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A new method for evaluation of the Fisher information matrix for discrete mixed effect models using Monte Carlo sampling and adaptive Gaussian quadrature

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  • Ueckert, Sebastian
  • Mentré, France

Abstract

The design of experiments for discrete mixed effect models is challenging due to the unavailability of a closed-form expression for the Fisher information matrix (FIM), on which most optimality criteria depend. Existing approaches for the computation of the FIM for those models are all based on approximations of the likelihood. A new method is presented which is based on derivatives of the exact conditional likelihood and which uses Monte Carlo (MC) simulations as well as adaptive Gaussian quadrature (AGQ) to integrate those derivatives over the data and random effects. The method is implemented in R and evaluated with respect to the influence of the tuning parameter, the accuracy of the FIM approximation, and computational complexity. The accuracy evaluation is performed by comparing the expected relative standard errors (RSE) from the MC/AGQ FIM with RSE obtained in a simulation study with four different discrete data models (two binary, one count and one repeated time-to-event model) and three different estimation algorithms. Additionally, the results from the MC/AGQ FIM are compared with expected RSE from a marginal quasi-likelihood (MQL) approximated FIM. The comparison resulted in close agreement between the MC/AGQ-based RSE and empirical RSE for all models investigated, and better performance of MC/AGQ than the MQL approximated FIM for variance parameters. The MC/AGQ method also proved to be well suited to calculate the expected power to detect a group effect for a model with binary outcomes.

Suggested Citation

  • Ueckert, Sebastian & Mentré, France, 2017. "A new method for evaluation of the Fisher information matrix for discrete mixed effect models using Monte Carlo sampling and adaptive Gaussian quadrature," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 203-219.
    • Handle: RePEc:eee:csdana:v:111:y:2017:i:c:p:203-219
    DOI: 10.1016/j.csda.2016.10.011
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    References listed on IDEAS

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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Pan, Jianxin & Thompson, Robin, 2007. "Quasi-Monte Carlo estimation in generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5765-5775, August.
    3. Niaparast, Mehrdad, 2009. "On optimal design for a Poisson regression model with random intercept," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 741-747, March.
    4. Nguyen, Thu Thuy & Mentré, France, 2014. "Evaluation of the Fisher information matrix in nonlinear mixed effect models using adaptive Gaussian quadrature," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 57-69.
    5. T. W. Waite & D. C. Woods, 2015. "Designs for generalized linear models with random block effects via information matrix approximations," Biometrika, Biometrika Trust, vol. 102(3), pages 677-693.
    6. Engle, Robert F., 1984. "Wald, likelihood ratio, and Lagrange multiplier tests in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 13, pages 775-826, Elsevier.
    7. Tekle, Fetene B. & Tan, Frans E.S. & Berger, Martijn P.F., 2008. "Maximin D-optimal designs for binary longitudinal responses," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5253-5262, August.
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    1. Xiao-Dong Zhou & Yun-Juan Wang & Rong-Xian Yue, 2021. "Optimal designs for discrete-time survival models with random effects," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(2), pages 300-332, April.

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