Assessing Maximum Likelihood Estimates of Nonlinear Structural Equation Models with Missing at Random Data under Various Missing Rates

In behavioral and social sciences, it is very common to face latent variables. One of the best approaches to model these variables is using structural equation models which are constructed from a measurement equation and a structural equation. Relations between latent variables are taken into account by the structural equation. However, maximum likelihood theory and existing computer softwares such as LISREL (Joreskog and Sorbom, 1996, Scientific Software International: Hove and London) and EQS (Bentler, 1992, Los Angeles: BMDP Statistical Software) which are used in psychology and social studies to assess relations between variables, are based on a linear pattern and the assumption that complete data sets exist. On one side the presence of missing data and on the other side nonlinear relations between latent variables are very important to be considered to obtain significant models. Lee et al. (2003, J. Educat. Behav. Statist., 28,111-134) introduced an EM type algorithm which is used to obtain ML estimates of nonlinear structural equation models with missing at random data. In this algorithm to calculate complicated integrals in conditional expectation step, the E step is completed with a hybrid algorithm that combines Gibbs sampler (Geman and Geman, 1984, IEEE Trans. Pattern Anal. Machie Intell., 6, 721-741) and Metropolis-Hastings algorithm, while the M step is efficiently completed with conditional maximization. In this paper we assess the efficiency of this method in a simulation study with high missing rate.