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Evaluating Predictors of Dispersion: A Comparison of Dominance Analysis and Bayesian Model Averaging

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  • Yiyun Shou
  • Michael Smithson

Abstract

Conventional measures of predictor importance in linear models are applicable only when the assumption of homoscedasticity is satisfied. Moreover, they cannot be adapted to evaluating predictor importance in models of heteroscedasticity (i.e., dispersion), an issue that seems not to have been systematically addressed in the literature. We compare two suitable approaches, Dominance Analysis (DA) and Bayesian Model Averaging (BMA), for simultaneously evaluating predictor importance in models of location and dispersion. We apply them to the beta general linear model as a test-case, illustrating this with an example using real data. Simulations using several different model structures, sample sizes, and degrees of multicollinearity suggest that both DA and BMA largely agree on the relative importance of predictors of the mean, but differ when ranking predictors of dispersion. The main implication of these findings for researchers is that the choice between DA and BMA is most important when they wish to evaluate the importance of predictors of dispersion. Copyright The Psychometric Society 2015

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  • Yiyun Shou & Michael Smithson, 2015. "Evaluating Predictors of Dispersion: A Comparison of Dominance Analysis and Bayesian Model Averaging," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 236-256, March.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:1:p:236-256
    DOI: 10.1007/s11336-013-9375-8
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    1. Leamer, Edward E, 1973. "Multicollinearity: A Bayesian Interpretation," The Review of Economics and Statistics, MIT Press, vol. 55(3), pages 371-380, August.
    2. Kenneth A. Bollen & Surajit Ray & Jane Zavisca & Jeffrey J. Harden, 2012. "A Comparison of Bayes Factor Approximation Methods Including Two New Methods," Sociological Methods & Research, , vol. 41(2), pages 294-324, May.
    3. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    4. Chris Chatfield, 1995. "Model Uncertainty, Data Mining and Statistical Inference," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 158(3), pages 419-444, May.
    5. Fernandez, Carmen & Ley, Eduardo & Steel, Mark F. J., 2001. "Benchmark priors for Bayesian model averaging," Journal of Econometrics, Elsevier, vol. 100(2), pages 381-427, February.
    6. Kadane, Joseph B. & Lazar, Nicole A., 2004. "Methods and Criteria for Model Selection," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 279-290, January.
    7. Cribari-Neto, Francisco & Zeileis, Achim, 2010. "Beta Regression in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i02).
    8. Theo S. Eicher & Chris Papageorgiou & Adrian E. Raftery, 2011. "Default priors and predictive performance in Bayesian model averaging, with application to growth determinants," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(1), pages 30-55, January/F.
    9. Carmen Fernández & Eduardo Ley & Mark F. J. Steel, 2002. "Bayesian modelling of catch in a north‐west Atlantic fishery," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(3), pages 257-280, July.
    10. Ioannis Kosmidis & David Firth, 2009. "Bias reduction in exponential family nonlinear models," Biometrika, Biometrika Trust, vol. 96(4), pages 793-804.
    11. Duchateau, Luc & Janssen, Paul, 2005. "Understanding Heterogeneity in Generalized Mixed and Frailty Models," The American Statistician, American Statistical Association, vol. 59, pages 143-146, May.
    12. Raftery A.E. & Zheng Y., 2003. "Discussion: Performance of Bayesian Model Averaging," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 931-938, January.
    13. Ospina, Raydonal & Cribari-Neto, Francisco & Vasconcellos, Klaus L.P., 2006. "Improved point and interval estimation for a beta regression model," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 960-981, November.
    14. Simas, Alexandre B. & Barreto-Souza, Wagner & Rocha, Andréa V., 2010. "Improved estimators for a general class of beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 348-366, February.
    15. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
    16. Retzer, J.J. & Soofi, E.S. & Soyer, R., 2009. "Information importance of predictors: Concept, measures, Bayesian inference, and applications," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2363-2377, April.
    17. Raymond J. Carroll, 2003. "Variances Are Not Always Nuisance Parameters," Biometrics, The International Biometric Society, vol. 59(2), pages 211-220, June.
    18. Claudia Czado & Adrian Raftery, 2006. "Choosing the link function and accounting for link uncertainty in generalized linear models using Bayes factors," Statistical Papers, Springer, vol. 47(3), pages 419-442, June.
    19. Chris T. Volinsky & Adrian E. Raftery, 2000. "Bayesian Information Criterion for Censored Survival Models," Biometrics, The International Biometric Society, vol. 56(1), pages 256-262, March.
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