NAG Library Function Document

nag_pls_orth_scores_fit (g02lcc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{order}$ – 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 $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 3.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2:    $\mathbf{ip}$ – IntegerInput

On entry: $m$, the number of predictor variables in the fitted model.

Constraint: $\mathbf{ip}>1$.

3:    $\mathbf{my}$ – IntegerInput

On entry: $r$, the number of response variables.

Constraint: $\mathbf{my}\ge 1$.

4:    $\mathbf{maxfac}$ – IntegerInput

On entry: $k$, the number of factors available in the PLS model.

Constraint: $1\le \mathbf{maxfac}\le \mathbf{ip}$.

5:    $\mathbf{nfact}$ – IntegerInput

On entry: $l$, the number of factors to include in the calculation of parameter estimates.

Constraint: $1\le \mathbf{nfact}\le \mathbf{maxfac}$.

6:    $\mathbf{p}\left[\mathit{dim}\right]$ – const doubleInput

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

• $\max \left(1,\mathbf{pdp}\times \mathbf{maxfac}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{ip}\times \mathbf{pdp}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

The $\left(i,j\right)$th element of the matrix $P$ is stored in

• $\mathbf{p}\left[\left(j-1\right)\times \mathbf{pdp}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{p}\left[\left(i-1\right)\times \mathbf{pdp}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: $x$-loadings as returned from nag_pls_orth_scores_svd (g02lac) and nag_pls_orth_scores_wold (g02lbc).

7:    $\mathbf{pdp}$ – IntegerInput

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

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pdp}\ge \mathbf{ip}$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdp}\ge \mathbf{maxfac}$.

8:    $\mathbf{c}\left[\mathit{dim}\right]$ – const doubleInput

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

• $\max \left(1,\mathbf{pdc}\times \mathbf{maxfac}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{my}\times \mathbf{pdc}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

The $\left(i,j\right)$th element of the matrix $C$ is stored in

• $\mathbf{c}\left[\left(j-1\right)\times \mathbf{pdc}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{c}\left[\left(i-1\right)\times \mathbf{pdc}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: $y$-loadings as returned from nag_pls_orth_scores_svd (g02lac) and nag_pls_orth_scores_wold (g02lbc).

9:    $\mathbf{pdc}$ – IntegerInput

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

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pdc}\ge \mathbf{my}$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdc}\ge \mathbf{maxfac}$.

10:  $\mathbf{w}\left[\mathit{dim}\right]$ – const doubleInput

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

• $\max \left(1,\mathbf{pdw}\times \mathbf{maxfac}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{ip}\times \mathbf{pdw}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

The $\left(i,j\right)$th element of the matrix $W$ is stored in

• $\mathbf{w}\left[\left(j-1\right)\times \mathbf{pdw}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{w}\left[\left(i-1\right)\times \mathbf{pdw}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: $x$-weights as returned from nag_pls_orth_scores_svd (g02lac) and nag_pls_orth_scores_wold (g02lbc).

11:  $\mathbf{pdw}$ – IntegerInput

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

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pdw}\ge \mathbf{ip}$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdw}\ge \mathbf{maxfac}$.

12:  $\mathbf{rcond}$ – doubleInput

On entry: singular values of $P^{\mathrm{T}}W$ less than rcond times the maximum singular value are treated as zero when calculating parameter estimates. If rcond is negative, a value of $0.005$ is used.

13:  $\mathbf{b}\left[\mathit{dim}\right]$ – doubleOutput

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

• $\max \left(1,\mathbf{pdb}\times \mathbf{my}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{ip}\times \mathbf{pdb}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

Where $\mathbf{B}\left(i,j\right)$ appears in this document, it refers to the array element

• $\mathbf{b}\left[\left(j-1\right)\times \mathbf{pdb}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{b}\left[\left(i-1\right)\times \mathbf{pdb}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On exit: $\mathbf{B}\left(\mathit{i},\mathit{j}\right)$ contains the parameter estimate for the $\mathit{i}$th predictor variable in the model for the $\mathit{j}$th response variable, for $\mathit{i}=1,2,\dots ,\mathbf{ip}$ and $\mathit{j}=1,2,\dots ,\mathbf{my}$.

