Accurate item calibration in models of item response theory (IRT) requires rather large samples. For instance, [Formula: see text] respondents are typically recommended for the two-parameter logistic (2PL) model. Hence, this model is considered a large-scale application, and its use in small-sample contexts is limited. Hierarchical Bayesian approaches are frequently proposed to reduce the sample size requirements of the 2PL. This study compared the small-sample performance of an optimized Bayesian hierarchical 2PL (H2PL) model to its standard inverse Wishart specification, its nonhierarchical counterpart, and both unweighted and weighted least squares estimators (ULSMV and WLSMV) in terms of sampling efficiency and accuracy of estimation of the item parameters and their variance components. To alleviate shortcomings of hierarchical models, the optimized H2PL (a) was reparametrized to simplify the sampling process, (b) a strategy was used to separate item parameter covariances and their variance components, and (c) the variance components were given Cauchy and exponential hyperprior distributions. Results show that when combining these elements in the optimized H2PL, accurate item parameter estimates and trait scores are obtained even in sample sizes as small as [Formula: see text]. This indicates that the 2PL can also be applied to smaller sample sizes encountered in practice. The results of this study are discussed in the context of a recently proposed multiple imputation method to account for item calibration error in trait estimation.

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A new response time-based method for coding omitted item responses in computer-based testing is introduced and illustrated with empirical data. The new method is derived from the theory of missing data problems of Rubin and colleagues and embedded in an item response theory framework. Its basic idea is using item response times to statistically test for each individual item whether omitted responses are missing completely at random (MCAR) or missing due to a lack of ability and thus not at random (MNAR) with fixed type-1 and type-2 error levels. If the MCAR hypothesis is maintained, omitted responses are coded as not administered (NA), and as incorrect (0) otherwise. The empirical illustration draws from the responses given by = 766 students to 70 items of a computer-based ICT-skills test. The new method is compared with the two common deterministic methods of scoring omitted responses as 0 or as NA. In result, response time thresholds from 18 to 58 seconds were identified. With 61 %, more omitted responses were recoded into 0 than into NA (39 %). The differences in difficulty were larger when the new method was compared to deterministically scoring omitted responses as NA compared to scoring omitted responses as 0. The variances and reliabilities obtained under the three methods showed small differences. The paper concludes with a discussion of the practical relevance of the observed effect sizes, and with recommendations for the practical use of the new method as a method to be applied in the early stage of data processing.