Orthogonal Predictors: A Possible Resolution of the Hoffman-Ward Controversy

Gibson, Walker

doi:10.2466/pr0.1962.11.1.32

Cited by 40 publications

(28 citation statements)

References 3 publications

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“…Gibson, 30 Green et al, 46 Fabbris, 1 Genizi, 2 Johnson, 3 and Zuber and Strimmer 31 all introduced methods that are computationally less demanding than LMG and PMVD and decompose R 2 into non-negative summands. As the section title suggests, these six proposals reduce to three different ones: it will be shown here that the proposals by Gibson 30 and Zuber and Strimmer 31 coincide; the coincidence between the proposals by Fabbris, 1 Genizi 2 and Johnson 3 was, e.g., pointed out by Nimon and Oswald.…”

Section: Gibson Decomposition/car Scores Green Et Al Decomposition mentioning

confidence: 99%

“…The example in the next section will shed further light on the three approaches of this section in comparison to LMG/dominance analysis and PMVD. Most methods discussed in this section are implemented in R package relaimpo (Grömping 54 ; metrics 'genizi' and 'car' added in 2010): The Gibson 30 proposal-equivalent to squared CAR scores-is implemented under the name 'car', using underlying work by Zuber and Strimmer 31 (package care), while the Fabbris/Genizi/Johnson approach is implemented under the name 'genizi'. To the author's knowledge, the Green et al 46 approach is not available in R software.…”

Section: Gibson Decomposition/car Scores Green Et Al Decomposition mentioning

confidence: 99%

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Variable importance in regression models

Grömping

2015

WIREs Computational Stats

240

194

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Regression analysis is one of the most-used statistical methods. Often part of the research question is the identification of the most important regressors or an importance ranking of the regressors. Most regression models are not specifically suited for answering the variable importance question, so that many different proposals have been made. This article reviews in detail the various variable importance metrics for the linear model, particularly emphasizing variance decomposition metrics. All linear model metrics are illustrated by an example analysis. For nonlinear parametric models, several principles from linear models have been adapted, and machine-learning methods have their own set of variable importance methods. These are also briefly covered. Although there are many variable importance metrics, there is still no convincing theoretical basis for them, and they all have a heuristic touch. Nevertheless, some metrics are considered useful for a crude assessment in the absence of a good subject matter theory.

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Section: Gibson Decomposition/car Scores Green Et Al Decomposition mentioning

confidence: 99%

Section: Gibson Decomposition/car Scores Green Et Al Decomposition mentioning

confidence: 99%

Variable importance in regression models

Grömping

2015

WIREs Computational Stats

240

194

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“…Other evaluation methods include product measures (Pratt, 1987), usefulness (Darlington, 1968), structure coefficients (Courville and Thompson, 2001), dominance analysis (Budescu, 1993), orthogonal counterparts (Gibson, 1962;Johnson, 1966), relative weight analysis (Johnson, 2000), Shapley value regression (Lipovetsky and Conklin, 2001) and random forests (Liakhovitski et al, 2010). When predictors are uncorrelated, these measures lead to the same result and have the desirable property that their measures of the individual contributions of the predictor variables sum to R 2 , the proportion of the variation in the response that the regressors explain.…”

Section: Introductionmentioning

confidence: 99%

Contribution of individual variables to the regression sum of squares

Shabuz

Garthwaite

2019

MAS

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“…Among those are: ridge regressions (Hoerl & Kennard, 1970;Lipovetsky, 2010), Shapley value regression (SVR) based on cooperative game theory used for finding predictors' importance and adjusting the regression coefficients (Shapley, 1953;Roth, 1988;Lipovetsky & Conklin, 2001), nonlinear parameterization of linear regression coefficients by multinomial shares, using elasticity criterion for building regression coefficients by data gradients, Gibson-Johnson and Johnson indices of predictor importance, and other techniques (for more detail and references within: Gibson, 1962;R. Johnson, 1966;J.…”

Section: Introductionmentioning

confidence: 99%

Vol. 16, No. 2 (Full Issue)

2017

J. Mod. App. Stat. Meth.

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EDITORIAL ASSISTANCEJMASM (ISSN 1538−9472, http://digitalcommons.wayne.edu/jmasm) is an independent, open access electronic journal, published biannually in May and November by JMASM Inc. (PO Box 48023, Oak Park, MI, 48237) in collaboration with the Wayne State University Library System. JMASM seeks to publish (1) new statistical tests or procedures, or the comparison of existing statistical tests or procedures, using computer-intensive Monte Carlo, bootstrap, jackknife, or resampling methods, (2) the study of nonparametric, robust, permutation, exact, and approximate randomization methods, and (3) applications of computer programming, preferably in Fortran (all other programming environments are welcome), related to statistical algorithms, pseudo-random number generators, simulation techniques, and self-contained executable code to carry out new or interesting statistical methods.Journal correspondence (other than manuscript submissions) and requests for advertising may be forwarded to ea@jmasm.com. See back matter for instructions for authors. IntroductionComputer simulation studies represent an important tool for investigating statistical procedures difficult or impossible to study using mathematical theory or real data. Descriptors of these studies vary (e.g., statistical experiment, Monte Carlo simulation, computer experiment), but the examples of Hoaglin and Andrews (1975) and Hauck and Anderson (1984) are followed here with use of the term simulation studies. Extensive descriptions of simulation studies can be found in Lewis and Orav (1989) and Santner, Williams, and Notz (2003). In the behavioral sciences simulation studies have been used to study a wide array of statistical methods (e.g., Cribbie, Fiksenbaum, & Wilcox, 2012; Depaoli, 2012; Enders, Baraldi, & Cham, 2014; Hu & Bentler, 1999; Tomarken & Serlin, 1986). The general goal of these studies is to provide evidence of the behavior of statistical methods under a variety of data conditions that improves statistical practice and informs future statistical research. The goal here is to encourage methodological researchers to treat these studies as statistical sampling EXPERIMENTAL DESIGN AND DATA ANALYSIS IN SIMULATION 4 experiments subject to established principles of experimental design and data analysis.An underappreciated facet of simulation studies in statistics is their role in enhancing the reproducibility of scientific findings. The importance of reproducibility has gained momentum in numerous scientific arenas because of growing evidence that many findings cannot be replicated (Stodden, 2015). Concerns over reproducibility and the role of statistics were captured in Statistics and science: A report of the London workshop on the future of the statistical sciences (2014) which noted: "The reproducibility problem goes far beyond statistics, of course, because it involves the entire reward structure of the scientific enterprise. Nevertheless, statistics is a very important ingredient in both the problem and the remedy." (p. 27) Simulati...

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Orthogonal Predictors: A Possible Resolution of the Hoffman-Ward Controversy

Cited by 40 publications

References 3 publications

Variable importance in regression models

Variable importance in regression models

Contribution of individual variables to the regression sum of squares

Vol. 16, No. 2 (Full Issue)

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