For instance, the models proposed by De Boeck and Partchev ( 2012) do not allow for trees with more than two branches and rely on one-parameter logistic models, while Bockenholt ( 2012) is based on one-parameter probit models. These prior approaches, however, have some limitations. submitted) are some of the examples of how item response tree models have been utilized.
It should be noted that in the current practice of item analysis, the differences between various response/test formats are usually ignored and the responses are analyzed as if they were interval scale data or ordinal scale data (e.g., using ordinal factor/IRT models).ĭifferentiating slow and fast intelligence (Partchev and De Boeck 2012), modeling motivated misreports to sensitive survey questions (Boeckenholt 2013), examining content and response styles in multiple-choice items (Plieninger and Meiser 2014), and modeling skipped and non-reached item responses (Debeer et al. To describe Likert scales with a middle response category (e.g., ‘neither sad nor joyful’, ‘perhaps’, ‘not sure’, ‘undecided’, ‘?’, etc.), Tree (c) can be used where the first outcome 1 represents the undecided (middle) category while Categories 2 to 4 represent regular response categories. 1 can be used to describe a unipolar scale that includes choices such as ‘not at all sad’, ‘slightly sad’, ‘mostly sad’, and ‘completely sad’ while Tree (b) is utilized to describe a bipolar scale with options such as ‘completely sad’, ‘somewhat sad’, ‘somewhat joyful’, and ‘completely joyful’. Item response trees can also be utilized to describe distinctive features of item response categories.
Trees (a) and (b) are ‘binary’ trees because they involve a choice between two branches, whereas Trees (c) and (d) are ‘polytomous’ trees in that more than two branches are involved. Trees (c) and (d) can be seen as a combination of linear and nested trees. Tree (a) is denoted as a ‘linear’ tree in that at least one branch from each internal node leads to a terminal node, whereas Tree (b) is denoted as a ‘nested’ tree since branches from an internal node lead to another internal node. The selection between 3 and 4 involves a second decision.
In Tree (d), Categories 1 and 2 are two qualitatively distinct options, which are also differentiated from Categories 3 and 4. In Tree (c), the selection of Category 1 is qualitatively differentiated from the other three Categories (2, 3, and 4) and not choosing Category 1 requires a follow-up decision. Tree (a) represents a sequential selection of the response in order from Categories 1 to 4, while Tree (b) describes a two-stage selection process where a group of two adjacent categories is first chosen (either Categories 1 and 2 or Categories 3 and 4) and then the final answer is selected within the pair of adjacent categories. In a tree structure, circles represent nodes, arrows represent branches, and leaves are item response outcomes (1 to 4). The model will be referred to as an item response tree model due to its utilization of the tree structure (e.g., Boeckenholt, 2012 De Boeck and Partchev, 2012).įigure 1 illustrates four tree structures that can be used to represent different cognitive processes for an item with four response categories (numbered from 1 to 4). The leaves are the terminal nodes that represent the observed categorical item responses. The tree continues to diverge through branches until it reaches leaves. The model can describe a postulated internal decision process with a tree structure, which is composed of sub-trees and their corresponding internal nodes and branches. In this study, we are concerned with a new type of IRT model that focuses not only on the outcome but also on the internal cognitive or psychological decision process. Mathematically, the probability of selecting a particular response category can be explained as a function of the person’s latent trait and the item’s properties. IRT models focus on understanding the terminal outcome of a person’s choice among several discrete options.
Item response theory (IRT) models are widely used tools for analyzing categorical item responses in psychological and behavioral assessments.