| Summary: | 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.
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