One difficulty in regression analysis for longitudinal data is that the outcomes are oftenmissing in a non-ignorable way (Little & Rubin, 1987). Likelihood based approaches todeal with non-ignorable missing outcomes can be divided into selection models and patternmixture models based on the way the joint distribution of the outcome and the missing-dataindicators is partitioned. One new approach from each of these two classes of models isproposed. In the first approach, a normal copula-based selection model is constructed tocombine the distribution of the outcome of interest and that of the missing-data indicatorsgiven the covariates. Parameters in the model are estimated by a pseudo maximum likelihoodmethod (Gong & Samaniego, 1981). In the second approach, a pseudo maximum likelihoodmethod introduced by Gourieroux et al. (1984) is used to estimate the identifiable parametersin a pattern mixture model. This procedure provides consistent estimators when the meanstructure is correctly specified for each pattern, with further information on the variancestructure giving an efficient estimator. A Hausman type test (Hausman, 1978) of modelmisspecification is also developed for model simplification to improve efficiency. Separatesimulations are carried out to assess the performance of the two approaches, followed byapplications to real data sets from an epidemiological cohort study investigating dementia,including Alzheimer's disease
