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Errors-in-variables beta regression models

Author

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  • Jalmar M.F. Carrasco
  • Silvia L.P. Ferrari
  • Reinaldo B. Arellano-Valle

Abstract

Beta regression models provide an adequate approach for modeling continuous outcomes limited to the interval (0, 1). This paper deals with an extension of beta regression models that allow for explanatory variables to be measured with error. The structural approach, in which the covariates measured with error are assumed to be random variables, is employed. Three estimation methods are presented, namely maximum likelihood, maximum pseudo-likelihood and regression calibration. Monte Carlo simulations are used to evaluate the performance of the proposed estimators and the na�ve estimator. Also, a residual analysis for beta regression models with measurement errors is proposed. The results are illustrated in a real data set.

Suggested Citation

  • Jalmar M.F. Carrasco & Silvia L.P. Ferrari & Reinaldo B. Arellano-Valle, 2014. "Errors-in-variables beta regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(7), pages 1530-1547, July.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:7:p:1530-1547
    DOI: 10.1080/02664763.2014.881784
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    References listed on IDEAS

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    1. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521471626, January.
    2. 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.
    3. Skrondal, Anders & Kuha, Jouni, 2012. "Improved regression calibration," LSE Research Online Documents on Economics 44135, London School of Economics and Political Science, LSE Library.
    4. Anders Skrondal & Jouni Kuha, 2012. "Improved Regression Calibration," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 649-669, October.
    5. Silvia L. P. Ferrari & Patricia L. Espinheira & Francisco Cribari‐Neto, 2011. "Diagnostic tools in beta regression with varying dispersion," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(3), pages 337-351, August.
    6. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models 2 volume set," Cambridge Books, Cambridge University Press, number 9780521478373, July.
    7. 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.
    8. Bolfarine, Heleno & Arellano-Valle, Reinaldo B., 1998. "Weak nondifferential measurement error models," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 279-287, October.
    9. 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.
    10. R. Arellano-Valle & H. Bolfarine, 1996. "A note on the simple structural regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(1), pages 111-125, March.
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    Cited by:

    1. Jorge I. Figueroa-Zúñiga & Cristian L. Bayes & Víctor Leiva & Shuangzhe Liu, 2022. "Robust beta regression modeling with errors-in-variables: a Bayesian approach and numerical applications," Statistical Papers, Springer, vol. 63(3), pages 919-942, June.
    2. Yury R. Benites & Vicente G. Cancho & Edwin M. M. Ortega & Roberto Vila & Gauss M. Cordeiro, 2022. "A New Regression Model on the Unit Interval: Properties, Estimation, and Application," Mathematics, MDPI, vol. 10(17), pages 1-17, September.

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