Maximum likelihood estimation of nonlinear structural equation models with ignorable missing data

The existing maximum likelihood theory and its computer software in structural equation modeling are established on the basis of linear relationships among latent variables with fully observed data. However, in social and behavioral sciences, nonlinear relationships among the latent variables are important for establishing more meaningful models and it is very common to encounter missing data. In this article, an EM type algorithm is developed for maximum likelihood estimation of a general nonlinear structural equation model with ignorable missing data, which are missing at random with an ignorable mechanism. To avoid computation of the complicated multiple integrals involved in the conditional expectations, the E-step is completed by a hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm; while the M-step is completed efficiently by conditional maximization. Standard errors of the maximum likelihood estimates are obtained via Louis's formula. The methodology is illustrated with results obtained from a simulation study and a real data set with rather complicated missing patterns and a large number of missing entries.