IDEAS home Printed from https://ideas.repec.org/a/sae/jedbes/v37y2012i1p82-113.html
   My bibliography  Save this article

Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution

Author

Listed:
  • Jay Verkuilen

    (City University of New York)

  • Michael Smithson

    (The Australian National University)

Abstract

Doubly bounded continuous data are common in the social and behavioral sciences. Examples include judged probabilities, confidence ratings, derived proportions such as percent time on task, and bounded scale scores. Dependent variables of this kind are often difficult to analyze using normal theory models because their distributions may be quite poorly modeled by the normal distribution. The authors extend the beta-distributed generalized linear model (GLM) proposed in Smithson and Verkuilen (2006) to discrete and continuous mixtures of beta distributions, which enables modeling dependent data structures commonly found in real settings. The authors discuss estimation using both deterministic marginal maximum likelihood and stochastic Markov chain Monte Carlo (MCMC) methods. The results are illustrated using three data sets from cognitive psychology experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:jedbes:v:37:y:2012:i:1:p:82-113
    DOI: 10.3102/1076998610396895
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.3102/1076998610396895
    Download Restriction: no
    File URL: https://libkey.io/10.3102/1076998610396895?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
    ---><---

    References listed on IDEAS

    as
    1. Nicholas T. Longford, 2001. "Simulation‐based diagnostics in random‐coefficient models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(2), pages 259-273.
    2. Zhenguo Qiu & Peter X.‐K. Song & Ming Tan, 2008. "Simplex Mixed‐Effects Models for Longitudinal Proportional Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 577-596, December.
    3. W. J. Browne & S. V. Subramanian & K. Jones & H. Goldstein, 2005. "Variance partitioning in multilevel logistic models that exhibit overdispersion," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(3), pages 599-613, July.
    4. Patricia Espinheira & Silvia Ferrari & Francisco Cribari-Neto, 2008. "On beta regression residuals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(4), pages 407-419.
    5. Timothy Johnson, 2003. "On the use of heterogeneous thresholds ordinal regression models to account for individual differences in response style," Psychometrika, Springer;The Psychometric Society, vol. 68(4), pages 563-583, December.
    6. Raymond J. Carroll, 2003. "Variances Are Not Always Nuisance Parameters," Biometrics, The International Biometric Society, vol. 59(2), pages 211-220, June.
    7. Barndorff-Nielsen, O. E. & Jørgensen, B., 1991. "Some parametric models on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 106-116, October.
    8. Steiger J. H., 2001. "Driving Fast in Reverse," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 331-338, March.
    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. Martin J. Crowder, 1978. "Beta‐Binomial Anova for Proportions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(1), pages 34-37, March.
    11. Cox, Christopher, 1996. "Nonlinear quasi-likelihood models: applications to continuous proportions," Computational Statistics & Data Analysis, Elsevier, vol. 21(4), pages 449-461, April.
    12. 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.
    13. Paolino, Philip, 2001. "Maximum Likelihood Estimation of Models with Beta-Distributed Dependent Variables," Political Analysis, Cambridge University Press, vol. 9(4), pages 325-346, January.
    14. Papke, Leslie E & Wooldridge, Jeffrey M, 1996. "Econometric Methods for Fractional Response Variables with an Application to 401(K) Plan Participation Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 619-632, Nov.-Dec..
    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. Katharina Elisabeth Fischer & Tom Stargardt, 2016. "The diffusion of generics after patent expiry in Germany," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 17(8), pages 1027-1040, November.
    2. Wagner Hugo Bonat & Paulo Justiniano Ribeiro & Walmes Marques Zeviani, 2015. "Likelihood analysis for a class of beta mixed models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 252-266, February.
    3. Hu, Hao & Yao, Weixin & Wu, Yichao, 2017. "The robust EM-type algorithms for log-concave mixtures of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 14-26.
    4. Maria Gheorghe & Susan Picavet & Monique Verschuren & Werner B. F. Brouwer & Pieter H. M. Baal, 2017. "Health losses at the end of life: a Bayesian mixed beta regression approach," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(3), pages 723-749, June.
    5. Phillip Li, 2018. "Efficient MCMC estimation of inflated beta regression models," Computational Statistics, Springer, vol. 33(1), pages 127-158, March.

    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. Lucio Masserini & Matilde Bini & Monica Pratesi, 2017. "Effectiveness of non-selective evaluation test scores for predicting first-year performance in university career: a zero-inflated beta regression approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(2), pages 693-708, March.
    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. Wagner Hugo Bonat & Paulo Justiniano Ribeiro & Walmes Marques Zeviani, 2015. "Likelihood analysis for a class of beta mixed models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 252-266, February.
    4. Josip Glaurdić & Vuk Vuković, 2015. "Prosperity and peace: Economic interests and war legacy in Croatia’s EU referendum vote," European Union Politics, , vol. 16(4), pages 577-600, December.
    5. Latouche, Karine & Rouviere, Elodie, 2011. "Brokers vs. Retailers: Evidence from the French Imports Industry of Fresh Produce," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114398, European Association of Agricultural Economists.
    6. Harald Oberhofer & Michael Pfaffermayr, 2014. "Two-Part Models for Fractional Responses Defined as Ratios of Integers," Econometrics, MDPI, vol. 2(3), pages 1-22, September.
    7. 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.
    8. Reboul, E. & Guérin, I. & Nordman, C.J., 2021. "The gender of debt and credit: Insights from rural Tamil Nadu," World Development, Elsevier, vol. 142(C).
    9. Claus Michelsen & Peter Boenisch & Benny Geys, 2014. "(De)Centralization and voter turnout: theory and evidence from German municipalities," Public Choice, Springer, vol. 159(3), pages 469-483, June.
    10. 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.
    11. Xiong, Qizhou, 2015. "Censored Fractional Response Model: Estimating Heterogeneous Relative Risk Aversion of European Households," IWH Discussion Papers 11/2015, Halle Institute for Economic Research (IWH).
    12. 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.
    13. José M. R. Murteira & Joaquim J. S. Ramalho, 2016. "Regression Analysis of Multivariate Fractional Data," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 515-552, April.
    14. Phillip Li, 2018. "Efficient MCMC estimation of inflated beta regression models," Computational Statistics, Springer, vol. 33(1), pages 127-158, March.
    15. Maria Simona Andreano & Roberto Benedetti & Federica Piersimoni & Giovanni Savio, 2021. "Mapping Poverty of Latin American and Caribbean Countries from Heaven Through Night-Light Satellite Images," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 156(2), pages 533-562, August.
    16. Ospina, Raydonal & Ferrari, Silvia L.P., 2012. "A general class of zero-or-one inflated beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1609-1623.
    17. 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.
    18. Esmeralda A. Ramalho & Joaquim J.S. Ramalho & José M.R. Murteira, 2011. "Alternative Estimating And Testing Empirical Strategies For Fractional Regression Models," Journal of Economic Surveys, Wiley Blackwell, vol. 25(1), pages 19-68, February.
    19. Patrícia L. Espinheira & Alisson Oliveira Silva, 2020. "Residual and influence analysis to a general class of simplex regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 523-552, June.
    20. Souza, M.A.O. & Migon, H.S. & Pereira, J.B.M., 2018. "Extended dynamic generalized linear models: The two-parameter exponential family," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 164-179.

    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:sae:jedbes:v:37:y:2012:i:1:p:82-113. 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: SAGE Publications (email available below). General contact details of provider: .

    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.