nag_regsn_mult_linear_delete_var (g02dfc) (PDF version)
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NAG Library Manual

NAG Library Function Document

nag_regsn_mult_linear_delete_var (g02dfc)


    1  Purpose
    7  Accuracy

1  Purpose

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

2  Specification

#include <nag.h>
#include <nagg02.h>
void  nag_regsn_mult_linear_delete_var (Integer ip, double q[], Integer tdq, Integer indx, double *rss, NagError *fail)

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. nag_regsn_mult_linear_delete_var (g02dfc) updates the QR  decomposition used in the computation of the linear regression model. The QR  decomposition may come from nag_regsn_mult_linear (g02dac), nag_regsn_mult_linear_addrem_obs (g02dcc), nag_regsn_mult_linear_add_var (g02dec) or a previous call to nag_regsn_mult_linear_delete_var (g02dfc).
For the general linear regression model with p  independent variables fitted, nag_regsn_mult_linear (g02dac) or nag_regsn_mult_linear_add_var (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 nag_regsn_mult_linear_add_var (g02dec) cannot be made after a call to nag_regsn_mult_linear_delete_var (g02dfc).
nag_regsn_mult_linear_upd_model (g02ddc) can be used to calculate the parameter estimates, β ^ , from the information provided by nag_regsn_mult_linear_delete_var (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 IntegerInput
On entry: the number of independent variables already in the model, p .
Constraint: ip1 .
2:     q[ip×tdq] doubleInput/Output
Note: the i,jth 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 nag_regsn_mult_linear (g02dac), nag_regsn_mult_linear_addrem_obs (g02dcc), nag_regsn_mult_linear_add_var (g02dec) or previous calls to nag_regsn_mult_linear_delete_var (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 IntegerInput
On entry: the stride separating matrix column elements in the array q.
Constraint: tdq ip + 1 .
4:     indx IntegerInput
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 2.7 in How to Use the NAG Library and its Documentation).

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 nag_regsn_mult_linear (g02dac).

8  Parallelism and Performance

nag_regsn_mult_linear_delete_var (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 nag_regsn_mult_linear (g02dac). The value of indx is read in and that variable dropped from the regression. The parameter estimates are calculated by nag_regsn_mult_linear_upd_model (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)

nag_regsn_mult_linear_delete_var (g02dfc) (PDF version)
g02 Chapter Contents
g02 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2016