This article examines the interdependency of two context effects that are known to occur regularly in large-scale assessments: item position effects and effects of test-taking effort on the probability of correctly answering an item. A microlongitudinal design was used to measure test-taking effort over the course of a large-scale assessment of 60 min. Two components of test-taking effort were investigated: initial effort and change in effort. Both components of test-taking effort significantly affected the probability to solve an item. In addition, it was found that participants’ current test-taking effort diminished considerably across the course of the test. Furthermore, a substantial linear position effect was found, which indicated that item difficulty increased during the test. This position effect varied considerably across persons. Concerning the interplay of position effects and test-taking effort, it was found that only the change in effort moderates the position effect and that persons differ with respect to this moderation effect. The consequences of these results concerning the reliability and validity of large-scale assessments are discussed.

Item position effects can seriously bias analyses in educational measurement, especially when multiple matrix sampling designs are deployed. In such designs, item position effects may easily occur if not explicitly controlled for. Still, in practice it usually turns out to be rather difficult—or even impossible—to completely control for effects due to the position of items. The objectives of this article are to show how item position effects can be modeled using the linear logistic test model with additional error term (LLTM +ε) in the framework of generalized linear mixed models (GLMMs), to explore in a simulation study how well the LLTM +ε holds the nominal Type I risk threshold, to conduct power analysis for this model, and to examine the sensitivity of the LLTM +ε to designs that are not completely balanced concerning item position. Overall, the LLTM +ε proved suitable for modeling item position effects when a balanced design is used. With decreasing balance, the model tends to be more conservative in the sense that true item position effects are more unlikely to be detected. Implications for linking and equating procedures which use common items are discussed.

Bayesian modeling using Markov chain Monte Carlo (MCMC) estimation requires researchers to decide not only whether estimation has converged but also whether the Bayesian estimates are well-approximated by summary statistics from the chain. On the contrary, software such as the Bayes module in Mplus, which helps researchers check whether convergence has been achieved by comparing the potential scale reduction (PSR) with a prespecified maximum PSR, the size of the MCMC error or, equivalently, the effective sample size (ESS), is not monitored. Zitzmann and Hecht (2019) proposed a method that can be used to check whether a minimum ESS has been reached in Mplus. In this article, we evaluated this method with a computer simulation. Specifically, we fit a multilevel structural equation model to a large number of simulated data sets and compared different prespecified minimum ESS values with the actual (empirical) ESS values. The empirical values were approximately equal to or larger than the prespecified minimum ones, thus indicating the validity of the method.

In order to measure the proficiency of person populations in various domains, large-scale assessments often use marginal maximum likelihood IRT models where person proficiency is modelled as a random variable. Thus, the model does not provide proficiency estimates for any single person. A popular approach to derive these proficiency estimates is the multiple imputation of plausible values (PV) to enable subsequent analyses on complete data sets. The main drawback is that all variables that are to be analyzed later have to be included in the imputation model to allow the distribution of plausible values to be conditional on these variables. These background variables (e.g., sex, age) have to be fully observed which is highly unlikely in practice. In several current large-scale assessment programs missing observations on background variables are dummy coded, and subsequently, dummy codes are used additionally in the PV imputation model. However, this approach is only appropriate for small proportions of missing data. Otherwise the resulting population scores may be biased.

Bayesian MCMC is a widely used model estimation technique, and software from the BUGS family, such as JAGS, have been popular for over two decades. Recently, Stan entered the market with promises of higher efficiency fueled by advanced and more sophisticated algorithms. With this study, we want to contribute empirical results to the discussion about the sampling efficiency of JAGS and Stan. We conducted three simulation studies in which we varied the number of warmup iterations, the prior informativeness, and sample sizes and employed the multi-level intercept-only model in the covariance- and mean-based and in the classic parametrization. The target outcome was MCMC efficiency measured as effective sample size per second (ESS/s). Based on our specific (and limited) study setup, we found that (1) MCMC efficiency is much higher for the covariance- and mean-based parametrization than for the classic parametrization, (2) Stan clearly outperforms JAGS when the covariance- and mean-based parametrization is used, and that (3) JAGS clearly outperforms Stan when the classic parametrization is used.

Combining items from an item pool into test forms (test assembly) is a frequent task in psychological and educational testing. Although efficient methods for automated test assembly exist, these are often unknown or unavailable to practitioners. In this paper we present the R package eatATA, which allows using several mixed-integer programming solvers for automated test assembly in R. We describe the general functionality and the common work flow of eatATA using a minimal example. We also provide four more elaborate use cases of automated test assembly: (a) The assembly of multiple test forms for a pilot study; (b) the assembly of blocks of items for a multiple matrix booklet design in the context of a large-scale assessment; (c) the assembly of two linear test forms for individual diagnostic purposes; (d) the assembly of multi-stage testing modules for individual diagnostic purposes. All use cases are accompanied with example item pools and commented R code.