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Flexible Modeling of Binary Data Using the Log-Burr Link

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  • Kaeding, Matthias

Abstract

Popular link functions often fit skewed binary data poorly. We propose the log-Burr link as flexible alternative. The link nests the complementary-log-log and logit link as special cases, determined by a shape parameter which can be estimated from the data. Shrinkage priors are used for the shape parameter, furthermore the parameter is allowed to vary between subgroups for clustered data. For modeling of nonlinear effects basis function expansions are used. Inference is done in a fully Bayesian framework. Posterior simulation is done via the No-U-Turn sampler implemented in Stan, avoiding convergence problems of the Gibbs sampler and allowing for easy use of nonconjugate priors. Regression coefficients associated with basis functions are reparameterized as random effects to speed up convergence. The proposed methods and the effect of misspecification of the modeled dgp are investigated in a simulation study. The approach is applied on large scale unemployment data.

Suggested Citation

  • Kaeding, Matthias, 2015. "Flexible Modeling of Binary Data Using the Log-Burr Link," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113043, Verein für Socialpolitik / German Economic Association.
    • Handle: RePEc:zbw:vfsc15:113043
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    1. Vom Berge, Philipp & König, Marion & Seth, Stefan, 2013. "Sample of Integrated Labour Market Biographies (SIAB) 1975-2010," FDZ Datenreport. Documentation on Labour Market Data 201301_en, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany].
    2. Chib, Siddhartha & Jeliazkov, Ivan, 2006. "Inference in Semiparametric Dynamic Models for Binary Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 685-700, June.
    3. Hess, Wolfgang, 2009. "A Flexible Hazard Rate Model for Grouped Duration Data," Working Papers 2009:18, Lund University, Department of Economics.
    4. Fahrmeir, Ludwig & Kneib, Thomas, 2011. "Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data," OUP Catalogue, Oxford University Press, number 9780199533022.
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    More about this item

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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