Title: Instrument, variable and model selection with nonignorable nonresponse
Authors: Jun Shao - University of Wisconsin - Madison (United States) [presenting]
Abstract: With nonignorable nonresponse, an effective method to construct valid estimators of population parameters is to use a covariate vector, called instrument, that can be excluded from the nonresponse propensity, but contains still useful covariates, even when other covariates are conditioned. The existing work in this approach assumes such an instrument is given, which is frequently not the case in applications. We investigate how to search for an instrument from a given set of covariates. The method for estimation is the pseudo likelihood which assumes that the distribution of response given covariates is parametric and the propensity is nonparametric. Thus, in addition to the challenge of searching an instrument, we also need to do variable and model selection simultaneously. We propose a method for instrument, variable, and model selection and show that our method produces consistent instrument and model selection as the sample size tends to infinity, under some regularity conditions. Empirical results including two simulation studies and two real examples are present to show that the proposed method works well.