EO Ogundimu and JL Hutton
A Unified Approvach to Multilevel Sample Selection Models
Abstract: Scores derived from response to questionnaires are widely used in health and social studies to measure aspects of health and well being. Respondent to studies do not always complete all questions, which result in two levels of missing data. If a subject declines participation, we have unit non-response; if questions are skipped, we have item non-response. We can regard the observed outcomes as the result of a two level selection process. We propose a unified approach for multilevel sample selection models in a parametric framework by treating the outcome variable as the non-truncated marginal of a truncated multivariate normal distribution. The resulting density for the outcome is the continuous component of the sample selection density, and has links with the closed skew-normal distribution. The closed skew-normal distribution provides a framework which simplifies the derivation of the conditional expectation and variance of the observed data. We use this to generalize the Heckman's two-step method to a multilevel sample selection model. Finite sample performance of the full information maximum likelihood estimator of this model is studied through a Monte Carlo simulation and issues about local identi_ability of model parameters are discussed in the context of non-singularity of the information matrix. The method is applied to a clinical trial data of neck injuries with unit and item non-response.