Nonignorable data in IRT models: Polytomous responses and response propensity models with covariates

Missing data usually present special problems for statistical analyses, especially when the data are not missing at random, that is, when the ignorability principle defined by Rubin (1976) does not hold. Recently, a substantial number of articles have been published on model-based procedures to handle nonignorable missing data due to item nonresponse (Holman & Glas, 2005; Glas & Pimentel, 2008; Rose, von Davier & Xu, 2010; Pohl, Grӓfe & Rose, 2014). In this approach, an item response theory (IRT) model for the observed data is estimated concurrently with an IRT model for the propensity of the missing data. The present article elaborates on this approach in two directions. Firstly, the preceding articles only consider dichotomously scored items; in the present article it is shown that the approach equally works for polytomously scored items. Secondly, it is shown that the methods can be generalized to allow for covariates in the model for the missing data. Simulation studies are presented to illustrate the efficiency of the proposed methods.