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Conditional local influence in case‐weights linear regression
Author(s) -
Poon WaiYin,
Poon Yat Sun
Publication year - 2001
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711001159375
Subject(s) - curvature , mathematics , measure (data warehouse) , linear regression , regression , masking (illustration) , regression analysis , conditional probability distribution , statistics , econometrics , computer science , data mining , art , geometry , visual arts
The local influence approach proposed by Cook (1986) makes use of the normal curvature and the direction achieving the maximum curvature to assess the local influence of minor perturbation of statistical models. When the approach is applied to the linear regression model, the result provides information concerning the data structure different from that contributed by Cook's distance. One of the main advantages of the local influence approach is its ability to handle the simultaneous effect of several cases, namely, the ability to address the problem of ‘masking’. However, Lawrance (1995) points out that there are two notions of ‘masking’ effects, the joint influence and the conditional influence, which are distinct in nature. The normal curvature and the direction of maximum curvature are capable of addressing effects under the category of joint influences but not conditional influences. We construct a new measure to define and detect conditional local influences and use the linear regression model for illustration. Several reported data sets are used to demonstrate that new information can be revealed by this proposed measure.