Efficient Computation of Subset Influence in Regression

Barrett, Bruce E.; Gray, J. Brian

doi:10.2307/1390784

Cited by 4 publications

(12 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We first state several inequalities for psd matrices that are used to establish these bounds. Those stated without proof are given in Barrett and Gray (1992).…”

Section: Barrett and Graymentioning

confidence: 99%

“…While subset influence is of interest to the practitioner, it is often ignored because of the *e-mail: bbarrett @ua lvm.ua.edu ]'e-mail: bgray@alston.cba.ua.edu 0960-3174 9 1996 Chapman & Hall computational infeasibility associated with the large number of subsets that must be considered. Barrett and Gray (1992) describe methods for efficient subset influence computation when the influence measure of interest is either Cook's distance or one of its close kin (see also Cook and Weisberg, 1980). These measures were described in Barrett and Ling (1992) as belonging to the trace class of influence measures because they are expressible as the trace of a product of positive semidefinite (psd) matrices.…”

Section: Introductionmentioning

confidence: 99%

“…The approach is similar to that of Barrett and Gray (1992) in that we develop bounds on the measure which require substantially less calculation than does computation of the actual influence value. Since the great majority of subsets are rather ordinary, these bounds enable us to eliminate many subsets from further consideration, leaving relatively few for which the influence must be explicitly calculated.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Computation of determinantal subset influence in regression

Barrett

Gray

1996

Stat Comput

Self Cite

View full text Add to dashboard Cite

One of the important goals of regression diagnostics is the detection of cases or groups of cases which have an inordinate impact on the regression results. Such observations are generally described as 'influential'. A number of influence measures have been proposed, each focusing on a different aspect of the regression. For single cases, these measures are relatively simple and inexpensive to calculate. However, the detection of multiple-case or joint influence is more difficult on two counts. First, calculation of influence for a single subset is more involved than for an individual case, and second, the sheer number of subsets of cases makes the computation overwhelming for all but the smallest data sets.Barrett and Gray (1992) described methods for efficiently examining subset influence for those measures that can be expressed as the trace of a product of positive semidefinite (psd) matrices. There are, however, other popular measures that do not take this form, but rather are expressible as the ratio of determinants of psd matrices. This article focuses on reducing the computation for the determinantal ratio measures by making use of upper and lower bounds on the influence to limit the number of subsets for which the actual influence must be explicitly determined.

show abstract

“…We first state several inequalities for psd matrices that are used to establish these bounds. Those stated without proof are given in Barrett and Gray (1992).…”

Section: Barrett and Graymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Computation of determinantal subset influence in regression

Barrett

Gray

1996

Stat Comput

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

“…Among those measures many researchers have concentrated on the topic of reducing the computation time for Cook's Distance. For a review of such methods, see Cook and Weisberg (1980), Gray and Ling(1984), and Barrett and Gray (1992).Our choice gives rise to a suggestion for an efficient computational method for the measure, CDm (X'(Dm)X(Dm ), pS2(Dm )), proposed by Cook and Weisberg (1982). Barrett and Ling proposed the method that computes CD m (X' (Dm)X(Dm ), pS2 (Dm )) by operating matrices case by case.…”

mentioning

confidence: 99%

A Stepwise Approach for Detection of Influential Observations

Choi¹,

Kim

1993

Journal of the Japanese Society of Computational Statistics

View full text Add to dashboard Cite

Various measureshave been proposed for detecting the influential observations in linear regression model but most of them require a large amount of computing time in practical problems. This article concerns an efficient computational method for computing the influential measure, CDm (X'(Dm)X(Dm), pS2(Dm)), proposed by Cook and Weisberg (1982). IntroductionIn the statistical literature on regression analysis, much attention has been given to problems of detecting observations which, individually or jointly, exert a disproportionate influence on the outcome of linear regression analysis and to problems of assessing the influence of such cases. Most approaches are ways of measuring the change in some feature of analysis on the deletion of one or more observations. Various measures have been proposed which emphasize different aspects of influence on the linear regression. Gentleman and Wilk (1975), Cook (1977Cook ( , 1979, Belsley, Kith and Welsch (1980), Cook andWeisberg (1980, 1982), and Chatterjee and Hadi (1986) gave fine reviews of such measures. Among those measures many researchers have concentrated on the topic of reducing the computation time for Cook's Distance. For a review of such methods, see Cook and Weisberg (1980), Gray and Ling(1984), and Barrett and Gray (1992).Our choice gives rise to a suggestion for an efficient computational method for the measure, CDm (X'(Dm)X(Dm ), pS2(Dm )), proposed by Cook and Weisberg (1982). Barrett and Ling proposed the method that computes CD m (X' (Dm)X(Dm ), pS2 (Dm )) by operating matrices case by case.To continue with the article, let us consider the modelwhere Y is an n x 1 vector of observations, X is an n x p full rank matrix of known constants, /Q is a p x 1 vector of unknown parameters, and c is an n x 1 vector of independent random variables each with mean of zero and variance of u2. It is well known that the least squares estimator of B is that Dm is an index set with m elements in {1, 2,.. . , n}. For the matrices associated with (1.1), let XDm be the submatrix of X, whose m rows are indexed by Dm, and let X (Dm) be its complement, the submatrix of X with X Dm deleted. The vectors Y(Dm ), ~(Dm) and EDm are similarly defined in Y, c and E, respectively. If an integer, i, is substituted for Dm, then x= represents the ith row in X and X(i) is the submatrix of X with ith row deleted. For the quantities calculated from the data, we use the notation (Dm) to indicate that the cases indexed by Dm have been deleted prior to calculation. For example, will mainly focus on CDm (X'(Dm )X(Dm), pS2(Dm )). Belsley et al. (1980) proposed an influential measure, MDFEIT, which is the special case of CDm (M, a) with M = X'(Dm)X(Dm) and a =1, that is, MDFFIT{Dm.} . (B -B(Dm))'X'(Dm.)X(Dm,)(B -B(Dm)).(1.11)Also they suggested a computational method, the triangular factorization. Jones and Ling (1988) showed that MDFFIT(Dm) and S2(Dm) can be represented as Th e above two computational methods are considered for a given subset Dm case by case and therefore cannot use the...

show abstract

Leverage, residual, and interaction diagnostics for subsets of cases in least squares regression

Barrett

Gray

1997

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

Efficient Computation of Subset Influence in Regression

Cited by 4 publications

References 0 publications

Computation of determinantal subset influence in regression

Computation of determinantal subset influence in regression

A Stepwise Approach for Detection of Influential Observations

Leverage, residual, and interaction diagnostics for subsets of cases in least squares regression

Contact Info

Product

Resources

About