A Monte Carlo investigation of robustness to nonnormal incomplete data of multilevel modeling
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Due to its increasing popularity, hierarchical linear modeling (HLM) has been used along with structural equation modeling (SEM) to analyze data with nested structure. In spite of the extensive research on commonly encountered problems such as violation of normality and missing data treatment within the framework of SEM, these areas have been much less explored in HLM. The present study compared HLM and multilevel SEM through a Monte Carlo study from the perspectives of the influence of nonnormality and performance of multiple imputation based on the expectationmaximization (EM) algorithm under various combinations of sample sizes at two levels. The statistical power, parameter estimates, standard errors, and estimation bias for the main effects and cross-level interaction in a two- level model were compared across the four design factors: analysis method, normality condition, missing data proportion, and sample size. HLM and multilevel SEM appeared to have similar power detecting the main effect, while HLM had better power for the cross- level interaction. Neither seemed to be sensitive to violation of the normality assumption. A higher proportion of missing data resulted in larger standard errors and estimation bias. Sample sizes at both the individual and cluster levels played a role in the statistical power for parameter estimates. The two-way interactions for the four factors were generally nonzero. Overall, both HLM and multilevel SEM were quite robust to violation of normality. SEM appears more useful in more complex path models while HLM is superior in detecting main effects. Multiple imputation based on the EM algorithm performed well in producing stable parameter estimates for up to 30% missing data. Sample size design should take into account the level at which the research is most focused.
Zhang, Duan (2005). A Monte Carlo investigation of robustness to nonnormal incomplete data of multilevel modeling. Doctoral dissertation, Texas A&M University. Texas A&M University. Available electronically from