Estimating the joint item-score density using an unrestricted latent class model: advancing flexibility in computerized adaptive testing

Computerized adaptive testing (CAT) reduces cognitive fatigue and response burden while maintaining measurement precision by administering items tailored to the respondent. However, the assumptions of item response theory models—commonly used inCAT—might be too stringent for some tests. This study investigated the bias and accuracy of a flexible CAT procedure, called LSCAT (for latent-class sum-score CAT).In the calibration phase, an unrestricted latent class model estimates the joint item-score density (𝛑𝛑) and the total-score density (𝛑𝛑+); in the operational phase, the respondents’expected total scores are estimated. The paper’s first study indicated that using theBayesian information criterion (BIC) to determine the number of latent classes produced the most accurate estimates of 𝛑𝛑and𝛑𝛑+. The second study showed that the unrestricted latent class model more accurately estimated 𝛑𝛑and 𝛑𝛑+ than the two-parameter logisticmodel, especially under a complex data-generating mechanism. As a proof of concept, thethird study compared the precision of LSCAT and a traditional CAT procedure using thetwo-parameter logistic model with a single empirical dataset. The two CAT procedureswere approximately equally precise. Although the two procedures had the same fixed efficiency, LSCAT was more efficient for the high- and low-scoring respondents, whiletraditional CAT was more efficient for respondents in the middle.