Abstract
In this paper, the coefficients of the two-level regression model with random intercept are estimated. The performance of the parametric restricted maximum likelihood (REML) method and four re-sampling techniques: bootstrap all responses, nested bootstrap, permutation of all responses and nested permutation, are compared. The REML is used as an estimation method for regression coefficients in the four previously mentioned re-sampling techniques. The comparison is based on three main factors: the bias of the estimated regression coefficients, the size of testing significance of each regression coefficient and the power of those tests. In particular, the simulation study is based on four different criteria, which are intra-class correlation (ICC), sample size, level of balance and the distribution of the random error terms. The study shows that the bootstrap technique outperforms the REML method when the residuals are not normally distributed. Even when the normality is satisfied, the bootstrap method still performs better in the case of small number of units at both groups and individuals' levels.