Comparison of HLM and MLwiN multilevel analysis software packages: A Monte Carlo investigation into the quality of the estimates.

다국어 초록 (Multilingual Abstract)

The quality of the parameter estimates obtained from MLwiN and HLM multilevel software packages are compared. Monte-Carlo methods are used to generate multilevel data to run 1000 replications for each of the following comparison conditions: sample size (groups and cases), model complexity and centering method (group mean centered or grand mean centered). Convergence rates were also tracked. The following main effects were found to result in better quality estimates: less complex models; greater sample size (more groups, more cases per group); and the use of group mean centering. In addition to main effects, a number of interaction effects were significant. Less complex models with more groups have better quality estimates, as expected. For intercepts and variances, MSE was lower for group mean centered models and decreased as the number of groups increased. For slopes, MSE is lower for grand mean centered models, and MSE also decreased as the number of groups increased. There were differences in the quality of the estimates produced by the two software packages, but these differences were not consistent, and were distorted by extreme differences in convergence rates for low sample sizes. For group mean centered models, MLwiN had better convergence rates than HLM, particularly when sample sizes were low. For grand mean centered models, HLM had better convergence rates than MLwiN when models were more complex. It should be noted that the software default options were used to run all of the models. Both MLwiN and HLM have non-default options that could possibly improve convergence rates as well as the quality of the parameter estimates.