NAG Toolbox: nag_correg_pls_pred (g02ld)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{orig}$ – int64int32nag_int scalar

Indicates how parameter estimates are supplied.

$\mathbf{orig}=1$

Parameter estimates are for the original data.

$\mathbf{orig}=-1$

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

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

2:     $\mathrm{xbar}\left(\mathbf{ip}\right)$ – double array

If $\mathbf{orig}=-1$, xbar must contain mean values of predictor variables in the model; otherwise xbar is not referenced.

3:     $\mathrm{ybar}\left(\mathbf{my}\right)$ – double array

If $\mathbf{orig}=-1$, ybar must contain the mean value of each response variable in the model; otherwise ybar is not referenced.

4:     $\mathrm{iscale}$ – int64int32nag_int scalar

If $\mathbf{orig}=-1$, iscale must take the value supplied to either nag_correg_pls_svd (g02la) or nag_correg_pls_wold (g02lb); otherwise iscale is not referenced.

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

5:     $\mathrm{xstd}\left(\mathbf{ip}\right)$ – double array

If $\mathbf{orig}=-1$ and $\mathbf{iscale}\ne -1$, xstd must contain the scalings of predictor variables in the model as returned from either nag_correg_pls_svd (g02la) or nag_correg_pls_wold (g02lb); otherwise xstd is not referenced.

6:     $\mathrm{ystd}\left(\mathbf{my}\right)$ – double array

If $\mathbf{orig}=-1$ and $\mathbf{iscale}\ne -1$, ystd must contain the scalings of response variables as returned from either nag_correg_pls_svd (g02la) or nag_correg_pls_wold (g02lb); otherwise ystd is not referenced.

7:     $\mathrm{b}\left(\mathit{ldb},\mathbf{my}\right)$ – double array

ldb, the first dimension of the array, must satisfy the constraint

• if $\mathbf{orig}=-1$, $\mathit{ldb}\ge \mathbf{ip}$;
• if $\mathbf{orig}=1$, $\mathit{ldb}\ge 1+\mathbf{ip}$.

If $\mathbf{orig}=-1$, b must contain the parameter estimate for the centred, and possibly scaled, data as returned by nag_correg_pls_fit (g02lc); otherwise b must contain the parameter estimates for the original data as returned by nag_correg_pls_fit (g02lc).

8:     $\mathrm{isz}\left(\mathbf{mz}\right)$ – int64int32nag_int array

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.

If $\mathbf{isz}\left(\mathit{j}\right)=1$, the $\mathit{j}$th predictor variable is included in the model, for $\mathit{j}=1,2,\dots ,\mathbf{mz}$, otherwise $\mathbf{isz}\left(j\right)=0$.

Constraints:

• $\mathbf{isz}\left(\mathit{j}\right)=0\text{ or }1$, for $\mathit{j}=1,2,\dots ,\mathbf{mz}$;
• ${\sum }_j\mathbf{isz}\left(j\right)=\mathbf{ip}$.

9:     $\mathrm{z}\left(\mathit{ldz},\mathbf{mz}\right)$ – double array

ldz, the first dimension of the array, must satisfy the constraint $\mathit{ldz}\ge \mathbf{n}$.

$\mathbf{z}\left(\mathit{i},\mathit{j}\right)$ contains the $\mathit{i}$th observation on the $\mathit{j}$th available predictor variable, for $\mathit{i}=1,2,\dots ,\mathbf{n}$ and $\mathit{j}=1,2,\dots ,\mathbf{mz}$.

Optional Input Parameters

1:     $\mathrm{ip}$ – int64int32nag_int scalar

Default: the dimension of the arrays xbar, xstd. (An error is raised if these dimensions are not equal.)

The number of predictor variables in the fitted model. ip must take the same value as that supplied to nag_correg_pls_svd (g02la) or nag_correg_pls_wold (g02lb) to fit the model.

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

2:     $\mathrm{my}$ – int64int32nag_int scalar

Default: the dimension of the arrays ybar, ystd and the second dimension of the array b. (An error is raised if these dimensions are not equal.)

The number of response variables in the fitted model. my must take the same value as that supplied to nag_correg_pls_svd (g02la) or nag_correg_pls_wold (g02lb) to fit the model.

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

3:     $\mathrm{n}$ – int64int32nag_int scalar

Default: the first dimension of the array z.

$n$, the number of observations in the test data $Z$.

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

4:     $\mathrm{mz}$ – int64int32nag_int scalar

Default: the dimension of the array isz and the second dimension of the array z. (An error is raised if these dimensions are not equal.)

The number of available predictor variables in the test data.

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

Output Parameters

1:     $\mathrm{yhat}\left(\mathit{ldyhat},\mathbf{my}\right)$ – double array

$\mathbf{yhat}\left(i,j\right)$ contains the $i$th predicted value of the $j$th $y$-variable in the model.

2:     $\mathrm{ifail}$ – int64int32nag_int scalar

$\mathbf{ifail}=\mathbf{0}$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

   $\mathbf{ifail}=1$

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

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

Constraint: $\mathbf{isz}\left(j\right)=0\text{ or }1$.

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

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

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

   $\mathbf{ifail}=2$

Constraint: if $\mathbf{orig}=1$, $\mathit{ldb}\ge 1+\mathbf{ip}$.

Constraint: if $\mathbf{orig}=-1$, $\mathit{ldb}\ge \mathbf{ip}$.

