Showing papers on "Interpretability published in 1984"
TL;DR: It is shown that regression data should be mean-centered before being diagnosed for collinearity (ill conditioning), and that in order to assess conditioning meaningfully, the data must be in a form that possesses structural interpretability.
Abstract: It is often thought that regression data should be mean-centered before being diagnosed for collinearity (ill conditioning). This view is shown not generally to be correct. Such centering can mask elements of ill conditioning and produce meaningless and misleading collinearity diagnostics. In order to assess conditioning meaningfully, the data must be in a form that possesses structural interpretability.
126 citations
Book•
01 Jul 1984
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92 citations
01 Mar 1984
TL;DR: A sentence q is F-conservative over T if T + q F- 4 implies T T- 4 for every 4 E F, and this concept is investigated.
Abstract: A sentence q is F-conservative over T if T + q F- 4 implies T F- 4 for every 4 E F. In ?1 this concept for F = 7?+ I and fHO+, is investigated. In ?2 results from ?1 are applied to interpretability in theories containing arithmetic.
32 citations
TL;DR: In this article, the syntactic notion of relative interpretability is characterized semantically, through the existence of a suitable reduction functor on models, and the latter mathematical condition itself suggests a natural generalization, whose syntactic equivalent turns out to be a notion of interpretability quite close to that of Ershov [1], Szczerba [5] and Gaifman [2].
Abstract: Of the various notions of reduction in the logical literature, relative interpretability in the sense of Tarskiet al. [6] appears to be the central one. In the present note, this syntactic notion is characterized semantically, through the existence of a suitable reduction functor on models. The latter mathematical condition itself suggests a natural generalization, whose syntactic equivalent turns out to be a notion of interpretability quite close to that of Ershov [1], Szczerba [5] and Gaifman [2].
27 citations
Journal Article•
TL;DR: It is found that one of the most difficult and controversial problems facing data analysts is related to redundant predictor variables in a regression analysis.
Abstract: The present investigation is concerned with a review of the foundations upon which regression methodology is based, taking into account a study of regression diagnostics conducted by Belsey et al. (1980). It is found that one of the most difficult and controversial problems facing data analysts is related to redundant predictor variables in a regression analysis. Collinearity diagnostics are only meaningful when interpreted in terms of 'basic variables' which are 'structurally interpretable'. Conflicting perspectives are discussed, giving attention to the role of centering when diagnosing collinearity. The definition of collinearity and collinearity measures are considered along with questions regarding 'structural interpretability' as a universally accepted principle in model formulation, and the importance of the detection of collinearity with the constant term.
18 citations
16 citations