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Multivariate mixed models accounting for don't know options in ordinal data.

Ralitza Gueorguieva1, Maria Iannario2

  • 1Department of Biostatistics, Yale School of Public Health, 300 George St, New Haven, 06511, Connecticut, United States.

Journal of the Royal Statistical Society. Series A, (Statistics in Society)
|January 9, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a new statistical model for analyzing survey data with "don't know" options. The model accurately captures response patterns and covariate effects in partially ordinal data, improving analysis of social and behavioral surveys.

Keywords:
Cumulative logit modelJoint modelingLocation scale modelLocation shift modelRandom effectsSemi-ordinal data

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Area of Science:

  • Social and Behavioral Sciences
  • Statistics
  • Survey Methodology

Background:

  • Multivariate ordinal data with heterogeneity and "don't know" options are common in surveys.
  • Standard models for ordinal or nominal data are inadequate for partially ordinal scales.
  • Ignoring "don't know" responses can lead to biased results.

Purpose of the Study:

  • To develop a statistical framework for jointly modeling "don't know" selections and ordinal ratings.
  • To address between-subject heterogeneity and response styles in survey data.
  • To provide a robust method for analyzing partially ordinal data in social and behavioral research.

Main Methods:

  • Proposed multivariate mixed-effects models to jointly analyze ordinal ratings and "don't know" choices.
  • Utilized likelihood-based inference for parameter estimation and model comparison.
  • Applied the models to case studies on financial risk perception and tobacco knowledge.

Main Results:

  • The proposed models effectively handle response heterogeneity and styles.
  • Demonstrated unbiased and efficient estimation of model parameters through simulation.
  • Case studies illustrated the practical application and interpretability of the approach.

Conclusions:

  • The developed models offer a flexible and robust solution for analyzing partially ordinal survey data.
  • This approach improves the reliability and accuracy of findings in social and behavioral surveys.
  • Facilitates a deeper understanding of complex response patterns, including the use of "don't know" options.