EM algorithm for an improved random intercept model

Traditional multilevel model assumed independence between groups. Datasets are different from traditional hierarchical data when it is grouped by geographical units. The individual is influenced by not only its region but also the adjacent regions. It could include spatial dependence between groups. Therefore, it is necessary to build a new model and estimation method. In this paper, spatial statistics and spatial econometric models are introduced to random intercept model. Spatial dependence is reflected by spatial lag model in traditional level-2 model. Four types of parameters which include fixed effects, random level-1 coefficients, variance-covariance components, and spatial correlation error parameter need to estimate. Maximum likelihood estimation based on EM algorithm and Fisher scoring algorithm for improved random intercept model is employed.