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Comparing flexible modelling approaches: the varying-thresholds model versus quantile regression

Author

Listed:
  • Niccolò Ducci

    (Agenzia delle Entrate)

  • Leonardo Grilli

    (Department of Statistics, Computer Science, Applications “Giuseppe Parenti” (DISIA))

  • Marta Pittavino

    (University of Venice)

Abstract

The varying-thresholds model (VTM) is a novel methodology proposed by Tutz ( Flexible predictive distributions from varying-thresholds modelling. https://doi.org/10.48550/arXiv.2103.13324 , arXiv:2103.13324 2021) capable of estimating the whole conditional distribution of a response variable in a regression setting. It can be used for continuous, ordinal and count responses. In this study, conditional quantiles and prediction intervals estimated through VTM are compared with those of quantile regression. The comparison is based on a set of data-generating models to assess the performance of the two methodologies regarding the coverage and width of prediction intervals. The simulation study encompasses settings with several functional forms and types of errors. In addition, a discrete version of the continuous ranked probability score is proposed as a tool to choose the best link function for the binary models used in the fitting of VTM. In summary, the varying-thresholds model is a flexible methodology that can be broadly applied with light assumptions; it is advantageous over quantile regression when the conditional quantile function is misspecified.

Suggested Citation

  • Niccolò Ducci & Leonardo Grilli & Marta Pittavino, 2025. "Comparing flexible modelling approaches: the varying-thresholds model versus quantile regression," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 19(2), pages 493-514, June.
    • Handle: RePEc:spr:advdac:v:19:y:2025:i:2:d:10.1007_s11634-025-00635-8
    DOI: 10.1007/s11634-025-00635-8
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    References listed on IDEAS

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    1. Roger Koenker, 2017. "Quantile Regression: 40 Years On," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 155-176, September.
    2. Gerhard Tutz, 2022. "Item Response Thresholds Models: A General Class of Models for Varying Types of Items," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1238-1269, December.
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    4. Roger Koenker, 2017. "Quantile regression 40 years on," CeMMAP working papers CWP36/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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