IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v80y2015i1p236-256.html
   My bibliography  Save this article

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

Author

Listed:
  • 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

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11336-013-9375-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11336-013-9375-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ioannis Kosmidis & David Firth, 2009. "Bias reduction in exponential family nonlinear models," Biometrika, Biometrika Trust, vol. 96(4), pages 793-804.
    2. 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.
    3. 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.
    4. Leamer, Edward E, 1973. "Multicollinearity: A Bayesian Interpretation," The Review of Economics and Statistics, MIT Press, vol. 55(3), pages 371-380, August.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Raymond J. Carroll, 2003. "Variances Are Not Always Nuisance Parameters," Biometrics, The International Biometric Society, vol. 59(2), pages 211-220, June.
    16. Cribari-Neto, Francisco & Zeileis, Achim, 2010. "Beta Regression in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i02).
    17. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hyemin Han, 2024. "Bayesian Model Averaging and Regularized Regression as Methods for Data-Driven Model Exploration, with Practical Considerations," Stats, MDPI, vol. 7(3), pages 1-13, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mark F. J. Steel, 2020. "Model Averaging and Its Use in Economics," Journal of Economic Literature, American Economic Association, vol. 58(3), pages 644-719, September.
    2. Oscar Melo & Carlos Melo & Jorge Mateu, 2015. "Distance-based beta regression for prediction of mutual funds," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 83-106, January.
    3. Grün, Bettina & Kosmidis, Ioannis & Zeileis, Achim, 2012. "Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i11).
    4. Diego Ramos Canterle & Fábio Mariano Bayer, 2019. "Variable dispersion beta regressions with parametric link functions," Statistical Papers, Springer, vol. 60(5), pages 1541-1567, October.
    5. Pablo Mitnik & Sunyoung Baek, 2013. "The Kumaraswamy distribution: median-dispersion re-parameterizations for regression modeling and simulation-based estimation," Statistical Papers, Springer, vol. 54(1), pages 177-192, February.
    6. Dimitris Korobilis & Kenichi Shimizu, 2022. "Bayesian Approaches to Shrinkage and Sparse Estimation," Foundations and Trends(R) in Econometrics, now publishers, vol. 11(4), pages 230-354, June.
    7. David Kaplan, 2021. "On the Quantification of Model Uncertainty: A Bayesian Perspective," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 215-238, March.
    8. Anna Sokolova, 2023. "Marginal Propensity to Consume and Unemployment: a Meta-analysis," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 51, pages 813-846, December.
    9. Ley, Eduardo & Steel, Mark F.J., 2012. "Mixtures of g-priors for Bayesian model averaging with economic applications," Journal of Econometrics, Elsevier, vol. 171(2), pages 251-266.
    10. Ley, Eduardo & Steel, Mark F. J., 2007. "On the effect of prior assumptions in Bayesian model averaging with applications to growth regression," Policy Research Working Paper Series 4238, The World Bank.
    11. Aart Kraay & Norikazu Tawara, 2013. "Can specific policy indicators identify reform priorities?," Journal of Economic Growth, Springer, vol. 18(3), pages 253-283, September.
    12. Bruns, Stephan B. & Ioannidis, John P.A., 2020. "Determinants of economic growth: Different time different answer?," Journal of Macroeconomics, Elsevier, vol. 63(C).
    13. Cristine Rauber & Francisco Cribari-Neto & Fábio M. Bayer, 2020. "Improved testing inferences for beta regressions with parametric mean link function," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 687-717, December.
    14. Li-Chu Chien, 2013. "Multiple deletion diagnostics in beta regression models," Computational Statistics, Springer, vol. 28(4), pages 1639-1661, August.
    15. Jay Verkuilen & Michael Smithson, 2012. "Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution," Journal of Educational and Behavioral Statistics, , vol. 37(1), pages 82-113, February.
    16. Njindan Iyke, Bernard, 2015. "Macro Determinants of the Real Exchange Rate in a Small Open Small Island Economy: Evidence from Mauritius via BMA," MPRA Paper 68968, University Library of Munich, Germany.
    17. Frank A. La Sorte & Alison Johnston & Toby R. Ault, 2021. "Global trends in the frequency and duration of temperature extremes," Climatic Change, Springer, vol. 166(1), pages 1-14, May.
    18. Kourtellos, Andros & Marr, Christa & Tan, Chih Ming, 2016. "Robust determinants of intergenerational mobility in the land of opportunity," European Economic Review, Elsevier, vol. 81(C), pages 132-147.
    19. Tariq Maqsood & Mark Edwards & Ioanna Ioannou & Ioannis Kosmidis & Tiziana Rossetto & Neil Corby, 2016. "Seismic vulnerability functions for Australian buildings by using GEM empirical vulnerability assessment guidelines," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 80(3), pages 1625-1650, February.
    20. Balima, Hippolyte W. & Sokolova, Anna, 2021. "IMF programs and economic growth: A meta-analysis," Journal of Development Economics, Elsevier, vol. 153(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:80:y:2015:i:1:p:236-256. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.