This chapter focuses on next-generation selection models that allow us to expand on the Heckman model using copula and control function models that allow one to estimate selection models for a large range of other statistical distributions. This chapter also shows how to generate weights that account for nonignorable nonresponse; not only do these weights increase the weight on demographic groups that respond with lower probabilities, they also increase weights on people with opinions that may make them less inclined to respond. This chapter also shows how to modify a Heckman model to allow for estimation of a nonignorable nonresponse selection model when we have a response-related variable that is available only for people in the survey sample.

This chapter highlights the critical importance of having the right kind of data for selection models that address nonignorable nonresponse. In general, we need a variable that is included in our response model and excluded from our outcome model. The best approach is creating a randomized response instrument that affects whether someone responds, but does not affect the content of their response. In many polling contexts, it is easy to create randomized response instruments. The pollster simply needs to figure out some protocol that affects response rate and then randomize it. Section 10.1 makes it clear that knowing the correct functional form is not enough to save a selection model. Section 10.2 highlights the difficulty of using observational response instruments. Section 10.3 discusses how and why to create randomized response instruments. Section 10.4 shows how to use randomized response instruments in a simple test for diagnosing nonignorable nonresponse. Section 10.5 shows how randomized response instruments enable us to use the full suite of selection models even when we do not observe data for nonrespondents.