Building Adaptive Assessments for Psychological Assessments with Bounded-Continuous Response Formats

This paper introduces a Beta-Bernoulli mixture item response model (BBM-IRT) for bounded-continuous items such as those often utilized in continuous rating scales and slider-bar assessments. These item types are commonly used in psychological research but, to date, these assessments have primarily been utilized in fixed-length situations, where the same set of items are administered to all respondents, and have not been utilized within an adaptive testing framework. An adaptive testing framework offers several benefits, including the ability to obtain higher quality measurement precision with fewer items as items are targeted and administered based on the respondent’s previous responses. In addition to introducing the BBM-IRT model, this work also explores the use of the model within an adaptive testing framework. In particular, the item and test information functions – a component necessary for building adaptive assessments – is derived and presented in closed form. Through a series of simulation studies, we provide empirical evidence that it is possible to create adaptive assessments for bounded-continuous item types. An application with real data is also provided showing how the BBM-IRT model can be utilized in practical assessment situations.