This paper proposes an extension of linear equating that may be useful in one of two fairly common assessment scenarios. One is where different students have taken different combinations of test forms. This might occur, for example, where students have some free choice over the exam papers they take within a particular qualification. In this…

Item parameter estimation using an item response theory (IRT) model with fixed ability estimates is useful in equating with small samples on anchor items. The current study explores the impact of three ability estimation methods (weighted likelihood estimation [WLE], maximum a posteriori [MAP], and posterior ability distribution estimation [PST])…

An interval estimation procedure is discussed that can be used to evaluate the probability of a particular response for a binary or binary scored item at a pre-specified point along an underlying latent continuum. The item is assumed to: (a) be part of a unidimensional multi-component measuring instrument that may contain also polytomous items,…

The last series of Raven's standard progressive matrices (SPM-LS) test was studied with respect to its psychometric properties in a series of recent papers. In this paper, the SPM-LS dataset is analyzed with regularized latent class models (RLCMs). For dichotomous item response data, an alternative estimation approach based on fused regularization…

Rasch common-item equating is often used in high-stakes testing to maintain equivalent passing standards across test administrations. If unaddressed, item parameter drift poses a major threat to the accuracy of Rasch common-item equating. We compared the performance of well-established and newly developed drift detection methods in small and large…

Simulations concerning the distributional assumptions of coefficient alpha are contradictory. To provide a more principled theoretical framework, this article relies on the Fréchet-Hoeffding bounds, in order to showcase that the distribution of the items play a role on the estimation of correlations and covariances. More specifically, these bounds…

Among all, Cronbach's Alpha and McDonald's Omega are commonly used for reliability estimations. The alpha uses inter-item correlations while omega is based on a factor analysis result. This study uses simulated ordinal data sets to test whether the alpha and omega produce different estimates. Their performances were compared according to the…

In applications of item response theory (IRT) models, it is known that empirical violations of the local independence (LI) assumption can significantly bias parameter estimates. To address this issue, we propose a threshold-autoregressive item response theory (TAR-IRT) model that additionally accounts for order dependence among the item responses…

The present study proposes a Bayesian approach for estimating and testing the operation-specific learning model, a variant of the linear logistic test model that allows for the measurement of the learning that occurs during a test as a result of the repeated use of the operations involved in the items. The advantages of using a Bayesian framework…

This Monte Carlo study assessed Type I error in differential item functioning analyses using Lord's chi-square (LC), Likelihood Ratio Test (LRT), and Mantel-Haenszel (MH) procedure. Two research interests were investigated: item response theory (IRT) model specification in LC and the LRT and continuity correction in the MH procedure. This study…

Kelley's Discrimination Index (DI) is a simple and robust, classical non-parametric short-cut to estimate the item discrimination power (IDP) in the practical educational settings. Unlike item-total correlation, DI can reach the ultimate values of +1 and -1, and it is stable against the outliers. Because of the computational easiness, DI is…

Decades of research has shown that spacing practice trials over time can improve later memory, but there are few concrete recommendations concerning how to optimally space practice. We show that existing recommendations are inherently suboptimal due to their insensitivity to time costs and individual- and item-level differences. We introduce an…

Decades of research has shown that spacing practice trials over time can improve later memory, but there are few concrete recommendations concerning how to optimally space practice. We show that existing recommendations are inherently suboptimal due to their insensitivity to time costs and individual- and item-level differences. We introduce an…

In applications of item response theory (IRT), fixed parameter calibration (FPC) has been used to estimate the item parameters of a new test form on the existing ability scale of an item pool. The present paper presents an application of FPC to multiple examinee groups test data that are linked to the item pool via anchor items, and investigates…

Mplus is a powerful latent variable modeling software program that has become an increasingly popular choice for fitting complex item response theory models. In this short note, we demonstrate that the two-parameter logistic testlet model can be estimated as a constrained bifactor model in Mplus with three estimators encompassing limited- and…