Multidimensional and longitudinal item response models for non-ignorable data

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 it...

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Bibliographic Details
Published in:Computational statistics & data analysis 2016-11, Vol.103, p.91-110
Main Authors: Santos, Vera Lúcia F., Moura, Fernando A.S., Andrade, Dalton F., Gonçalves, Kelly C.M.
Format: Article
Language:English
Subjects:
Bayesian inference
Computer simulation
Data processing
Education
Education evaluation
Efficiency
Mathematical models
MCMC
Non-ignorable missing data
Recovering
Scoring
Statistics
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Summary: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. •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.
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2016.05.002