A Hierarchical Model for Accuracy and Choice on Standardized Tests

Certainty-Based Marking on Multiple-Choice Items: Psychometrics Meets Decision Theory

When a response to a multiple-choice item consists of selecting a single-best answer, it is not possible for examiners to differentiate between a response that is a product of knowledge and one that is largely a product of uncertainty. Certainty-based marking (CBM) is one testing format that requires examinees to express their degree of certainty on the response option they have selected, leading to an item score that depends both on the correctness of an answer and the certainty expressed. The expected score is maximized if examinees truthfully report their level of certainty. However, prospect theory states that people do not always make rational choices of the optimal outcome due to varying risk attitudes. By integrating a psychometric model and a decision-making perspective, the present study looks into the response behaviors of 334 first-year students of physiotherapy on six multiple-choice examinations with CBM in a case study. We used item response theory to model the objective probability of students giving a correct response to an item, and cumulative prospect theory to estimate their risk attitudes when students choose to report their certainty. The results showed that with the given CBM scoring matrix, students' choices of a certainty level were affected by their risk attitudes. Students were generally risk averse and loss averse when they had a high success probability on an item, leading to an under-reporting of their certainty. Meanwhile, they were risk seeking in case of small success probabilities on the items, resulting in the over-reporting of certainty.

Item Response Theory Modeling for Examinee-selected Items with Rater Effect

Some large-scale testing requires examinees to select and answer a fixed number of items from given items (e.g., select one out of the three items). Usually, they are constructed-response items that are marked by human raters. In this examinee-selected item (ESI) design, some examinees may benefit more than others from choosing easier items to answer, and so the missing data induced by the design become missing not at random (MNAR). Although item response theory (IRT) models have recently been developed to account for MNAR data in the ESI design, they do not consider the rater effect; thus, their utility is seriously restricted. In this study, two methods are developed: the first one is a new IRT model to account for both MNAR data and rater severity simultaneously, and the second one adapts conditional maximum likelihood estimation and pairwise estimation methods to the ESI design with the rater effect. A series of simulations was then conducted to compare their performance with those of conventional IRT models that ignored MNAR data or rater severity. The results indicated a good parameter recovery for the new model. The conditional maximum likelihood estimation and pairwise estimation methods were applicable when the Rasch models fit the data, but the conventional IRT models yielded biased parameter estimates. An empirical example was given to illustrate these new initiatives.