, Volume 70, Issue 1, pp 147-167

First online:

On muthén’s maximum likelihood for two-level covariance structure models

  • Ke-Hai YuanAffiliated withUniversity of Notre DameUniversity of Notre Dame Email author 
  • , Kentaro HayashiAffiliated withUniversity Of Hawaii at Manoa

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Data in social and behavioral sciences are often hierarchically organized. Special statistical procedures that take into account the dependence of such observations have been developed. Among procedures for 2-level covariance structure analysis, Muthén’s maximum likelihood (MUML) has the advantage of easier computation and faster convergence. When data are balanced, MUML is equivalent to the maximum likelihood procedure. Simulation results in the literature endorse the MUML procedure also for unbalanced data. This paper studies the analytical properties of the MUML procedure in general. The results indicate that the MUML procedure leads to correct model inference asymptotically when level-2 sample size goes to infinity and the coefficient of variation of the level-1 sample sizes goes to zero. The study clearly identifies the impact of level-1 and level-2 sample sizes on the standard errors and test statistic of the MUML procedure. Analytical results explain previous simulation results and will guide the design or data collection for the future applications of MUML.


asymptotics likelihood ratio statistic multilevel covariance structure standard error estimates