14:  $\mathbf{pdb}$ – IntegerInput

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

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pdb}\ge \mathbf{ip}$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdb}\ge \mathbf{my}$.

15:  $\mathbf{orig}$ – Nag_EstimatesOptionInput

On entry: indicates how parameter estimates are calculated.

$\mathbf{orig}=\mathrm{Nag\_EstimatesStand}$

Parameter estimates for the centred, and possibly, scaled data.

$\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$

Parameter estimates for the original data.

Constraint: $\mathbf{orig}=\mathrm{Nag\_EstimatesStand}$ or $\mathrm{Nag\_EstimatesOrig}$.

16:  $\mathbf{xbar}\left[\mathbf{ip}\right]$ – const doubleInput

On entry: if $\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$, mean values of predictor variables in the model; otherwise xbar is not referenced.

17:  $\mathbf{ybar}\left[\mathbf{my}\right]$ – const doubleInput

On entry: if $\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$, mean value of each response variable in the model; otherwise ybar is not referenced.

18:  $\mathbf{iscale}$ – Nag_ScalePredictorInput

On entry: if $\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$, 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 $\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$, $\mathbf{iscale}=\mathrm{Nag\_PredNoScale}$, $\mathrm{Nag\_PredStdScale}$ or $\mathrm{Nag\_PredUserScale}$.

19:  $\mathbf{xstd}\left[\mathbf{ip}\right]$ – const doubleInput

On entry: if $\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$ and $\mathbf{iscale}\ne \mathrm{Nag\_PredNoScale}$, 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.

20:  $\mathbf{ystd}\left[\mathbf{my}\right]$ – const doubleInput

On entry: if $\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$ and $\mathbf{iscale}\ne \mathrm{Nag\_PredNoScale}$, 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.

21:  $\mathbf{ob}\left[\mathit{dim}\right]$ – doubleOutput

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

• $\mathbf{pdob}\times \mathbf{my}$ when $\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$ and $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\left(\mathbf{ip}+1\right)\times \mathbf{pdob}\right)$ when $\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$ and $\mathbf{order}=\mathrm{Nag\_RowMajor}$;
• $1$ otherwise.

Where $\mathbf{OB}\left(i,j\right)$ appears in this document, it refers to the array element

• $\mathbf{ob}\left[\left(j-1\right)\times \mathbf{pdob}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{ob}\left[\left(i-1\right)\times \mathbf{pdob}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On exit: if $\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$, $\mathbf{OB}\left(1,\mathit{j}\right)$ contains the intercept value for the $\mathit{j}$th response variable, and $\mathbf{OB}\left(\mathit{i}+1,\mathit{j}\right)$ contains the parameter estimate on the original scale for the $\mathit{i}$th predictor variable in the model, for $\mathit{i}=1,2,\dots ,\mathbf{ip}$ and $\mathit{j}=1,2,\dots ,\mathbf{my}$. Otherwise ob is not referenced.

22:  $\mathbf{pdob}$ – IntegerInput

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

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$,
  • if $\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$, $\mathbf{pdob}\ge \mathbf{ip}+1$;
  • otherwise $\mathbf{pdob}\ge 1$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$,
  • if $\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$, $\mathbf{pdob}\ge \mathbf{my}$;
  • otherwise $\mathbf{pdob}\ge 1$.

23:  $\mathbf{vipopt}$ – IntegerInput

On entry: a flag that determines variable influence on projections (VIP) options.

$\mathbf{vipopt}=0$

VIP are not calculated.

$\mathbf{vipopt}=1$

VIP are calculated for predictor variables using the mean explained variance in responses.

$\mathbf{vipopt}=\mathbf{my}$

VIP are calculated for predictor variables for each response variable in the model.

