On-line item generation is becoming increasingly feasible for many cognitive tests. Item generation seemingly conflicts with the well established principle of measuring persons from items with known psychometric properties. This paper examines psychometric principles and models required for measurement from on-line item generation. Three psychometric issues are elaborated for item generation. First, design principles to generate items are considered. A cognitive design system approach is elaborated and then illustrated with an application to a test of abstract reasoning. Second, psychometric models for calibrating generating principles, rather than specific items, are required. Existing item response theory (IRT) models are reviewed and a new IRT model that includes the impact on item discrimination, as well as difficulty, is developed. Third, the impact of item parameter uncertainty on person estimates is considered. Results from both fixed content and adaptive testing are presented.

Various different item response theory (IRT) models can be used in educational and psychological measurement to analyze test data. One of the major drawbacks of these models is that efficient parameter estimation can only be achieved with very large data sets. Therefore, it is often worthwhile to search for designs of the test data that in some way will optimize the parameter estimates. The results from the statistical theory on optimal design can be applied for efficient estimation of the parameters.

A major problem in finding an optimal design for IRT models is that the designs are only optimal for a given set of parameters, that is, they are locally optimal. Locally optimal designs can be constructed with a sequential design procedure. In this paper minimax designs are proposed for IRT models to overcome the problem of local optimality. Minimax designs are compared to sequentially constructed designs for the two parameter logistic model and the results show that minimax design can be nearly as efficient as sequentially constructed designs.

Computerized assessment provides rich multidimensional data including trial-by-trial accuracy and response time (RT) measures. A key question in modeling this type of data is how to incorporate RT data, for example, in aid of ability estimation in item response theory (IRT) models. To address this, we propose a joint model consisting of a two-parameter IRT model for the dichotomous item response data, a log-normal model for the continuous RT data, and a normal model for corresponding paper-and-pencil scores. Then, we reformulate and reparameterize the model to capture the relationship between the model parameters, to facilitate the prior specification, and to make the Bayesian computation more efficient. Further, we propose several new model assessment criteria based on the decomposition of deviance information criterion (DIC) the logarithm of the pseudo-marginal likelihood (LPML). The proposed criteria can quantify the improvement in the fit of one part of the multidimensional data given the other parts. Finally, we have conducted several simulation studies to examine the empirical performance of the proposed model assessment criteria and have illustrated the application of these criteria using a real dataset from a computerized educational assessment program.

In a broad class of item response theory (IRT) models for dichotomous items the unweighted total score has monotone likelihood ratio (MLR) in the latent trait θ. In this study, it is shown that for polytomous items MLR holds for the partial credit model and a trivial generalization of this model. MLR does not necessarily hold if the slopes of the item step response functions vary over items, item steps, or both. MLR holds neither for Samejima's graded response model, nor for nonparametric versions of these three polytomous models. These results are surprising in the context of Grayson's and Huynh's results on MLR for nonparametric dichotomous IRT models, and suggest that establishing stochastic ordering properties for nonparametric polytomous IRT models will be much harder.

Cognitive theories disagree about the processes and the number of abilities involved in transitive reasoning. This led to controversies about the influence of task characteristics on individuals' performance and the development of transitive reasoning. In this study, a computer test was constructed containing 16 transitive reasoning tasks having different characteristics with respect to presentation form, task format, and task content. Both product and strategy information were analyzed to measure the performance of 6- to 13-year-old children. Three methods (MSP, DETECT, and Improved DIMTEST) were used to determine the number of abilities involved and to test the assumptions imposed on the data by item response models. Nonparametric IRT models were used to construct a scale for transitive reasoning. Multiple regression was used to determine the influence of task characteristics on the difficulty level of the tasks. It was concluded that: (1) the qualitatively distinct abilities predicted by Piaget's theory could not be distinguished by means of different dimensions in the data structure; (2) transitive reasoning could be described by one ability, and some task characteristics influenced the difficulty of a task; and (3) strategy information provided a stronger scale than product information.

Using the well-known strategy in which parameters are linked to the sampling distribution via an identification analysis, we offer an interpretation of the item parameters in the one-parameter logistic with guessing model (1PL-G) and the nested Rasch model. The interpretations are based on measures of informativeness that are defined in terms of odds of correctly answering the items. It is shown that the interpretation of what is called the difficulty parameter in the random-effects 1PL-G model differs from that of the item parameter in a random-effects Rasch model. It is also shown that the traditional interpretation of the guessing parameter in the 1PL-G model changes, depending on whether fixed-effects or random-effects versions of both models are considered.

In latent scaling applications, such as the positioning of political parties, differential item functioning (DIF) may occur because of measurement issues or because of substantive differences in the association between latent and manifest variables. While the first source of DIF has received considerable attention, the second has not, although it is of potential interest to comparative scholars. In this research note, we introduce a novel hierarchical Bayesian item response model that allows us to disentangle different sources of DIF. Drawing on the 2019 Chapel Hill Expert Survey (CHES), we highlight how the same issues are unequally politicized across Western Europe, and how some issues are less ideologically determined than others. Our model can be adapted to alternate settings, allowing researchers to shine a light on variation in, e.g., ideology, issue politicization, or party competition.

Data sets quantifying phenomena of social-scientific interest often use multiple experts to code latent concepts. While it remains standard practice to report the average score across experts, experts likely vary in both their expertise and their interpretation of question scales. As a result, the mean may be an inaccurate statistic. Item-response theory (IRT) models provide an intuitive method for taking these forms of expert disagreement into account when aggregating ordinal ratings produced by experts, but they have rarely been applied to cross-national expert-coded panel data. We investigate the utility of IRT models for aggregating expert-coded data by comparing the performance of various IRT models to the standard practice of reporting average expert codes, using both data from the V-Dem data set and ecologically motivated simulated data. We find that IRT approaches outperform simple averages when experts vary in reliability and exhibit differential item functioning (DIF). IRT models are also generally robust even in the absence of simulated DIF or varying expert reliability. Our findings suggest that producers of cross-national data sets should adopt IRT techniques to aggregate expert-coded data measuring latent concepts.