Modeling “don't know” responses in rating scales

We propose a probabilistic framework for the treatment of ``don't know'' responses in surveys aimed at investigating human perceptions through expressed ratings. The rationale behind the proposal is that ``don't know'' is a valid response to all extents because it informs about a specific state of mind of the respondent, and therefore, it is not correct to treat it as a missing value, as it is usually treated. The actual insightfulness of the proposed model depends on the chosen probability distributions. The required assumptions of these distributions first pertain to the expressed ratings and then to the state of mind of ``don't know'' respondents toward the ratings. Regarding the former, we worked in the CUB model framework, while for the latter, we proposed using the Uniform distribution for formal and empirical reasons. We show that these two choices provide a solution that is both tractable and easy to interpret, where ``don't know'' responses can be taken into account by simply adjusting one parameter in the model.