Note that setting $\mathbf{vipopt}=\mathbf{my}$ when $\mathbf{my}=1$ gives the same result as setting $\mathbf{vipopt}=1$ directly.

Constraint: $\mathbf{vipopt}=0$, $1$, $$ or $\mathbf{my}$.

24:  $\mathbf{ycv}\left[\mathit{dim}\right]$ – const doubleInput

Note: the dimension, dim, of the array ycv must be at least $\mathbf{my}$ when $\mathbf{vipopt}\ne 0$.

Where $\mathbf{YCV}\left(i,j\right)$ appears in this document, it refers to the array element

• $\mathbf{ycv}\left[\left(j-1\right)\times \mathbf{pdycv}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{ycv}\left[\left(i-1\right)\times \mathbf{pdycv}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: if $\mathbf{vipopt}\ne 0$, $\mathbf{YCV}\left(\mathit{i},\mathit{j}\right)$ is the cumulative percentage of variance of the $\mathit{j}$th response variable explained by the first $\mathit{i}$ factors, for $\mathit{i}=1,2,\dots ,\mathbf{nfact}$ and $\mathit{j}=1,2,\dots ,\mathbf{my}$; otherwise ycv is not referenced.

25:  $\mathbf{pdycv}$ – IntegerInput

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

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, if $\mathbf{vipopt}\ne 0$, $\mathbf{pdycv}\ge \mathbf{nfact}$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$,
  • if $\mathbf{vipopt}\ne 0$, $\mathbf{pdycv}\ge \mathbf{my}$.

26:  $\mathbf{vip}\left[\mathit{dim}\right]$ – doubleOutput

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

• $\max \left(1,\mathbf{pdvip}\times \mathbf{vipopt}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{ip}\times \mathbf{pdvip}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$ and $\mathbf{vipopt}\ne 0$.

Where $\mathbf{VIP}\left(i,j\right)$ appears in this document, it refers to the array element

• $\mathbf{vip}\left[\left(j-1\right)\times \mathbf{pdvip}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{vip}\left[\left(i-1\right)\times \mathbf{pdvip}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On exit: if $\mathbf{vipopt}=1$, $\mathbf{VIP}\left(\mathit{i},1\right)$ contains the VIP statistic for the $\mathit{i}$th predictor variable in the model for all response variables, for $\mathit{i}=1,2,\dots ,\mathbf{ip}$.

If $\mathbf{vipopt}=\mathbf{my}$, $\mathbf{VIP}\left(\mathit{i},\mathit{j}\right)$ contains the VIP statistic for the $\mathit{i}$th predictor variable in the model for the $\mathit{j}$th response variable, for $\mathit{i}=1,2,\dots ,\mathbf{ip}$ and $\mathit{j}=1,2,\dots ,\mathbf{my}$.

Otherwise vip is not referenced.

27:  $\mathbf{pdvip}$ – IntegerInput

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

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, if $\mathbf{vipopt}\ne 0$, $\mathbf{pdvip}\ge \mathbf{ip}$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdvip}\ge \mathbf{vipopt}$.

28:  $\mathbf{fail}$ – 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_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_ENUM_INT

On entry, $\mathbf{iscale}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$, $\mathbf{iscale}=\mathrm{Nag\_PredNoScale}$ or $\mathrm{Nag\_PredStdScale}$.

On entry, $\mathbf{orig}=〈\mathit{\text{value}}〉$ and $\mathbf{my}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{my}>0$.

NE_ENUM_INT_2

On entry, $\mathbf{orig}=〈\mathit{\text{value}}〉$, $\mathbf{pdob}=〈\mathit{\text{value}}〉$, $\mathbf{my}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$, $\mathbf{pdob}\ge \mathbf{my}$;
otherwise $\mathbf{pdob}\ge 1$.

NE_INT

On entry, $\mathbf{ip}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ip}>1$.

