Asymptotic robustness of the normal theory likelihood ratio statistic for two-level covariance structure models

Data in social and behavioral sciences are often hierarchically organized. Special statistical procedures have been developed to analyze such data while taking into account the resulting dependence of observations. Most of these developments require a multivariate normality distribution assumption. It is important to know whether normal theory-based inference can still be valid when applied to nonnormal hierarchical data sets. Using an analytical approach for balanced data and numerical illustrations for unbalanced data, this paper shows that the likelihood ratio statistic based on the normality assumption is asymptotically robust for many nonnormal distributions. The result extends the scope of asymptotic robustness theory that has been established in different contexts.