Graduation Year

2011

Document Type

Dissertation

Degree

Ph.D.

Degree Granting Department

Educational Measurement and Research

Major Professor

John M. Ferron, Ph.D.

Committee Member

Robert F. Dedrick, Ph.D.

Committee Member

Liliana Rodriguez-Campos, Ph.D.

Committee Member

Julia Ogg, Ph.D.

Keywords

single-subject, research synthesis, multilevel modeling, hierarchical linear modeling, simulation

Abstract

Numerous ways to meta-analyze single-case data have been proposed in the literature, however, consensus on the most appropriate method has not been reached. One method that has been proposed involves multilevel modeling. This study used Monte Carlo methods to examine the appropriateness of Van den Noortgate and Onghena's (2008) raw data multilevel modeling approach to the meta-analysis of single-case data. Specifically, the study examined the fixed effects (i.e., the overall average baseline level and the overall average treatment effect) and the variance components (e.g., the between person within study variance in the average baseline level, the between study variance in the overall average baseline level, the between person within study variance in the average treatment effect) in a three level multilevel model (repeated observations nested within individuals nested within studies). More specifically, bias of point estimates, confidence interval coverage rates, and interval widths were examined as a function of specific design and data factors. Factors investigated included (a) number of primary studies per meta-analysis, (b) modal number of participants per primary study, (c) modal series length per primary study, (d) level of autocorrelation, and (3) variances of the error terms. The results of this study suggest that the degree to which the findings of this study are supportive of using Van den Noortgate and Onghena's (2008) raw data multilevel modeling approach to meta-analyzing single-case data depends on the particular effect of interest. Estimates of the fixed effects tended to be unbiased and produced confidence intervals that tended to overcover but came close to the nominal level as level-3 sample size increased. Conversely, estimates of the variance components tended to be biased and the confidence intervals for those estimates were inaccurate.

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