| In statistical linear models, most procedures available for estimating the variance components of the mixed model are usually based on the assumption that the error terms and each set of random effects in the model are normally distributed with zero means and some variance-covariance structure. However, in certain research situations, there is little doubt that the error terms and each set of random effects in the mixed model can be characterized as moderately or even distinctly non-normal with heavy tails or badly skewed distributions.; Efron (1979) discussed the use of a technique called the bootstrap to generate sampling distributions of statistics and thereby to draw inferences about parameters without requiring any distributional properties. Besides the fact that the bootstrap liberates statisticians from over-reliance on distributional assumptions, the method makes it possible to attack more complicated problems which may not have closed-form expressions.; This study utilized the bootstrap procedure to estimate the sampling distribution of estimators, their standard errors and thereby setting confidence intervals about the parameters of a mixed HLM under a variety of conditions. Applicability of the bootstrap on data originating from real research situations was demonstrated through the estimation of the effects of school, classroom, and teacher variables on the teachers' self-efficacy.; Based on the usual MINQUE and bootstrap estimators, the study showed that the success of estimation is typically affected by the nature and size of the tails of the distribution of the errors and sets of random effects parameters of the model. The bootstrap generally followed MINQUE quite closely in estimating the fixed and random effects of the model under both the normal and double exponential distributions. Particularly in estimating the population inter-class variance, {dollar}tausp2{dollar} at the 0.01 level of the intra-class correlation, the bootstrap was surprisingly closer to the parameter value than the MINQUE.; Due to the fact that the bootstrap procedure is highly dependent on the computer, the study recommended that software to implement the bootstrap algorithm be developed to make the method available to research practitioners. Availability of the method to research practitioners will provide an important and flexible tool, typically unavailable through classical methods, of estimating the sampling distributions of statistics, their standard errors, and thereby setting confidence intervals about parameters. |
