NAG CL Interface
g02dfc (linregm_​var_​del)

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1 Purpose

g02dfc deletes an independent variable from a general linear regression model.

2 Specification

#include <nag.h>
void  g02dfc (Integer ip, double q[], Integer tdq, Integer indx, double *rss, NagError *fail)
The function may be called by the names: g02dfc, nag_correg_linregm_var_del or nag_regsn_mult_linear_delete_var.

3 Description

When selecting a linear regression model it is sometimes useful to drop independent variables from the model and to examine the resulting sub-model. g02dfc updates the QR decomposition used in the computation of the linear regression model. The QR decomposition may come from g02dac, g02dcc, g02dec or a previous call to g02dfc.
For the general linear regression model with p independent variables fitted, g02dac or g02dec computes a QR decomposition of the (weighted) independent variables and forms an upper triangular matrix R and a vector c . To remove an independent variable R and c have to be updated. The column of R corresponding to the variable to be dropped is removed and the matrix is then restored to upper triangular form by applying a series of Givens rotations. The rotations are then applied to c . Note that only the first p elements of c are affected.
The method used means that while the updated values of R and c are computed an updated value of Q from the QR decomposition is not available so a call to g02dec cannot be made after a call to g02dfc.
g02ddc can be used to calculate the parameter estimates, β ^ , from the information provided by g02dfc.

4 References

Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
Hammarling S (1985) The singular value decomposition in multivariate statistics SIGNUM Newsl. 20(3) 2–25

5 Arguments

1: ip Integer Input
On entry: the number of independent variables already in the model, p .
Constraint: ip1 .
2: q[ip×tdq] double Input/Output
Note: the (i,j)th element of the matrix Q is stored in q[(i-1)×tdq+j-1].
On entry: the results of the QR decomposition as returned by g02dac, g02dcc, g02dec or previous calls to g02dfc.
On exit: the updated QR decomposition. The first ip elements of the first column of q contain the updated value of c , the upper triangular part of columns 2 to ip contain the updated R matrix.
3: tdq Integer Input
On entry: the stride separating matrix column elements in the array q.
Constraint: tdq ip + 1 .
4: indx Integer Input
On entry: indicates which independent variable is to be deleted from the model.
Constraint: 1 indx ip .
5: rss double * Input/Output
On entry: the residual sum of squares for the full regression.
Constraint: rss0.0 .
On exit: the residual sum of squares with the (indx)th variable removed. Note that the residual sum of squares will only be valid if the regression is of full rank.
6: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

On entry, indx=value while ip=value . These arguments must satisfy indxip .
On entry, tdq=value while ip + 1 = value. These arguments must satisfy tdq ip + 1 .
Dynamic memory allocation failed.
On entry, a diagonal element, value, of R is zero.
On entry, indx=value.
Constraint: indx1.
On entry, ip=value.
Constraint: ip1.
On entry, rss must not be less than 0.0: rss=value .

7 Accuracy

There will inevitably be some loss in accuracy in fitting a model by dropping terms from a more complex model rather than fitting it afresh using g02dac.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g02dfc is not threaded in any implementation.

9 Further Comments


10 Example

A dataset consisting of 12 observations on four independent variables and one dependent variable is read in. The full model, including a mean term, is fitted using g02dac. The value of indx is read in and that variable dropped from the regression. The parameter estimates are calculated by g02ddc and printed. This process is repeated until indx is 0.

10.1 Program Text

Program Text (g02dfce.c)

10.2 Program Data

Program Data (g02dfce.d)

10.3 Program Results

Program Results (g02dfce.r)