Many latent traits in the human sciences have a hierarchical structure. This study aimed to develop a new class of higher order item response theory models for hierarchical latent traits that are flexible in accommodating both dichotomous and polytomous items, to estimate both item and person parameters jointly, to allow users to specify…

Individuals routinely rate themselves higher than their peers on a number of attributes and capabilities, including their satisfaction with life. However, the construct validity of this above-average effect requires specific psychometric properties of ratings of one's contentment and ratings of others' perceived contentment. This article tests…

An item response model is proposed for the analysis of continuous response formats in an item response theory (IRT) framework. With such formats, respondents are asked to report their response as a mark on a fixed-length graphical segment whose ends are labeled with extreme responses. An interpolation process is proposed as the response mechanism…