Multilevel modeling of complex survey data

We describe a multivariate, multilevel, pseudo maxi-mum likelihood estimation method for multistage strati-fied cluster sampling designs, including finite population and unequal probability sampling. Multilevel models can be estimated with this method while incorporating the sampling design in the standard error computation. De-sign based adjustment of the likelihood ratio test (LRT) statistic is proposed. We also discuss multiple group and subpopulation analysis in this context. Simulation studies are conducted to evaluate the performance of the proposed estimator and test statistic. We also compare the estimators and the LRT adjustments implemented in Mplus and LISREL in simulation studies