Effect of Sample Size on the Profile Likelihood Estimates for Two-stage Hierarchical Linear Models

Abstract

Determining sample size to produce accurate parameter estimates and make valid inferences about population parameter is a pivotal problem in any well planned research. The issue of sample size becomes more complex in hierarchical linear models because the units at different levels are hierarchically nested. Many studies have been carried out to determine sample sizes at different levels of a nested data model. However, most of the studies assume that the sample size is large enough to conduct the significance test. Some alternative methods can be used to relax the assumption of large sample. Profile likelihood method is more robust in case of small sample and when the variance components need to be estimated. In this study, we investigate the effect of sample sizes on the performance of parameter estimates at the group-level and individual-level of a two-level regression model. We consider a more appropriate statistical approach, profile likelihood method, to check the reliability of estimates of fixed coefficients and variance components.