Constraint: $\mathit{ldyhat}\ge \mathbf{n}$.

Constraint: $\mathit{ldz}\ge \mathbf{n}$.

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

   $\mathbf{ifail}=3$

On entry, the number of elements of isz equal to $1$ is not ip.

   $\mathbf{ifail}=-99$

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

   $\mathbf{ifail}=-399$

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

   $\mathbf{ifail}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: g02ld_example

function g02ld_example


fprintf('g02ld example results\n\n');

n = 15;
z = zeros(n,n);
z(:,1:8) = ...
       [-2.6931, -2.5271, -1.2871, 3.0777,  0.3891, -0.0701,  1.9607, -1.6324;
        -2.6931, -2.5271, -1.2871, 3.0777,  0.3891, -0.0701,  1.9607, -1.6324;
        -2.6931, -2.5271, -1.2871, 3.0777,  0.3891, -0.0701,  0.0744, -1.7333;
        -2.6931, -2.5271, -1.2871, 3.0777,  0.3891, -0.0701,  0.0744, -1.7333;
        -2.6931, -2.5271, -1.2871, 2.8369,  1.4092, -3.1398,  0.0744, -1.7333;
        -2.6931, -2.5271, -1.2871, 3.0777,  0.3891, -0.0701, -4.7548,  3.6521;
        -2.6931, -2.5271, -1.2871, 3.0777,  0.3891, -0.0701,  0.0744, -1.7333;
        -2.6931, -2.5271, -1.2871, 3.0777,  0.3891, -0.0701,  2.4064,  1.7438;
        -2.6931, -2.5271, -1.2871, 0.0744, -1.7333,  0.0902,  0.0744, -1.7333;
         2.2261, -5.3648,  0.3049, 3.0777,  0.3891, -0.0701,  0.0744, -1.7333;
        -4.1921, -1.0285, -0.9801, 3.0777,  0.3891, -0.0701,  0.0744, -1.7333;
        -4.9217,  1.2977,  0.4473, 3.0777,  0.3891, -0.0701,  0.0744, -1.7333;
        -2.6931, -2.5271, -1.2871, 3.0777,  0.3891, -0.0701,  2.2261, -5.3648;
        -2.6931, -2.5271, -1.2871, 3.0777,  0.3891, -0.0701, -4.9217,  1.2977;
        -2.6931, -2.5271, -1.2871, 3.0777,  0.3891, -0.0701, -4.1921, -1.0285];
z(:,9:n) = ...
       [ 0.5746,  1.9607, -1.6324, 0.5740,  2.8369,  1.4092, -3.1398;
         0.5746,  0.0744, -1.7333, 0.0902,  2.8369,  1.4092, -3.1398;
         0.0902,  1.9607, -1.6324, 0.5746,  2.8369,  1.4092, -3.1398;
         0.0902,  0.0744, -1.7333, 0.0902,  2.8369,  1.4092, -3.1398;
         0.0902,  0.0744, -1.7333, 0.0902,  2.8369,  1.4092, -3.1398;
         0.8524,  0.0744, -1.7333, 0.0902,  2.8369,  1.4092, -3.1398;
         0.0902,  0.0744, -1.7333, 0.0902, -1.2201,  0.8829,  2.2253;
         1.1057,  0.0744, -1.7333, 0.0902,  2.8369,  1.4092, -3.1398;
         0.0902,  0.0744, -1.7333, 0.0902,  2.8369,  1.4092, -3.1398;
         0.0902,  0.0744, -1.7333, 0.0902,  2.8369,  1.4092, -3.1398;
         0.0902,  0.0744, -1.7333, 0.0902,  2.8369,  1.4092, -3.1398;
         0.0902,  0.0744, -1.7333, 0.0902,  2.8369,  1.4092, -3.1398;
         0.3049,  2.2261, -5.3648, 0.3049,  2.8369,  1.4092, -3.1398;
         0.4473,  0.0744, -1.7333, 0.0902,  2.8369,  1.4092, -3.1398;
        -0.9801,  0.0744, -1.7333, 0.0902,  2.8369,  1.4092, -3.1398];


% Means and scalings
orig = int64(-1);
xbar = [-2.6137; -2.3614; -1.0449;  2.8614;  0.3156;
        -0.2641; -0.3146; -1.1221;  0.2401;  0.4694;
        -1.9619;  0.1691;  2.5664;  1.3741; -2.7821];
ybar = [0.452];
iscale = int64(1);
xstd = [ 1.4956;  1.3233;  0.5829;  0.7735;  0.6247;
         0.7966;  2.4113;  2.0421;  0.4678;  0.8197;
         0.9420;  0.1735;  1.0475;  0.1359;  1.3853];
ystd = [0.9062];

b    = [-0.1383;  0.0572; -0.1906;  0.1238;  0.0591;
         0.0936; -0.2842;  0.4713;  0.2661; -0.0914;
         0.1226; -0.0488;  0.0332;  0.0332; -0.0332];
isz = ones(n, 1, 'int64');

% Calculate predictions
[yhat, ifail] = g02ld( ...
                       orig, xbar, ybar, iscale, xstd, ystd, b, isz, z);

% Display results
disp('Predicted values');
disp(yhat);

g02ld example results

Predicted values
    0.2132
    0.5152
    0.1437
    0.4459
    0.1716
    2.4809
    0.0964
    1.4475
   -0.1546
   -0.5492
    0.5393
    0.2686
   -1.1332
    1.7975
    0.4973