Diagnostic Classification Models for a Mixture of Ordered and Non-ordered Response Options in Rating Scales

When developing ordinal rating scales, we may include potentially unordered response options such as "Neither Agree nor Disagree," "Neutral," "Don't Know," "No Opinion," or "Hard to Say." To handle responses to a mixture of ordered and unordered options, Huggins-Manley et al. (2018) proposed a class of semi-ordered models under the unidimensional item response theory framework. This study extends the concept of semi-ordered models into the area of diagnostic classification models. Specifically, we propose a flexible framework of semi-ordered DCMs that accommodates most earlier DCMs and allows for analyzing the relationship between those potentially unordered responses and the measured traits. Results from an operational study and two simulation studies show that the proposed framework can incorporate both ordered and non-ordered responses into the estimation of the latent traits and thus provide useful information about both the items and the respondents.