Maximum likelihood estimation for unbalanced multilevel covariance structure models via the EM algorithm

Recent investigations have revealed that widely available software can be adapted to provide maximum likelihood (ML) estimates for a general class of multilevel covariance structure models if the data are balanced (e.g. equal numbers of students in each of many schools). When the data are unbalanced, finding ML estimates is more challenging. However, by viewing the ‘complete data’ as balanced, one can calculate ML estimates for unbalanced data by constructing a comparatively simple EM algorithm. Computation using standard single‐level structural equation software performs the ‘M step’, and an auxiliary program computes the E‐step. Simple computational formulas for this E‐step are provided in the case of two‐level data, and recent experience with its implementation discussed. Asymptotic standard errors are found by computing the observed‐data information matrix at convergence.