLS model and prediction data, and the PLS model predictions are calculated.

NAG Library Function Documentnag_pls_orth_scores_pred (g02ldc)

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG Library Function Document

nag_pls_orth_scores_pred (g02ldc)