Multidimensional and longitudinal item response models for non-ignorable data

• Multidimensional IRT models are proposed to non-ignorable responses in multiple-choice educational data.
• Proficiencies of the examinees and their propensities for omission are jointly modeled.
• A model for longitudinal data with non-ignorable missing item responses is also proposed.
• Application to a Brazilian multidimensional and longitudinal educational evaluation is presented.

A multidimensional item response approach is proposed to model non-ignorable responses in multiple-choice educational data. The model considers latent traits related to individual proficiency as well as the propensity to answer items. Thus, in addition to modeling the probability of scoring on an item, the probability of answering it is also modeled. Simulation studies are presented to evaluate the efficiency of the estimation procedure in recovering the true values of the model parameters considering several particular cases of the dimensions of proficiency and propensity. The simulation study also compares the proposed approach with others commonly applied in practice. A further extension to cope with longitudinal data with non-ignorable missing item responses is also proposed, together with an application to a Brazilian longitudinal educational evaluation study.