General Classes of Influence Measures for Multivariate Regression

Barrett, Bruce E.; Ling, Robert F.

doi:10.1080/01621459.1992.10475191

Cited by 41 publications

(16 citation statements)

References 12 publications

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“…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. There are, however, other influence measures that do not assume this form.…”

Section: Introductionmentioning

confidence: 99%

Computation of determinantal subset influence in regression

Barrett

Gray

1996

Stat Comput

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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.

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Section: Introductionmentioning

confidence: 99%

Computation of determinantal subset influence in regression

Barrett

Gray

1996

Stat Comput

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“…It is well known that MANOVA is very sensitive to influential observations. We identified seven such observations using methods to detect influential observations in multi-response regression [9]. Chi-square QQ-plot and the tests of multivariate normality reflect that the data deviates significantly from multivariate normal even after the removal of the influential observations.…”

Section: Initial Processing Of the Datamentioning

confidence: 99%

Effect of stroke prevention medication on aortic atheroma progression assessed using new statistical paradigm

Rudra¹,

Sen²,

Dennis³

et al. 2016

J Med Stat Inform

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Background: Progression of aortic arch atheroma (AA) is associated with vascular events in patients with stroke or transient ischemic attack (TIA). Studies investigating effect of stroke prevention medication on AA progression are limited to post-cerebral segments that may not be related to stroke pathophysiology and do not use information from the relevant segments adjacent to the origin of the cerebral blood vessels. Methods: AA atheroma was detected on baseline transesophageal echocardiogram (TEE) in 167 consecutive patients who had stroke or TIA. Of these, 125 consented to a follow-up TEE at12 months. Adequate paired AA images were obtained in 117 (78 with strokes, 39 with TIAs), which allowed detailed measurements of plaques. On admission for their index stroke or TIA, patients were assessed for stroke risk factors and stroke prevention medications (Statins, Antiplatelet therapy and oral anticoagulant). We assessed three segments of the AA adjacent to the origin of the cerebral blood vessels for plaque thickness by TEE and analyzed the effect of medication using joint modeling, with due consideration to confounding covariates. The statistical paradigm included a permutation testing procedure to determine the significance of medication effect on plaque progression in the three segments in combination. Results: Using the specified statistical paradigm, it is evident that statin therapy is effective in arresting the AA progression; however, there is no significant change induced by anticoagulant therapy. The cleaned data, after removal of influential observations, shows even more significance for the statin therapy. The constrained hypothesis tests in both cases show a smaller p-value suggesting that the statin therapy may be effective in arresting the AA progression. Conclusions: In this preliminary study of stroke/TIA patients with AA atheroma on transesophageal echocardiogram, AA atheroma progression was arrested by statin therapy, without any significant change induced by anticoagulant therapy. The statistical paradigm with due consideration of all segments implicated in stroke pathophysiology may be used to test the effect of other stroke prevention medications on AA progression.

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“…For the case of multiple outliers, Hadi and Simonoff (1993) proposed procedures to detect outliers in univariate linear regression model. Barrett and Ling (1992) presented general classes of multivariate influence measure for a univariate regression based on Cook's influence measure. The outlier detection in circular regression mainly focuses on the circular-circular regression models.…”

Section: Introductionmentioning

confidence: 99%