Unfolding item response theory (IRT) models are important alternatives to dominance IRT models in describing the response processes on self-report tests. Their usage is common in personality measures, since they indicate potential differentiations in test score interpretation. This paper aims to gain a better insight into the structure of trait personality, by investigating whether the dominance or alternatively the unfolding IRT model are better descriptors of the response processes on a personality measure constructed under the dominance response theorem. For the assessment of the dominant model, the Graded Response Model (GRM) is used; while for the unfolding model, the Generalized Graded Unfolding Model (GGUM) was examined. All analyses are conducted with the freely available R. A sample of 1340 Greek adults, employed in private and public organizations, fulfilled the Trait Personality Questionnaire 5 short-form (TPQue5). Findings contradict previous research on trait personality. In accordance to the construction method employed, the TPQue5 items are best understood by monotonically increasing item response functions (IRFs). Individuals responding to the TPQue5 increase their probability of endorsing its items as their trait level increases; this stands for all personality dimensions, although Openness to Experience exhibited mixed type of item response patterns. Further research directions, implications and limitations are also discussed.