Modeling Achievement Trajectories When Attrition Is Informative

In longitudinal education studies, assuming that dropout and missing data occur completely at random is often unrealistic. When the probability of dropout depends on covariates and observed responses (called missing at random [MAR]), or on values of responses that are missing (called informative or not missing at random [NMAR]), inappropriate analysis can cause biased estimates. NMAR requires explicit modeling of the missingness process together with the response variable. In this article, we review assumptions needed for consistent estimation of hierarchical linear growth models using common missing-data approaches. We also suggest a joint model for the longitudinal data and missingness process to handle the situation where data are NMAR. The different approaches are applied to the NELS:88 study, as well as simulated data. Results from the NELS:88 analyses were similar between the MAR and NMAR models. However, use of listwise deletion and mean imputation resulted in significant bias, both for the NELS:88 study and simulated data. Simulation results showed that incorrectly assuming MAR leads to greater bias for the growth-factor variance–covariance matrix than for the growth factor means, the former being severe with as little as 10% missing data and the latter with 40% missing data when departure from MAR is strong.