Diggle and Kenward (1994) proposed a selection model for continuous longitudinal data subject to possible non-random dropout. Their method in general, and the milk protein example in particular, has provoked a large debate about the role of such models. The original enthusiasm was followed by skepticism about the strong but untestable assumption upon which this type of models invariably rests. Concern was raised about the very nature of incompleteness which is arguably more due to design reasons (the experiment was stopped due to insufficient feed supply), than to genuine dropout. In the meantime, the view has emerged that these models should ideally be made part of a sensitivity analysis. This paper presents a formal and flexible approach to such a sensitivity assessment, based on both global influence (Chatterjee and Hadi, 1988) as well as local influence (Cook, 1986). It will be argued that local influence is more apt to zoom in on a particular source of influence, such as the assumed non-response mechanism. The method is applied to a set of data on milk protein contents in dairy cattle. The same data were used in the original paper by Diggle and Kenward (1994), who concluded that the dropout process was non-random.