A Monte Carlo investigation of multilevel modeling in meta-analysis of single-subject research data
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Multilevel modeling represents a potentially viable method for meta-analyzing single-subject research, but questions remain concerning its methodological properties with regard to characteristics of single-subject data. For this dissertation, Monte Carlo methods were used to investigate the properties of a 3 level model (i.e., with a quadratic equation at level 1), and three different level 1 error specifications (i.e., different variance components and covariances of 0, lag-1 autoregressive covariance structures, and separate error terms for each phase, with different variance components and covariances of 0). Data for simulated subjects were generated to have characteristics typical of published single-subject data (e.g., typical variances and magnitudes of effect). Samples were simulated for conditions which varied in number of data points per phase, number of subjects per study, number of studies meta-analyzed, level of autocorrelation in residuals, and continuity of variance across phases. Outcome variables examined included rates of convergence of analyses, power for statistical tests of fixed effects, and relative parameter bias of estimates of fixed effects, random effects’ variance components, and autocorrelation estimates. Convergence rates were found to be 100% for all level 1 error specifications and data conditions. Power for statistical tests of fixed effects was observed to be adequate when 10 or more data points were generated per phase and 60 or more total subjects were included in meta-analyses. The relative biases of estimates of fixed effects were found to have limited associations with numbers of data points per phase, levels of autocorrelation, and the continuity/discontinuity of variance across phases. Random effects’ variance components were observed to be frequently biased. Associations between relative bias and data conditions were found to vary by random effect. Finally, autocorrelation estimates were found to be biased in all conditions for which autocorrelation was generated. Results are discussed with regard to study strengths and limitations, and their implications for the meta-analysis of single subject data and primary single subject research.