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Symmetric pattern models: a latent variable approach to item non‐response in attitude scales

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  • C. O'Muircheartaigh
  • I. Moustaki

Abstract

This paper proposes a new approach to the treatment of item non‐response in attitude scales. It combines the ideas of latent variable identification with the issues of non‐response adjustment in sample surveys. The latent variable approach allows missing values to be included in the analysis and, equally importantly, allows information about attitude to be inferred from non‐response. We present a symmetric pattern methodology for handling item non‐response in attitude scales. The methodology is symmetric in that all the variables are given equivalent status in the analysis (none is designated a ‘dependent’ variable) and is pattern based in that the pattern of responses and non‐responses across individuals is a key element in the analysis. Our approach to the problem is through a latent variable model with two latent dimensions: one to summarize response propensity and the other to summarize attitude, ability or belief. The methodology presented here can handle binary, metric and mixed (binary and metric) manifest items with missing values. Examples using both artificial data sets and two real data sets are used to illustrate the mechanism and the advantages of the methodology proposed.

Suggested Citation

  • C. O'Muircheartaigh & I. Moustaki, 1999. "Symmetric pattern models: a latent variable approach to item non‐response in attitude scales," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(2), pages 177-194.
  • Handle: RePEc:bla:jorssa:v:162:y:1999:i:2:p:177-194
    DOI: 10.1111/1467-985X.00129
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    Cited by:

    1. Bartolucci, Francesco & Giorgio E., Montanari & Pandolfi, Silvia, 2012. "Item selection by an extended Latent Class model: An application to nursing homes evaluation," MPRA Paper 38757, University Library of Munich, Germany.
    2. Jiwei Zhang & Zhaoyuan Zhang & Jian Tao, 2021. "A Bayesian algorithm based on auxiliary variables for estimating GRM with non-ignorable missing data," Computational Statistics, Springer, vol. 36(4), pages 2643-2669, December.
    3. Chen, Yunxiao & Lu, Yan & Moustaki, Irini, 2022. "Detection of two-way outliers in multivariate data and application to cheating detection in educational tests," LSE Research Online Documents on Economics 112499, London School of Economics and Political Science, LSE Library.
    4. Steffi Pohl & Esther Ulitzsch & Matthias Davier, 2019. "Using Response Times to Model Not-Reached Items due to Time Limits," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 892-920, September.
    5. Irannezhad, Elnaz & Prato, Carlo & Hickman, Mark, 2019. "A joint hybrid model of the choices of container terminals and of dwell time," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 121(C), pages 119-133.
    6. Simon Grund & Oliver Lüdtke & Alexander Robitzsch, 2021. "On the Treatment of Missing Data in Background Questionnaires in Educational Large-Scale Assessments: An Evaluation of Different Procedures," Journal of Educational and Behavioral Statistics, , vol. 46(4), pages 430-465, August.
    7. Norman Rose & Matthias Davier & Benjamin Nagengast, 2017. "Modeling Omitted and Not-Reached Items in IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 795-819, September.
    8. 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.
    9. Merkle, Edgar C. & Steyvers, Mark & Mellers, Barbara & Tetlock, Philip E., 2017. "A neglected dimension of good forecasting judgment: The questions we choose also matter," International Journal of Forecasting, Elsevier, vol. 33(4), pages 817-832.
    10. Kano, Yutaka & Takai, Keiji, 2011. "Analysis of NMAR missing data without specifying missing-data mechanisms in a linear latent variate model," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1241-1255, October.
    11. Jinxin Guo & Xin Xu & Zhiliang Ying & Susu Zhang, 2022. "Modeling Not-Reached Items in Timed Tests: A Response Time Censoring Approach," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 835-867, September.

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