A multilevel structural equation model for homebuilding customer satisfaction data

The main purpose of this paper is to show the limitation of conventional SEM and multilevel SEM for homebuilding customer satisfaction data and present a more feasible model. In this paper, we present the conventional SEM and multilevel SEM in section 2 and 3 and discuss their limitation and shortage briefly. In section 4, we extend the conventional multilevel SEM to a more general form which take into account the group difference in structural model. The new model leads to a likelihood function that can not be written in closed form. So, the conventional estimation approaches (ML, WLS) can not apply to this new model. In the final of the paper, we describe how to estimate the model using simulation-based Bayesian approach.