NAG Library Routine Document

g02lcf  (pls_fit)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{ip}$ – IntegerInput

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

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

2:     $\mathbf{my}$ – IntegerInput

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

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

3:     $\mathbf{maxfac}$ – IntegerInput

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

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

4:     $\mathbf{nfact}$ – IntegerInput

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

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

5:     $\mathbf{p}\left(\mathbf{ldp},\mathbf{maxfac}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: $x$-loadings as returned from g02laf and g02lbf.

6:     $\mathbf{ldp}$ – IntegerInput

On entry: the first dimension of the array p as declared in the (sub)program from which g02lcf is called.

Constraint: $\mathbf{ldp}\ge \mathbf{ip}$.

7:     $\mathbf{c}\left(\mathbf{ldc},\mathbf{maxfac}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: $y$-loadings as returned from g02laf and g02lbf.

8:     $\mathbf{ldc}$ – IntegerInput

On entry: the first dimension of the array c as declared in the (sub)program from which g02lcf is called.

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

9:     $\mathbf{w}\left(\mathbf{ldw},\mathbf{maxfac}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: $x$-weights as returned from g02laf and g02lbf.

10:   $\mathbf{ldw}$ – IntegerInput

On entry: the first dimension of the array w as declared in the (sub)program from which g02lcf is called.

Constraint: $\mathbf{ldw}\ge \mathbf{ip}$.

11:   $\mathbf{rcond}$ – Real (Kind=nag_wp)Input

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.

12:   $\mathbf{b}\left(\mathbf{ldb},\mathbf{my}\right)$ – Real (Kind=nag_wp) arrayOutput

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 $\mathit{j}=1,2,\dots ,\mathbf{my}$.

13:   $\mathbf{ldb}$ – IntegerInput

On entry: the first dimension of the array b as declared in the (sub)program from which g02lcf is called.

Constraint: $\mathbf{ldb}\ge \mathbf{ip}$.

14:   $\mathbf{orig}$ – IntegerInput

On entry: indicates how parameter estimates are calculated.

$\mathbf{orig}=-1$

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

$\mathbf{orig}=1$

Parameter estimates for the original data.

Constraint: $\mathbf{orig}=-1$ or $1$.

15:   $\mathbf{xbar}\left(\mathbf{ip}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: if $\mathbf{orig}=1$, mean values of predictor variables in the model; otherwise xbar is not referenced.

16:   $\mathbf{ybar}\left(\mathbf{my}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: if $\mathbf{orig}=1$, mean value of each response variable in the model; otherwise ybar is not referenced.

17:   $\mathbf{iscale}$ – IntegerInput

On entry: if $\mathbf{orig}=1$, iscale must take the value supplied to either g02laf or g02lbf; otherwise iscale is not referenced.

Constraint: if $\mathbf{orig}=1$, $\mathbf{iscale}=-1$, $1$ or $2$.

18:   $\mathbf{xstd}\left(\mathbf{ip}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: if $\mathbf{orig}=1$ and $\mathbf{iscale}\ne -1$, the scalings of predictor variables in the model as returned from either g02laf or g02lbf; otherwise xstd is not referenced.

19:   $\mathbf{ystd}\left(\mathbf{my}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: if $\mathbf{orig}=1$ and $\mathbf{iscale}\ne -1$, the scalings of response variables as returned from either g02laf or g02lbf; otherwise ystd is not referenced.

20:   $\mathbf{ob}\left(\mathbf{ldob},\mathbf{my}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: if $\mathbf{orig}=1$, $\mathbf{ob}\left(1,\mathit{j}\right)$ 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.

21:   $\mathbf{ldob}$ – IntegerInput

On entry: the first dimension of the array ob as declared in the (sub)program from which g02lcf is called.

Constraints:

• if $\mathbf{orig}=1$, $\mathbf{ldob}\ge \mathbf{ip}+1$;
• otherwise $\mathbf{ldob}\ge 1$.

22:   $\mathbf{vipopt}$ – 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 $\mathbf{my}$.

23:   $\mathbf{ycv}\left(\mathbf{ldycv},\mathbf{my}\right)$ – Real (Kind=nag_wp) arrayInput

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.

24:   $\mathbf{ldycv}$ – IntegerInput

On entry: the first dimension of the array ycv as declared in the (sub)program from which g02lcf is called.

Constraint: if $\mathbf{vipopt}\ne 0$, $\mathbf{ldycv}\ge \mathbf{nfact}$.

25:   $\mathbf{vip}\left(\mathbf{ldvip},\mathbf{vipopt}\right)$ – Real (Kind=nag_wp) arrayOutput

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.

26:   $\mathbf{ldvip}$ – IntegerInput

On entry: the first dimension of the array vip as declared in the (sub)program from which g02lcf is called.

Constraint: if $\mathbf{vipopt}\ne 0$, $\mathbf{ldvip}\ge \mathbf{ip}$.

27:   $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

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

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

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

On entry, $\mathbf{iscale}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{orig}=1$, $\mathbf{iscale}=-1$ or $1$.

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

On entry, $\mathbf{orig}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{orig}=-1$ or $1$.

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

$\mathbf{ifail}=2$

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

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

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

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

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

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

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

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

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 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 (g02lcfe.f90)

10.2

Program Data

Program Data (g02lcfe.d)

10.3

Program Results

Program Results (g02lcfe.r)