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Longitudinal Mixed Models with t Random Effects for Repeated Count and Binary Data

  • R. Prabhakar RaoEmail author
  • Brajendra C. Sutradhar
  • V. N. Pandit
Conference paper
Part of the Lecture Notes in Statistics book series (LNS, volume 218)

Abstract

Unlike the estimation for the parameters in a linear longitudinal mixed model with independent t errors, the estimation of parameters of a generalized linear longitudinal mixed model (GLLMM) for discrete such as count and binary data with independent t random effects involved in the linear predictor of the model, may be challenging. The main difficulty arises in the estimation of the degrees of freedom parameter of the t distribution of the random effects involved in such models for discrete data. This is because, when the random effects follow a heavy tailed t-distribution, one can no longer compute the basic properties analytically, because of the fact that moment generating function of the t random variable is unknown or can not be computed, even though characteristic function exists and can be computed. In this paper, we develop a simulations based numerical approach to resolve this issue. The parameters involved in the numerically computed unconditional mean, variance and correlations are estimated by using the well known generalized quasi-likelihood (GQL) and method of moments approach. It is demonstrated that the marginal GQL estimator for the regression effects asymptotically follow a multivariate Gaussian distribution. The asymptotic properties of the estimators for the rest of the parameters are also indicated.

Keywords

Asymptotic normal distribution Consistent estimation Count and binary panel data Generalized quasi-likelihood Regression effects t random effects Simulating t observations Stationary and non-stationary covariates Unconditional mean Variance and correlations 

Notes

Acknowledgements

The authors thank a referee for comments and suggestions. The second author presented a part of this paper in the symposium as a part of his Key Note address part I. Special thanks go to the audience of the symposium for their feedback.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • R. Prabhakar Rao
    • 1
    Email author
  • Brajendra C. Sutradhar
    • 2
  • V. N. Pandit
    • 1
  1. 1.Department of EconomicsSri Sathya Sai Institute of Higher LearningAndhra PradeshIndia
  2. 2.Department of Mathematics and StatisticsMemorial UniversitySt. John’sCanada

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