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Bayesian estimation for an item response tree model for nonresponse modeling

Author

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  • Yu-Wei Chang

    (National Chengchi University)

  • Jyun-Ye Tu

    (Feng Chia University)

Abstract

Nonresponse data are common in achievement tests or questionnaires. Chang et al. (Br J Math Stat Psychol 74:487–512, 2021) proposed an Item Response tree model, namely TR4, for modeling some potential mechanisms underlying nonresponses so that the estimates of parameters of interest would not be biased due to missing not at random (Rubin in Biometrika 63:581–592, 1976). TR4 has two notable degenerate cases, both with insightful practical meanings. When TR4 is fitted to data originated from some degenerate cases, there exist model identifiability issues so that the existing frequentist inference for the TR4 model is not suitable. In the current study, we propose a Bayesian estimation procedure that incorporates the Markov chain Monte Carlo technique for estimating the TR4 model. We conducted simulation studies to demonstrate the effectiveness of the Bayesian estimation procedure in solving the model unidentifiability issue. In addition, the TR4 model is further extended in the present study to effectively accommodate the complexity underlying some real data. The advantage of the extended models over TR4 is demonstrated in the real data analysis where we apply our method to the data of a geography test for college admission in Taiwan.

Suggested Citation

  • Yu-Wei Chang & Jyun-Ye Tu, 2022. "Bayesian estimation for an item response tree model for nonresponse modeling," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(8), pages 1023-1047, November.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:8:d:10.1007_s00184-022-00858-1
    DOI: 10.1007/s00184-022-00858-1
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    References listed on IDEAS

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    1. Yu-Wei Chang & Rung-Ching Tsai & Nan-Jung Hsu, 2014. "A Speeded Item Response Model: Leave the Harder till Later," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 255-274, April.
    2. Jing Cao & S. Stokes, 2008. "Bayesian IRT Guessing Models for Partial Guessing Behaviors," Psychometrika, Springer;The Psychometric Society, vol. 73(2), pages 209-230, June.
    3. Seock-Ho Kim & Allan Cohen & Frank Baker & Michael Subkoviak & Tom Leonard, 1994. "An investigation of hierarchical Bayes procedures in item response theory," Psychometrika, Springer;The Psychometric Society, vol. 59(3), pages 405-421, September.
    4. Yuri Goegebeur & Paul Boeck & James Wollack & Allan Cohen, 2008. "A Speeded Item Response Model with Gradual Process Change," Psychometrika, Springer;The Psychometric Society, vol. 73(1), pages 65-87, March.
    5. Hariharan Swaminathan & Janice Gifford, 1986. "Bayesian estimation in the three-parameter logistic model," Psychometrika, Springer;The Psychometric Society, vol. 51(4), pages 589-601, December.
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