NAG Library Routine Document

g02dcf  (linregm_obs_edit)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{update}$ – Character(1)Input

On entry: indicates if an observation is to be added or deleted.

$\mathbf{update}=\text{'A'}$

The observation is added.

$\mathbf{update}=\text{'D'}$

The observation is deleted.

Constraint: $\mathbf{update}=\text{'A'}$ or $\text{'D'}$.

2:     $\mathbf{mean}$ – Character(1)Input

On entry: indicates if a mean has been used in the model.

$\mathbf{mean}=\text{'M'}$

A mean term or intercept will have been included in the model by g02daf.

$\mathbf{mean}=\text{'Z'}$

A model with no mean term or intercept will have been fitted by g02daf.

Constraint: $\mathbf{mean}=\text{'M'}$ or $\text{'Z'}$.

3:     $\mathbf{weight}$ – Character(1)Input

On entry: indicates if a weight is to be used.

$\mathbf{weight}=\text{'U'}$

The new observation is unweighted.

$\mathbf{weight}=\text{'W'}$

The new observation is to be weighted and the weight must be supplied in wt.

Constraint: $\mathbf{weight}=\text{'U'}$ or $\text{'W'}$.

4:     $\mathbf{m}$ – IntegerInput

On entry: $m$, the total number of independent variables in the dataset.

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

5:     $\mathbf{isx}\left(\mathbf{m}\right)$ – Integer arrayInput

On entry: if $\mathbf{isx}\left(\mathit{j}\right)$ is greater than $0$, the value contained in $\mathbf{x}\left(\left(\mathit{j}-1\right)\times \mathbf{ix}+1\right)$ is to be included as a value of $x^{\mathrm{T}}$, for $\mathit{j}=1,2,\dots ,\mathbf{m}$.

Constraint: if $\mathbf{mean}=\text{'M'}$, exactly $\mathbf{ip}-1$ elements of isx must be $>0$ and if $\mathbf{mean}=\text{'Z'}$, exactly ip elements of isx must be $>0$.

6:     $\mathbf{q}\left(\mathbf{ldq},\mathbf{ip}+1\right)$ – Real (Kind=nag_wp) arrayInput/Output

On entry: must be array q as output by g02daf, g02def, g02dff or g02eef, or a previous call to g02dcf.

On exit: the first ip elements of the first column of q will contain $c_1^{*}$ the upper triangular part of columns $2$ to $\mathbf{ip}+1$ will contain $R^{*}$ the remainder is unchanged.

7:     $\mathbf{ldq}$ – IntegerInput

On entry: the first dimension of the array q as declared in the (sub)program from which g02dcf is called.

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

8:     $\mathbf{ip}$ – IntegerInput

On entry: the number of linear terms in general linear regression model (including mean if there is one).

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

9:     $\mathbf{x}\left(*\right)$ – Real (Kind=nag_wp) arrayInput

Note: the dimension of the array x must be at least $\left(\mathbf{m}-1\right)\times \mathbf{ix}+1$.

On entry: the ip values for the dependent variables of the new observation, $x^{\mathrm{T}}$. The positions will depend on the value of ix.

10:   $\mathbf{ix}$ – IntegerInput

On entry: the increment for elements of x. Two situations are common:

$\mathbf{ix}=1$

The values of $x$ are to be chosen from consecutive locations in x, i.e., $\mathbf{x}\left(1\right),\mathbf{x}\left(2\right),\dots ,\mathbf{x}\left(\mathbf{m}\right)$.

$\mathbf{ix}=\mathbf{ldx}$

The values of $x$ are to be chosen from a row of a two-dimensional array with first dimension ldx, i.e., $\mathbf{x}\left(1\right),\mathbf{x}\left(\mathbf{ldx}+1\right),\dots ,\mathbf{x}\left(\left(\mathbf{m}-1\right)\mathbf{ldx}+1\right)$.

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

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

On entry: the value of the dependent variable for the new observation, $y_{\text{new}}$.

12:   $\mathbf{wt}$ – Real (Kind=nag_wp)Input

On entry: if $\mathbf{weight}=\text{'W'}$, wt must contain the weight to be used with the new observation.

If $\mathbf{wt}=0.0$, the observation is not included in the model.

If $\mathbf{weight}=\text{'U'}$, wt is not referenced.

Constraint: if $\mathbf{wt}\ge 0.0$, $\mathbf{weight}=\text{'W'}$.

13:   $\mathbf{rss}$ – Real (Kind=nag_wp)Input/Output

On entry: the value of the residual sums of squares for the original set of observations.

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

On exit: the updated values of the residual sums of squares.

Note:  this will only be valid if the model is of full rank.

14:   $\mathbf{wk}\left(3\times \mathbf{ip}\right)$ – Real (Kind=nag_wp) arrayWorkspace

15:   $\mathbf{ifail}$ – 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, $〈\mathit{\text{value}}〉$ elements of $\mathbf{isx}>0$ instead of $\mathbf{ip}=〈\mathit{\text{value}}〉$.

On entry, $〈\mathit{\text{value}}〉$ elements of $\mathbf{isx}>0$ instead of $\mathbf{ip}-1$ (for mean) $=〈\mathit{\text{value}}〉$.

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

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

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

On entry, $\mathbf{mean}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{mean}=\text{'M'}$ or $\text{'Z'}$.

On entry, $\mathbf{rss}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{rss}\ge 0.0$.

On entry, $\mathbf{update}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{update}=\text{'A'}$ or $\text{'D'}$.

On entry, $\mathbf{weight}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{weight}=\text{'U'}$ or $\text{'W'}$.

$\mathbf{ifail}=2$

On entry, $\mathbf{wt}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{wt}\ge 0.0$.

$\mathbf{ifail}=3$

The $R$ matrix could not be updated. This may occur if an attempt is made to delete an observation which was not in the original dataset or to add an observation to a $R$ matrix with a zero diagonal element. This error is also possible when removing an observation which reduces the rank of design matrix. In such cases the model should be recomputed using g02daf.

$\mathbf{ifail}=4$

The residual sums of squares cannot be updated. This will occur if the input residual sum of squares is less than the calculated decrease in residual sum of squares when the new observation is deleted.

$\mathbf{ifail}=-99$

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 (g02dcfe.f90)

10.2

Program Data

Program Data (g02dcfe.d)

10.3

Program Results

Program Results (g02dcfe.r)