When “Don’t Know” Indicates Nonignorable Missingness: Using the Estimation of Political Knowledge as an Example

The conventional procedure for measuring political knowledge is treating nonresponses such as “don’t know” as incorrect responses and counting the number of “correct” responses. In recent times, increasing attention has been paid to partial knowledge hidden within incorrect and nonresponses. This article explores partial knowledge indicated by incorrect and nonresponses and considers nonresponses as nonignorable missingness. We propose a model that combines the shared-parameter approach presented in the literature on missing data mechanisms and the methods of item response theory. We show that the proposed model can determine whether the people with nonresponses should be treated as more or less knowledgeable and detect whether it is appropriate to pool nonresponses and incorrect responses into the same category. Furthermore, we find partial knowledge hidden within women’s nonresponses, which confirms the possibility of the exaggeration of the gender gap in political knowledge.

Sequentially additive nonignorable missing data modelling using auxiliary marginal information

Summary We study a class of missingness mechanisms, referred to as sequentially additive nonignorable, for modelling multivariate data with item nonresponse. These mechanisms explicitly allow the probability of nonresponse for each variable to depend on the value of that variable, thereby representing nonignorable missingness mechanisms. These missing data models are identified by making use of auxiliary information on marginal distributions, such as marginal probabilities for multivariate categorical variables or moments for numeric variables. We prove identification results and illustrate the use of these mechanisms in an application.