Co-occurring dominance and ideal point processes: A general IRTree framework for multidimensional item responding.

Responding to rating scale items is a multidimensional process, since not only the substantive trait being measured but also additional personal characteristics can affect the respondents' category choices. A flexible model class for analyzing such multidimensional responses are IRTree models, in which rating responses are decomposed into a sequence of sub-decisions. Different response processes can be involved in item responding both sequentially across those sub-decisions and as co-occurring processes within sub-decisions. In the previous literature, modeling co-occurring processes has been exclusively limited to dominance models, where higher trait levels are associated with higher expected scores. However, some response processes may rather follow an ideal point rationale, where the expected score depends on the proximity of a person's trait level to the item's location. Therefore, we propose a new multidimensional IRT model of co-occurring dominance and ideal point processes (DI-MIRT model) as a flexible framework for parameterizing IRTree sub-decisions with multiple dominance processes, multiple ideal point processes, and combinations of both. The DI-MIRT parameterization opens up new application areas for the IRTree model class and allows the specification of a wide range of theoretical assumptions regarding the cognitive processing of item responding. A simulation study shows that IRTree models with DI-MIRT parameterization provide excellent parameter recovery and accurately reflect co-occurring dominance and ideal point processes. In addition, a clear advantage over traditional IRTree models with purely sequential processes is demonstrated. Two application examples from the field of response style analysis highlight the benefits of the general IRTree framework under real-world conditions.