On entry, $\mathbf{my}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{my}\ge 1$.

On entry, $\mathbf{pdb}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdb}>0$.

On entry, $\mathbf{pdc}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdc}>0$.

On entry, $\mathbf{pdob}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdob}>0$.

On entry, $\mathbf{pdp}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdp}>0$.

On entry, $\mathbf{pdvip}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdvip}>0$.

On entry, $\mathbf{pdw}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdw}>0$.

On entry, $\mathbf{pdycv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdycv}>0$.

NE_INT_2

On entry, $\mathbf{maxfac}=〈\mathit{\text{value}}〉$ and $\mathbf{ip}=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{maxfac}\le \mathbf{ip}$.

On entry, $\mathbf{nfact}=〈\mathit{\text{value}}〉$ and $\mathbf{maxfac}=〈\mathit{\text{value}}〉$.
Constraint: $1\le \mathbf{nfact}\le \mathbf{maxfac}$.

On entry, $\mathbf{pdb}=〈\mathit{\text{value}}〉$ and $\mathbf{ip}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdb}\ge \mathbf{ip}$.

On entry, $\mathbf{pdb}=〈\mathit{\text{value}}〉$ and $\mathbf{my}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdb}\ge \mathbf{my}$.

On entry, $\mathbf{pdc}=〈\mathit{\text{value}}〉$ and $\mathbf{maxfac}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdc}\ge \mathbf{maxfac}$.

On entry, $\mathbf{pdc}=〈\mathit{\text{value}}〉$ and $\mathbf{my}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdc}\ge \mathbf{my}$.

On entry, $\mathbf{pdob}=〈\mathit{\text{value}}〉$ and $\mathbf{ip}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{orig}=\mathrm{Nag\_EstimatesOrig}$, $\mathbf{pdob}\ge \mathbf{ip}+1$.

On entry, $\mathbf{pdp}=〈\mathit{\text{value}}〉$ and $\mathbf{ip}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdp}\ge \mathbf{ip}$.

On entry, $\mathbf{pdp}=〈\mathit{\text{value}}〉$ and $\mathbf{maxfac}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdp}\ge \mathbf{maxfac}$.

On entry, $\mathbf{pdvip}=〈\mathit{\text{value}}〉$ and $\mathbf{ip}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{vipopt}\ne 0$, $\mathbf{pdvip}\ge \mathbf{ip}$.

On entry, $\mathbf{pdvip}=〈\mathit{\text{value}}〉$ and $\mathbf{vipopt}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdvip}\ge \mathbf{vipopt}$.

On entry, $\mathbf{pdw}=〈\mathit{\text{value}}〉$ and $\mathbf{ip}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdw}\ge \mathbf{ip}$.

On entry, $\mathbf{pdw}=〈\mathit{\text{value}}〉$ and $\mathbf{maxfac}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdw}\ge \mathbf{maxfac}$.

On entry, $\mathbf{pdycv}=〈\mathit{\text{value}}〉$ and $\mathbf{nfact}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{vipopt}\ne 0$, $\mathbf{pdycv}\ge \mathbf{nfact}$.

On entry, $\mathbf{vipopt}=〈\mathit{\text{value}}〉$ and $\mathbf{my}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{my}>0$.

On entry, $\mathbf{vipopt}=〈\mathit{\text{value}}〉$ and $\mathbf{my}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{vipopt}=0$, $1$, $$ or $\mathbf{my}$.

NE_INT_3

On entry, $\mathbf{pdycv}=〈\mathit{\text{value}}〉$, $\mathbf{vipopt}=〈\mathit{\text{value}}〉$ and $\mathbf{my}=〈\mathit{\text{value}}〉$.
Constraint:
if $\mathbf{vipopt}\ne 0$, $\mathbf{pdycv}\ge \mathbf{my}$.

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_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

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g02lcce.c)

10.2

Program Data

Program Data (g02lcce.d)

10.3

Program Results

Program Results (g02lcce.r)