The Pseudo Maximum Likelihood Estimator for Quantiles of Survey Variables

The pseudo maximum likelihood approach has been employed in multilevel models for analysis of complex survey data. This approach may be inappropriate for many survey variables that are nonsymmetrically distributed with skewness and multimodality characteristics. This article intends to fill this gap in the literature by developing a pseudolikelihood estimator for quantiles of survey variables in the quantile regression framework. This approach is illustrated using a Monte Carlo simulation study and the body mass index data from the 1998-1999 Early Childhood Longitudinal Study. Results show that the proposed estimator is consistent and approximately unbiased for both informative and noninformative sampling designs.