NAG Toolbox: nag_correg_linregm_constrain (g02dk)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{p}\left(\mathbf{ip}\times \mathbf{ip}+2\times \mathbf{ip}\right)$ – double array

As returned by nag_correg_linregm_fit (g02da) and nag_correg_linregm_update (g02dd).

2:     $\mathrm{c}\left(\mathit{ldc},\mathbf{iconst}\right)$ – double array

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

The iconst constraints stored by column, i.e., the $i$th constraint is stored in the $i$th column of c.

3:     $\mathrm{b}\left(\mathbf{ip}\right)$ – double array

The parameter estimates computed by using the singular value decomposition, ${\hat{\beta }}_{\text{svd}}$.

4:     $\mathrm{rss}$ – double scalar

The residual sum of squares as returned by nag_correg_linregm_fit (g02da) or nag_correg_linregm_update (g02dd).

Constraint: $\mathbf{rss}>0.0$.

5:     $\mathrm{idf}$ – int64int32nag_int scalar

The degrees of freedom associated with the residual sum of squares as returned by nag_correg_linregm_fit (g02da) or nag_correg_linregm_update (g02dd).

Constraint: $\mathbf{idf}>0$.

Optional Input Parameters

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

Default: the dimension of the array b and the first dimension of the array c. (An error is raised if these dimensions are not equal.)

$p$, the number of terms in the linear model.

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

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

Default: the second dimension of the array c.

The number of constraints to be imposed on the arguments, $n_{\mathrm{c}}$.

Constraint: $0<\mathbf{iconst}<\mathbf{ip}$.

Output Parameters

1:     $\mathrm{b}\left(\mathbf{ip}\right)$ – double array

The parameter estimates of the arguments with the constraints imposed, ${\hat{\beta }}_{\mathrm{c}}$.

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

The standard error of the parameter estimates in b.

3:     $\mathrm{covar}\left(\mathbf{ip}\times \left(\mathbf{ip}+1\right)/2\right)$ – double array

The upper triangular part of the variance-covariance matrix of the ip parameter estimates given in b. They are stored packed by column, i.e., the covariance between the parameter estimate given in $\mathbf{b}\left(i\right)$ and the parameter estimate given in $\mathbf{b}\left(j\right)$, $j\ge i$, is stored in $\mathbf{covar}\left(\left(j\times \left(j-1\right)/2+i\right)\right)$.

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

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

Error Indicators and Warnings

   $\mathbf{ifail}=1$

On entry,	$\mathbf{ip}<1$,
or	$\mathbf{iconst}\le 0$,
or	$\mathbf{iconst}\ge \mathbf{ip}$,
or	$\mathit{ldc}<\mathbf{ip}$,
or	$\mathbf{rss}\le 0.0$,
or	$\mathbf{idf}\le 0$.

   $\mathbf{ifail}=2$

c does not give a model of full rank.

   $\mathbf{ifail}=-99$

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: g02dk_example

function g02dk_example


fprintf('g02dk example results\n\n');

x = [1, 0, 0, 0;
     0, 0, 0, 1;
     0, 1, 0, 0;
     0, 0, 1, 0;
     0, 0, 0, 1;
     0, 1, 0, 0;
     0, 0, 0, 1;
     1, 0, 0, 0;
     0, 0, 1, 0;
     1, 0, 0, 0;
     0, 0, 1, 0;
     0, 1, 0, 0];
y = [33.63;     39.62;     38.18;     41.46;     38.02;     35.83;
     35.99;     36.58;     42.92;     37.80;     40.43;     37.89];

[n,m]  = size(x);
isx    = ones(m,1,'int64');
mean_p = 'M';
ip     = int64(m+1);

% Fit general linear regression model
[rss, idf, b, se, covar, res, h, q, svd, irank, p, wk, ifail] = ...
  g02da(mean_p, x, isx, ip, y);

% Display initial estimate results
fprintf('Initial estimates\n\n');
fprintf('Residual sum of squares = %12.4e\n', rss);
fprintf('Degrees of freedom      = %4d\n', idf);
fprintf('\nVariable   Parameter estimate   Standard error\n\n');
ivar = double([1:ip]');
fprintf('%6d%20.4e%20.4e\n',[ivar b se]');

% Constraints
c = ones(ip,ip-irank);
c(1,1) = 0;

% Re-estimate using constraints
[b, se, covar, ifail] = g02dk( ...
                               p, c, b, rss, idf);

% Display constrined estimates
fprintf('\nEstimates using constraints\n\n');
fprintf('Variable   Parameter estimate   Standard error\n\n');
ivar = double([1:ip]');
fprintf('%6d%20.4e%20.4e\n',[ivar b se]');

g02dk example results

Initial estimates

Residual sum of squares =   2.2227e+01
Degrees of freedom      =    8

Variable   Parameter estimate   Standard error

     1          3.0557e+01          3.8494e-01
     2          5.4467e+00          8.3896e-01
     3          6.7433e+00          8.3896e-01
     4          1.1047e+01          8.3896e-01
     5          7.3200e+00          8.3896e-01

Estimates using constraints

Variable   Parameter estimate   Standard error

     1          3.8196e+01          4.8117e-01
     2         -2.1925e+00          8.3342e-01
     3         -8.9583e-01          8.3342e-01
     4          3.4075e+00          8.3342e-01
     5         -3.1917e-01          8.3342e-01