Type of Document Dissertation Author Delpish, Ayesha Nneka URN etd-06262006-100559 Title Comparison of Estimators in Hierarchical Linear Modeling: Restricted Maximum Likelihood Versus Bootstrap via Minimum Norm Quadratic Unbiased Estimators Degree Doctor of Philosophy Department Statistics, Department of Advisory Committee
Advisor Name Title Xu-Feng Niu Committee Chair Douglas Zahn Committee Member Fred W. Huffer Committee Member Richard L. Tate Committee Member Keywords
Date of Defense 2006-06-05 Availability unrestricted AbstractThe purpose of the study was to investigate the relative performance of two estimation
procedures, the restricted maximum likelihood (REML) and the bootstrap via MINQUE,
for a two-level hierarchical linear model under a variety of conditions. Specific focus lay on
observing whether the bootstrap via MINQUE procedure offered improved accuracy in the
estimation of the model parameters and their standard errors in situations where normality
may not be guaranteed.
Through Monte Carlo simulations, the importance of this assumption for the accuracy
of multilevel parameter estimates and their standard errors was assessed using the accuracy
index of relative bias and by observing the coverage percentages of 95% confidence intervals
constructed for both estimation procedures. The study systematically varied the number of
groups at level-2 (30 versus 100), the size of the intraclass correlation (0.01 versus 0.20) and
the distribution of the observations (normal versus chi-squared with 1 degree of freedom).
The number of groups and intraclass correlation factors produced effects consistent with
those previously reported—as the number of groups increased, the bias in the parameter
estimates decreased, with a more significant effect observed for those estimates obtained
via REML. High levels of the intraclass correlation also led to a decrease in the efficiency of parameter estimation under both methods. Study results show that while both the restricted maximum likelihood and the bootstrap via MINQUE estimates of the fixed effects were accurate, the efficiency of the estimates was affected by the distribution of errors with the
bootstrap via MINQUE procedure outperforming the REML. Both procedures produced less efficient estimators under the chi-squared distribution, particularly for the variance-covariance component estimates.
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