A Comparative Review of Selection Models in Longitudinal Continuous Response Data with Dropout

Missing values occur in studies of various disciplines such as social sciences, medicine, and economics. The missing mechanism in these studies should be investigated more carefully. In this article, some models, proposed in the literature on longitudinal data with dropout are reviewed and compared. In an applied example it is shown that the selection model of Hausman and Wise (1979, Econometrica 47, pp. 455-473) and the shared parameter model of Follmann and Wu (1995, Biometrics 51, pp. 151-168), two of the most used models for longitudinal data with dropout in economics and medical researches, respectively, cannot sufficiently consider the relation between response variables and missing mechanism. In this paper, the Follmann and Wu’s (1995) dropout model is also generalized by adding a previous time outcome component to the model. Having modified this model, in the case of longitudinal data with two time periods, a general form of this model is obtained, which is able to consider all relations between response and missing mechanism. This is proven in an implicit way. A test for missing at random in the generalized Hechman model (Crouchley and Ganjali, 2002, Stat. Model. 2, pp. 39-62) is also introduced where one has to use $delta$-method to find the variance of the test statistic.