NAG Toolbox: nag_correg_glm_estfunc (g02gn)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

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

$k$, the rank of the dependent 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:     $\mathrm{v}\left(\mathit{ldv},\mathbf{ip}+7\right)$ – double array

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

As returned by nag_correg_glm_normal (g02ga), nag_correg_glm_binomial (g02gb), nag_correg_glm_poisson (g02gc) and nag_correg_glm_gamma (g02gd).

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

$f$, the linear function to be estimated.

6:     $\mathrm{tol}$ – double scalar

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

If $\mathbf{tol}\le 0.0$ then $\sqrt{\epsilon }$, 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 and the first dimension of the array v. (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 z 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:     $\mathrm{z}$ – double scalar

If $\mathbf{est}=\mathit{true}$, z contains the $z$ 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	$\mathbf{irank}>\mathbf{ip}$,
or	$\mathit{ldv}<\mathbf{ip}$.

W  $\mathbf{ifail}=2$

On entry,

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

W  $\mathbf{ifail}=3$

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: g02gn_example

function g02gn_example


fprintf('g02gn example results\n\n');

x = [
     1  0  0  1  0  0  0  0;
     1  0  0  0  1  0  0  0;
     1  0  0  0  0  1  0  0;
     1  0  0  0  0  0  1  0;
     1  0  0  0  0  0  0  1;
     0  1  0  1  0  0  0  0;
     0  1  0  0  1  0  0  0;
     0  1  0  0  0  1  0  0;
     0  1  0  0  0  0  1  0;
     0  1  0  0  0  0  0  1;
     0  0  1  1  0  0  0  0;
     0  0  1  0  1  0  0  0;
     0  0  1  0  0  1  0  0;
     0  0  1  0  0  0  1  0;
     0  0  1  0  0  0  0  1];

y = [141  67 114  79  39 131  66 143  72  35  36  14  38  28  16];

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

link   = 'L';
mean_p = 'M';
eps = 1e-6;
tol = 5e-5;

% Fit generalized linear model with Poisson errors
[dev, idf, b, irank, se, covar, v, ifail] = ...
g02gc( ...
       link, mean_p, x, isx, ip, y, 'eps', eps, 'tol', tol);

% Display initial results
fprintf('Deviance           = %12.4e\n', dev);
fprintf('Degrees of freedom = %2d\n', idf);
fprintf('\nVariable   Parameter estimate   Standard error\n\n');
ivar = double([1:ip]');
fprintf('%6d%16.4f%20.4f\n',[ivar b se]');

f = [1  0  0;
     1  1  1;
     0 -1  0;
     0  0  0;
     1  0  0;
     0  0  0;
     0  0  0;
     0  0  0;
     0  0  0];
tol = 5e-05;

% Estimate the estimable functions
for j = 1:size(f,2)
  [est, stat, sestat, z, ifail] = ...
  g02gn( ...
         irank, b, covar, v, f(:,j), tol, 'ip', ip);

  % Display results
   fprintf('\nFunction %2d\n\n', j);
   fprintf('%6.1f', f(:,j)');
   if est
     fprintf('\n\nstat = %10.4f, se = %10.4f, z = %10.4f\n', stat, sestat, z);
   else
     fprintf('\n\nFunction not estimable\n');
   end
end

g02gn example results

Deviance           =   9.0379e+00
Degrees of freedom =  8

Variable   Parameter estimate   Standard error

     1          2.5977              0.0258
     2          1.2619              0.0438
     3          1.2777              0.0436
     4          0.0580              0.0668
     5          1.0307              0.0551
     6          0.2910              0.0732
     7          0.9876              0.0559
     8          0.4880              0.0675
     9         -0.1996              0.0904

Function  1

   1.0   1.0   0.0   0.0   1.0   0.0   0.0   0.0   0.0

stat =     4.8903, se =     0.0674, z =    72.5934

Function  2

   0.0   1.0  -1.0   0.0   0.0   0.0   0.0   0.0   0.0

stat =    -0.0158, se =     0.0672, z =    -0.2350

Function  3

   0.0   1.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0

Function not estimable