Sample Size Determination in Multilevel Models with Bayesian Approach

One of the most influential factors for each experimental research in various disciplines is to determine the sample size for the study. In statistical literature, the optimal sample size determination is depended on statistical power, confidence coefficient, effect size and cost function. Over all of these quantities, the special feature of the data under investigation has also has great impact on the sample size. If the data have intra-class correlation structure then the multilevel models are appropriate to analysis such data. In the present paper, we use three Bayesian performance criteria related to model parameters to determine the optimal sample size. Since the posterior distributions do not have closed forms, we should (and did) employ computational algorithms. However, the full conditional distributions of parameters had closed form, so to evaluate the performance of the relevant criterion the Gibbs sampling algorithm was performed to simulate the full conditional distributions of the model parameters.