Estimating Latent-Variable Panel Data Models Using Parameter-Expanded SEM Methods

The Expectation-Maximization (EM) algorithm is a popular tool for estimating models with latent variables. In complex models, simulated versions such as stochastic EM, are often implemented to overcome the difficulties in computing expectations analytically. A drawback of the EM algorithm and its variants is the slow convergence in some cases, especially when the models contain high-dimensional latent variables. Liu et al., 1998 proposed a parameter-expanded algorithm (PX-EM) to speed up convergence. This paper explores the potential of parameter expansion ideas for estimating nonlinear panel models using the stochastic EM algorithm. We develop PX-SEM methods for two types of nonlinear panel data models: 1) binary choice models with individual effects and persistent shocks, and 2) persistent-transitory dynamic quantile processes. We find that PX-SEM can greatly speed up convergence especially when the initial guess is relatively far away from true values.