The Effects of Sample Size in Multilevel Models via Sub-sampling Approach

There are numerous research topics in different fields of study including social، medical، and agricultural sciences which contain data having intra-class correlation structure. For such data، simple linear regression models do not have acceptable applicability since they do not consider the correlation involved. Models which are suitable for data of this kind are called ''multilevel'' models. Determining appropriate sample size at different levels in multilevel models is among the issues which has attracted the interest of researchers in applied sciences. In the present study، taking a sub-sampling method approach، the influence of different sizes of the sample size at the first and second levels on the estimation of fixed and random effects was studied. Furthermore، due to the close relation between determining sample size and the power of the statistical test related to the parameters under study، and also due to other factors such as design effect and significance level، different design sizes were evaluated using simulation. Results of the study indicate that increasing sample size at the second level of the two-level model increases the power of the statistical test related to the calculation of the fixed and random effects.