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The heterogeneous thresholds ordered response model: identification and inference

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  • Franco Peracchi
  • Claudio Rossetti
Abstract
Although surveys routinely ask respondents to evaluate various aspects of their life on an ordered scale, there is concern about interpersonal comparability of these self-assessments. Statistically, the problem is one of identification in ordered response models with heterogeneous thresholds. As a solution to the identification problem, King et al. (2004) proposed using anchoring vignettes, namely brief descriptions of hypothetical people or situations that survey respondents are asked to evaluate on the same scale they use to rate their own situation. While vignettes have been introduced in several social surveys and are increasingly employed in a variety of fields, reliability of this approach hinges crucially on the validity of the assumptions of response consistency and vignette equivalence. This paper proposes a joint test of these key assumptions based on the fact that the underlying statistical model is overidentified if the two assumptions hold. Monte Carlo results show that the proposed test has good size and power properties in finite samples. We apply our test to self-assessment of pain using data from the first wave of the Survey of Health, Ageing and Retirement in Europe (SHARE). We find that, when using only one of the three available vignettes, or when the test is carried out separately by subgroups of respondents, the overidentifying restrictions are less likely to be rejected.
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  • Franco Peracchi & Claudio Rossetti, 2013. "The heterogeneous thresholds ordered response model: identification and inference," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 176(3), pages 703-722, June.
    • Handle: RePEc:bla:jorssa:v:176:y:2013:i:3:p:703-722
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    File URL: http://hdl.handle.net/10.1111/j.1467-985X.2012.01066.x
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    3. Daniel J. Benjamin & Kristen Cooper & Ori Heffetz & Miles S. Kimball, 2023. "From Happiness Data to Economic Conclusions," NBER Working Papers 31727, National Bureau of Economic Research, Inc.
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    5. Rachel J. Knott & Nicole Black & Bruce Hollingsworth & Paula K. Lorgelly, 2017. "Response to comment by robone: Practical advice for the implementation of anchoring vignettes," Health Economics, John Wiley & Sons, Ltd., vol. 26(3), pages 398-400, March.
    6. Silvana Robone, 2017. "Comment on ‘Response –scale heterogeneity in the EQ‐5D: Can we use vignettes to address response‐scale heterogeneity in the EQ‐5D? Not if but how’," Health Economics, John Wiley & Sons, Ltd., vol. 26(3), pages 395-397, March.
    7. Kaiser, Caspar, 2022. "Using memories to assess the intrapersonal comparability of wellbeing reports," Journal of Economic Behavior & Organization, Elsevier, vol. 193(C), pages 410-442.
    8. Andrew M. Jones; Nigel Rice, Silvana Robone; & Nigel Rice; & Silvana Robone:, 2012. "A comparison of parametric and non-parametric adjustments using vignettes for self-reported data," Health, Econometrics and Data Group (HEDG) Working Papers 12/10, HEDG, c/o Department of Economics, University of York.
    9. Bertoni, Marco, 2015. "Hungry today, unhappy tomorrow? Childhood hunger and subjective wellbeing later in life," Journal of Health Economics, Elsevier, vol. 40(C), pages 40-53.
    10. Carmelo León & Jorge Araña & Javier León, 2013. "Correcting for Scale Perception Bias in Measuring Corruption: an Application to Chile and Spain," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 114(3), pages 977-995, December.
    11. William H. Greene & Mark N. Harris & Rachel J. Knott & Nigel Rice, 2021. "Specification and testing of hierarchical ordered response models with anchoring vignettes," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(1), pages 31-64, January.
    12. Gianluca Fiorentini & Silvana Robone & Rossella Verzulli, 2018. "How do hospital‐specialty characteristics influence health system responsiveness? An empirical evaluation of in‐patient care in the Italian region of Emilia‐Romagna," Health Economics, John Wiley & Sons, Ltd., vol. 27(2), pages 266-281, February.
    13. Xu, Ke-Li, 2018. "A semi-nonparametric estimator of regression discontinuity design with discrete duration outcomes," Journal of Econometrics, Elsevier, vol. 206(1), pages 258-278.
    14. Knott, Rachel J. & Lorgelly, Paula K. & Black, Nicole & Hollingsworth, Bruce, 2017. "Differential item functioning in quality of life measurement: An analysis using anchoring vignettes," Social Science & Medicine, Elsevier, vol. 190(C), pages 247-255.
    15. Riccardo Di Francesco, 2023. "Ordered Correlation Forest," Papers 2309.08755, arXiv.org.
    16. Arthur van Soest & Hana Vonkova, 2014. "Testing the specification of parametric models by using anchoring vignettes," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 177(1), pages 115-133, January.

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