Analysis of a two-level structural equation model with group-specific variables in LISREL

Two-level data sets are frequently encountered in social and behavioral science research. They arise when observations are drawn from a known hierarchical structure, as when individuals are randomly drawn from groups that are randomly drawn from a target population. When the covariance structures in the group level and the individual level are the same, standard structural equation modeling software such as LISREL can be used easily to analyze 2-level data sets. However, if the data set consists of variables that have group-level characteristics, LISREL cannot be used in a straightforward manner to implement the analysis of structural equation models that have different structures at the group and individual level. This article illustrates how 2-level structural equation models with additional group-level variables, and hence different structures at the group and individual levels, can be analyzed by LISREL with appropriate settings. A small-scale simulation study was conducted to examine the performance of the proposed method. The results indicate that the proposed method can produce reliable parameter estimates, standard errors, and goodness-of-fit test statistics. The proposed procedure was also used to analyze real data from a study on leadership effectiveness, which examines the correlation between self-ratings and ratings from multiple subordinates.