ABSTRACT
Methodologies for the analysis of two-level structural equation models (SEM for simplicity) have been proposed by a number of authors. These methodologies are usually suitable for some specific formulation of two-level SEM. Goldstein and McDonald (1988) proposed a general model for analysis of multilevel data that includes two-level SEM as its special case. McDonald and Goldstein (1989) proposed a general treatment for maximum likelihood (ML) analysis of two-level SEM. The importance of ML lies in its asymptotic optimality, that is, an estimator with the smallest standard error, meeting the Cramér-Rao lower bound. For an unbalanced design of a sample, McDonald and Goldstein’s (1989) algorithm seems to be computationally burdensome because a large number of inverse matrices have to be computed to obtain the maximum likelihood estimates (MLE) of model parameters. Muthén (1994) summarized the techniques in several papers in which he developed the so-called MUML analysis for two-level SEM. He implemented a pseudobalanced solution for unbalanced sample designs. MUML analysis of two-level SEM is a kind of approximate ML analysis (Hox, 2000). Raudenbush (1995) used a balanced complete data routine to show how ML analysis on two-level SEM with unbalanced designs can be done by available software. Lee (1990) proposed a simple formulation of two-level SEM and obtained general asymptotic properties of MLE for model parameters. Lee and Poon (1998) proposed a treatment for exact ML analysis of two-level SEM via EM type algorithms. An advantage of Lee and Poon’s (1998) method is that it is applicable to arbitrary (balanced and unbalanced) sample designs and their algorithm turns out to converge fast.
