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

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.