A model specification test for semiparametric nonignorable missing data modeling

The instrumental variable approaches have been demonstrated effective for semiparametrically modeling the propensity function in analyzing data that may be missing not at random. A model specification test is considered for a class of parsimonious semiparametric propensity models. The test is constructed based on assessing an over-identification so as to detect possible incompatibility in the moment conditions when the model and/or instrumental variables are misspecified. Validity of the test under the null hypothesis is established; and its power is studied when the model is misspecified. A data analysis and simulations are presented to demonstrate the effectiveness of our methods.