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Generalized linear models incorporating population level information: an empirical‐likelihood‐based approach

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  • Sanjay Chaudhuri
  • Mark S. Handcock
  • Michael S. Rendall

Abstract

Summary. In many situations information from a sample of individuals can be supplemented by population level information on the relationship between a dependent variable and explanatory variables. Inclusion of the population level information can reduce bias and increase the efficiency of the parameter estimates. Population level information can be incorporated via constraints on functions of the model parameters. In general the constraints are non‐linear, making the task of maximum likelihood estimation more difficult. We develop an alternative approach exploiting the notion of an empirical likelihood. It is shown that, within the framework of generalized linear models, the population level information corresponds to linear constraints, which are comparatively easy to handle. We provide a two‐step algorithm that produces parameter estimates by using only unconstrained estimation. We also provide computable expressions for the standard errors. We give an application to demographic hazard modelling by combining panel survey data with birth registration data to estimate annual birth probabilities by parity.

Suggested Citation

  • Sanjay Chaudhuri & Mark S. Handcock & Michael S. Rendall, 2008. "Generalized linear models incorporating population level information: an empirical‐likelihood‐based approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 311-328, April.
    • Handle: RePEc:bla:jorssb:v:70:y:2008:i:2:p:311-328
    DOI: 10.1111/j.1467-9868.2007.00637.x
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    Cited by:

    1. Tang, Cheng Yong & Leng, Chenlei, 2012. "An empirical likelihood approach to quantile regression with auxiliary information," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 29-36.
    2. Denis Devaud & Yves Tillé, 2019. "Deville and Särndal’s calibration: revisiting a 25-years-old successful optimization problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1033-1065, December.
    3. Igari Ryosuke & Takahiro Hoshino, 2017. "Semiparametric Quasi-Bayesian Inference with Dirichlet Process Priors: Application to Nonignorable Missing Responses," Keio-IES Discussion Paper Series 2017-020, Institute for Economics Studies, Keio University.
    4. Ryosuke Igari & Takahiro Hoshino, 2018. "A Bayesian Gamma Frailty Model Using the Sum of Independent Random Variables: Application of the Estimation of an Interpurchase Timing Model," Keio-IES Discussion Paper Series 2018-021, Institute for Economics Studies, Keio University.
    5. Igari, Ryosuke & Hoshino, Takahiro, 2018. "A Bayesian data combination approach for repeated durations under unobserved missing indicators: Application to interpurchase-timing in marketing," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 150-166.
    6. Liu, Tianqing & Yuan, Xiaohui, 2012. "Combining quasi and empirical likelihoods in generalized linear models with missing responses," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 39-58.
    7. Takahiro Hoshino & Ryosuke Igari, 2017. "Quasi-Bayesian Inference for Latent Variable Models with External Information: Application to generalized linear mixed models for biased data," Keio-IES Discussion Paper Series 2017-014, Institute for Economics Studies, Keio University.
    8. Bedoui, Adel & Lazar, Nicole A., 2020. "Bayesian empirical likelihood for ridge and lasso regressions," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    9. Han Zhang & Lu Deng & William Wheeler & Jing Qin & Kai Yu, 2022. "Integrative analysis of multiple case‐control studies," Biometrics, The International Biometric Society, vol. 78(3), pages 1080-1091, September.
    10. Y. G. Berger & O. De La Riva Torres, 2016. "Empirical likelihood confidence intervals for complex sampling designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 319-341, March.
    11. Oǧuz-Alper, Melike & Berger, Yves G., 2020. "Modelling multilevel data under complex sampling designs: An empirical likelihood approach," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    12. Sanjay Chaudhuri & Debashis Mondal & Teng Yin, 2017. "Hamiltonian Monte Carlo sampling in Bayesian empirical likelihood computation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 293-320, January.
    13. Ryo Kato & Takahiro Hoshino, 2020. "Semiparametric Bayesian Instrumental Variables Estimation for Nonignorable Missing Instruments," Discussion Paper Series DP2020-06, Research Institute for Economics & Business Administration, Kobe University.
    14. Yves G. Berger & Ewa Kabzińska, 2020. "Empirical Likelihood Approach for Aligning Information from Multiple Surveys," International Statistical Review, International Statistical Institute, vol. 88(1), pages 54-74, April.
    15. Yves G. Berger, 2016. "Empirical Likelihood Inference for the Rao-Hartley-Cochran Sampling Design," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 721-735, September.
    16. Berger, Yves G. & Patilea, Valentin, 2022. "A semi-parametric empirical likelihood approach for conditional estimating equations under endogenous selection," Econometrics and Statistics, Elsevier, vol. 24(C), pages 151-163.
    17. Yuan, Xiaohui & Liu, Tianqing & Lin, Nan & Zhang, Baoxue, 2010. "Combining conditional and unconditional moment restrictions with missing responses," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2420-2433, November.

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