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

Multivariate ordinal data characterised by between-subject heterogeneity or different response styles are prevalent in surveys and other observational studies. It is especially common in surveys designed to assess individual perceptions or knowledge to include a 'don't know' option on some or all survey questions. The latter makes the scales partially ordinal, which precludes the use of well-established models for ordinal data, whereas models for nominal data are inefficient and difficult to interpret. Ignoring the 'don't know' options may introduce bias as the subset of individuals who choose to provide ratings may not be representative of the population of interest. The suggested solution in this manuscript involves jointly modeling the selection of 'don't know' options and the ordinal ratings on multiple variables. The proposed multivariate mixed models are flexible, allow for heterogeneity in responses, response styles, and assessment of the effects of covariates on the ordinal ratings and on choosing the 'don't know' options. Likelihood-based inference and model comparisons are performed. Two case studies: one on financial risk perceptions and one on knowledge about the addictiveness of tobacco products are used for motivation and illustration. A simulation demonstrates that the proposed approach yields unbiased and efficient estimates. The results are straightforward to interpret, effectively capturing the complexity inherent in the data. This makes the proposed models particularly well-suited for analyzing partially ordinal ratings in social and behavioral surveys, providing a robust and reliable framework for such contexts.