Summary. The paper describes the use of a longitudinal tobit model to characterize cognitive decline over a 13-year period in a cohort of 2087 elderly Australians. Use of a tobit formulation allows for the so-called ‘ceiling effect’ wherein many subjects achieve perfect test scores. A Bayesian hierarchical joint model is presented that allows for random subject-specific intercepts and slopes, as well as for informative dropout. Results suggest several potential areas of intervention. For example, there is a clear dose–response effect of exercise whereby increasing levels of exercise are associated with higher cognitive scores.