Using Mx to Analyze Cross-Level Effects in Two-Level Structural Equation Models

Two-level data sets are frequently encountered in social and behavioral science research. They arise when observations are drawn from a known hierarchical structure, such as when individuals are randomly drawn from groups that are randomly drawn from a target population. Although 2-level data analysis in the context of structural equation modeling can be conducted by easily accessible software such as LISREL, the group- and individual-level effects are usually treated as though they are uncorrelated. When extra group variables are measured and their relationships with individual-level variables are studied, the analysis of cross-level covariance structures is of interest. In this article, we propose a model setup framework in Mx that allows the analysis of cross-level covariance structures. An illustrative example is given and a small-scale simulation study is conducted to examine the performance of the proposed procedure. The results show that the proposed method can produce reliable parameter and standard error estimates, and the goodness-of-fit statistics also follow the chi-square distribution in large samples.