Brazilian Journal of Probability and Statistics

Bayesian modelling of the abilities in dichotomous IRT models via regression with missing values in the covariates

Flávio B. Gonçalves and Bárbara C. C. Dias

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Abstract

Educational assessment usually considers a contextual questionnaire to extract relevant information from the applicants. This may include items related to socio-economical profile as well as items to extract other characteristics potentially related to applicant’s performance in the test. A careful analysis of the questionnaires jointly with the test’s results may evidence important relations between profiles and test performance. The most coherent way to perform this task in a statistical context is to use the information from the questionnaire to help explain the variability of the abilities in a joint model-based approach. Nevertheless, the responses to the questionnaire typically present missing values which, in some cases, may be missing not at random. This paper proposes a statistical methodology to model the abilities in dichotomous IRT models using the information of the contextual questionnaires via linear regression. The proposed methodology models the missing data jointly with the all the observed data, which allows for the estimation of the former. The missing data modelling is flexible enough to allow the specification of missing not at random structures. Furthermore, even if those structures are not assumed a priori, they can be estimated from the posterior results when assuming missing (completely) at random structures a priori. Statistical inference is performed under the Bayesian paradigm via an efficient MCMC algorithm. Simulated and real examples are presented to investigate the efficiency and applicability of the proposed methodology.

Article information

Source
Braz. J. Probab. Stat., Volume 33, Number 4 (2019), 782-800.

Dates
Received: October 2018
Accepted: April 2019
First available in Project Euclid: 26 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1566806433

Digital Object Identifier
doi:10.1214/19-BJPS443

Mathematical Reviews number (MathSciNet)
MR3996317

Keywords
3PNO model Bayesian inference MCMC

Citation

Gonçalves, Flávio B.; Dias, Bárbara C. C. Bayesian modelling of the abilities in dichotomous IRT models via regression with missing values in the covariates. Braz. J. Probab. Stat. 33 (2019), no. 4, 782--800. doi:10.1214/19-BJPS443. https://projecteuclid.org/euclid.bjps/1566806433


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