Zahra Zandi - Department of Statistics, University of Tabriz, Tabriz, Iran
Hossein Bevrani - Department of Statistics, University of Tabriz, Tabriz, Iran
Reza Arabi Belaghi - Department of Statistics, University of Tabriz, Tabriz, Iran

‎In this paper‎, ‎we consider the problem of parameter estimation in {color{blue} negative binomial mixed model} when it is suspected that some of the fixed parameters may be restricted to a subspace via linear shrinkage‎, ‎{color{blue} preliminary test}‎, ‎shrinkage {color{blue} preliminary test}‎, ‎shrinkage‎, ‎and positive shrinkage estimators along with the unrestricted maximum likelihood and restricted estimators‎. ‎The random effects are considered as nuisance parameters‎. ‎We conduct a Monte Carlo simulation study to evaluate the performance of each estimator in the sense of simulated relative efficiency‎. ‎The results of simulation study reveal that the proposed estimation strategies perform more better than {color{blue} the} maximum likelihood method‎. ‎The proposed estimators are applied to a real dataset to appraise their performance‎.

Longitudinal Data, Monte Carlo simulation, Negative Binomial Mixed Model, Over-dispersion, Shrinkage Estimators