Analysis of a Two-Level Structural Equation Model With Missing Data

Abstract

Structural equation models are widely used to model relationships among latent unobservable constructs and observable variables. In some studies, the data set used for analysis is comprised of observations that are drawn from a known hierarchical structure and involves missing entries. A two-level structural equation model can be used to analyze such data sets. Direct maximum likelihood methods for analyzing two-level structural equation models are available in software, such as LISREL and Mplus. These software programs also have options to handle missing observations. The authors develop an alternative procedure that uses an expectation maximization (EM) type algorithm. Using appropriate approximations, the procedure can be implemented using simple statistical software in combination with a basic structural equation modeling program. The authors address the implementation of the procedure in detail and provide syntax codes in R, which is available in the public domain, to implement the proposed procedure. The discussion of the procedure is made with reference to the analysis of a data set that studies job characteristic variables. The authors also use simulation studies to examine the performance of the proposed procedure. The results indicate that the proposed method, which is easily accessible to users, represents a reliable alternative for analyzing two-level structural equation models with missing data.