Random Intercept regression models  are used in modeling grouped data where the observations  are  correlated in each group. This paper present a comperative sinulation study between parametric and two robust estimation methods to assess the influence of the violation of the normality of the error distribution on the efficiency of the model peremeter estimates. The asymptotic relative efficiency is used under various factors including the number of groups, the group size and the intercalss correlation coefficient. The methos under consideration are applied to data on the faculty of social work's math-achievement at helwan university.