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)


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.


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 



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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