The common structure of several models for non-ignorable dropout

This paper presents a multivariate generalization of the classical Heckman selection model and applies it to non-ignorable dropout in repeated continuous responses. Many of the recent models for dropout in repeated continuous responses can be written as special forms of this generalized Heckman model. To illustrate this, we present the parameterizations needed to obtain the form of dropout model that occurs when (1) the separate models for the response and dropout are linked by common random parameters, (2) the dropout model is an explicit function of the previous responses and the possibly unobserved current response, (3) the dropout model is both a function of the current response and a common random parameter, and (4) there is a covariance between the stochastic disturbances of the response and dropout processes. We present the joint likelihood of the generalized Heckman model and a residual for the responses. We contrast two of the dropout models in a simulation study. We compare the results obtained from several dropout models on the well known mastitis data.