Joint Model of a Zero-One Inflated Continuous Item Response Theory Model and a Lognormal Response Time Model for Ability Measurement Using Bounded Continuous Responses and Response Times

Performance tests and computer-based testing increasingly yield continuous responses and rich process data,including response time. However, standard item response theory (IRT) analyses often discretize responses and ignoretime, undermining reliability when the number of items in a test is limited. We thus propose a joint IRT model thatleverages bounded continuous responses and response times to improve the reliability of ability measurement. Concretely,the proposed model integrates a zero-one-inflated beta continuous-response model with a log-normal modelfor response times through correlated latent traits for ability and response speed. This model structure enables abilityestimation that utilizes response time as auxiliary data while preserving continuous responses without informationloss due to discretization. We assess the performance of the proposed model through simulation experiments anda real-data application. Results show consistent gains in reliability over (i) a joint response-time model using discretizedresponses and (ii) continuous-response IRT without time, with the greatest benefits observed when the latenttraits for ability and speed are highly correlated.