Multivariate Statistical Modeling with Survey Data

We describe an extension of the pseudo maximum likelihood (PML) estimation method developed by Skinner (1989) to multistage strati ̄ed cluster sampling designs, including ̄nite population and unequal probability sampling. We conduct simulation studies to evaluate the performance of the proposed estimator. The estimator is also compared to the general estimating equation (GEE) method for linear regression implemented in SUDAAN. We investigate the distribution of the likelihood ratio test (LRT) statistic based on the pseudo log-likelihood value and describe an adjustment that gives correct chi-square distribution. The performance of the adjusted LRT is evaluated with a simulation study based on the Behrens-Fisher problem in a strati ̄ed cluster sampling design.