NAG Toolbox: nag_correg_linregm_estfunc (g02dn)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

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

$k$, the rank of the independent variables.

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

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

The ip values of the estimates of the arguments of the model, $\hat{\beta }$.

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

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

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

$f$, the linear function to be estimated.

6:     $\mathrm{tol}$ – double scalar

$\eta$, the tolerance value used in the check for estimability.

$\mathbf{tol}\le 0.0$

$\sqrt{\epsilon }$, where $\epsilon$ is the machine precision, is used instead.

Optional Input Parameters

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

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

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

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

Output Parameters

1:     $\mathrm{est}$ – logical scalar

Indicates if the function was estimable.

$\mathbf{est}=\mathit{true}$

The function is estimable.

$\mathbf{est}=\mathit{false}$

The function is not estimable and stat, sestat and t are not set.

2:     $\mathrm{stat}$ – double scalar

If $\mathbf{est}=\mathit{true}$, stat contains the estimate of the function, $f^{\mathrm{T}}\hat{\beta }$.

3:     $\mathrm{sestat}$ – double scalar

If $\mathbf{est}=\mathit{true}$, sestat contains the standard error of the estimate of the function, $\mathrm{se}\left(F\right)$.

4:     $\mathrm{t}$ – double scalar

If $\mathbf{est}=\mathit{true}$, t contains the $t$-statistic for the test of the function being equal to zero.

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

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

Error Indicators and Warnings

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

   $\mathbf{ifail}=1$

On entry,	$\mathbf{ip}<1$,
or	$\mathbf{irank}<1$,
or	$\mathbf{irank}>\mathbf{ip}$.

W  $\mathbf{ifail}=2$

On entry,

$\mathbf{irank}=\mathbf{ip}$. In this case est is returned as true and all statistics are calculated.

   $\mathbf{ifail}=3$

Standard error of statistic $=0.0$; this may be due to rounding errors if the standard error is very small or due to mis-specified inputs covar and f.

   $\mathbf{ifail}=-99$

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: g02dn_example

function g02dn_example


fprintf('g02dn 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 results
fprintf('Estimates from g02da\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]');

% Estimable functions
f = [1 1  0 0 0;
     0 1 -1 0 0;
     0 1  0 0 0];
nf = size(f,1);
tol = 1e-05;

% Loop over estimable functions
for j = 1:nf
  [est, stat, sestat, t, ifail] = ...
  g02dn(irank, b, covar, p, f(j,:), tol);

  % Display results
   fprintf('\nFunction %2d\n\n', j);
   fprintf('%8.2f', f(j,:));
   if est
     fprintf('\n\nstat = %10.4f, se = %10.4f, t = %10.4f\n', stat, sestat, t);
   else
     fprintf('\n\nFunction not estimable\n');
   end
end

g02dn example results

Estimates from g02da

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

Function  1

    1.00    1.00    0.00    0.00    0.00

stat =    36.0033, se =     0.9623, t =    37.4119

Function  2

    0.00    1.00   -1.00    0.00    0.00

stat =    -1.2967, se =     1.3610, t =    -0.9528

Function  3

    0.00    1.00    0.00    0.00    0.00

Function not estimable