Keywords: Multilevel model; pseudolikelihood; sampling weight; conditional quantile; bootstrapping; simplex algorithm
A pseudo-maximum likelihood approach is proposed for multilevel models in the quantile regression framework for complex surveys using multistage sampling design. This approach not only accounts for survey design effects (probability sampling weights, stratification and clustering at different sampling stages) at each quantile of the response, but enables estimation of cluster-specific random effects to account for intracluster correlation. Variance estimates are calculated by using the rescaling bootstrap method that adjusts sampling weights. The proposed approach is illustrated using a Monte Carlo simulation study and the baseline data on body mass index from Early Childhood Longitudinal Study (ECLS-K) 2011 administered by the National Center for Education Statistics (NCES).