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A shadow-test approach to the calibration of field-test items embedded in adaptive testing is presented. The objective function used in the shadow-test model selects both the operational and field-test items adaptively using a Bayesian version of the criterion of [Formula: see text]-optimality. The constraint set for the model can be used to hide the field-test items completely in the content of the test as well as to deal with such practical issues as random control of their exposure rates. The approach runs on efficient implementations of the Gibbs sampler for the real-time updating of the ability and field-test parameters. Optimal settings for the proposed algorithms were found and used to demonstrate item calibration with smaller than traditional sample sizes in runtimes fully comparable with conventional adaptive testing.

Parameter recovery and item utilization were investigated for different designs for online test item calibration. The design was adaptive in a double sense: it assumed both adaptive testing of examinees from an operational pool of previously calibrated items and adaptive assignment of field-test items to the examinees. Four criteria of optimality for the assignment of the field-test items were used, each of them based on the information in the posterior distributions of the examinee's ability parameter during adaptive testing as well as the sequentially updated posterior distributions of the field-test item parameters. In addition, different stopping rules based on target values for the posterior standard deviations of the field-test parameters and the size of the calibration sample were used. The impact of each of the criteria and stopping rules on the statistical efficiency of the estimates of the field-test parameters and on the time spent by the items in the calibration procedure was investigated. Recommendations as to the practical use of the designs are given.

An optimal adaptive design for test-item calibration based on Bayesian optimality criteria is presented. The design adapts the choice of field-test items to the examinees taking an operational adaptive test using both the information in the posterior distributions of their ability parameters and the current posterior distributions of the field-test parameters. Different criteria of optimality based on the two types of posterior distributions are possible. The design can be implemented using an MCMC scheme with alternating stages of sampling from the posterior distributions of the test takers' ability parameters and the parameters of the field-test items while reusing samples from earlier posterior distributions of the other parameters. Results from a simulation study demonstrated the feasibility of the proposed MCMC implementation for operational item calibration. A comparison of performances for different optimality criteria showed faster calibration of substantial numbers of items for the criterion of D-optimality relative to A-optimality, a special case of c-optimality, and random assignment of items to the test takers.

Educational politics never ceased to interest Don, and a few months before his passing away, he completed a book manuscript with all his reflections on a history of the developments during his academic career (Mellenbergh, in preparation). Gideon Jan Mellenbergh (known as Don to his friends and colleagues) was born in Amsterdam on August 9, 1938, and passed away in the same city on March 27, 2021. Van Naerssen influenced Don's thinking greatly, and Don would commemorate his ideas and contributions often in conversation. With Herman Adér, Don developed and taught the first courses on this topic, and wrote a book to be used in education of methodologists (Adér & Mellenbergh, [1]). [Extracted from the article]

Purpose: Most computerized adaptive testing (CAT) applications in patient-reported outcomes (PRO) measurement to date are reliability-centric, with a primary objective of maximizing measurement efficiency. A key concern and a potential threat to validity is that, when left unconstrained, individual CAT administrations could have items with systematically different attributes, e.g., sub-domain coverage. This paper aims to provide a solution to the problem from an optimal test design framework using the shadow-test approach to CAT.Methods: Following the approach, a case study was conducted using the PROMIS® (Patient-Reported Outcomes Measurement Information System) fatigue item bank both with empirical and simulated response data. Comparisons between CAT administrations without and with the enforcement of content and item pool usage constraints were examined.Results: The unconstrained CAT exhibited a high degree of variation in items selected from different substrata of the item bank. Contrastingly, the shadow-test approach delivered CAT administrations conforming to all specifications with a minimal loss in measurement efficiency.Conclusions: The optimal test design and shadow-test approach to CAT provide a flexible framework for solving complex test-assembly problems with better control of their domain coverage than for the conventional use of CAT in PRO measurement. Applications in a wide array of PRO domains are expected to lead to more controlled and balanced use of CAT in the field. [ABSTRACT FROM AUTHOR]

We present a novel application of a generalized item response tree model to investigate test takers’ answer change behavior. The model allows us to simultaneously model the observed patterns of the initial and final responses after an answer change as a function of a set of latent traits and item parameters. The proposed application is illustrated with large-scale mathematics test items. We also describe how the estimated results can be used to study the benefits of answer change and to further detect potential academic cheating. [ABSTRACT FROM AUTHOR]

According to a popular belief, test takers should trust their initial instinct and retain their initial responses when they have the opportunity to review test items. More than 80 years of empirical research on item review, however, has contradicted this belief and shown minor but consistently positive score gains for test takers who changed answers they found to be incorrect during review. This study reanalyzed the problem of the benefits of answer changes using item response theory modeling of the probability of an answer change as a function of the test taker's ability level and the properties of items. Our empirical results support the popular belief and reveal substantial losses due to changing initial responses for all ability levels. Both the contradiction of the earlier research and support of the popular belief are explained as a manifestation of Simpson's paradox in statistics. [ABSTRACT FROM AUTHOR]

Hierarchical modeling of responses and response times on test items facilitates the use of response times as collateral information in the estimation of the response parameters. In addition to the regular information in the response data, two sources of collateral information are identified: (a) the joint information in the responses and the response times summarized in the estimates of the second-level parameters and (b) the information in the posterior distribution of the response parameters given the response times. The latter is shown to be a natural empirical prior distribution for the estimation of the response parameters. Unlike traditional hierarchical item response theory (IRT) modeling, where the gain in estimation accuracy is typically paid for by an increase in bias, use of this posterior predictive distribution improves both the accuracy and the bias of IRT parameter estimates. In an empirical study, the improvements are demonstrated for the estimation of the person and item parameters in a three-parameter response model. [ABSTRACT FROM AUTHOR]

Several criteria from the optimal design literature are examined for use with item selection in multidimensional adaptive testing. In particular, it is examined what criteria are appropriate for adaptive testing in which all abilities are intentional, some should be considered as a nuisance, or the interest is in the testing of a composite of the abilities. Both the theoretical analyses and the studies of simulated data in this paper suggest that the criteria of A-optimality and D-optimality lead to the most accurate estimates when all abilities are intentional, with the former slightly outperforming the latter. The criterion of E-optimality showed occasional erratic behavior for this case of adaptive testing, and its use is not recommended. If some of the abilities are nuisances, application of the criterion of As-optimality (or Ds-optimality), which focuses on the subset of intentional abilities is recommended. For the measurement of a linear combination of abilities, the criterion of c-optimality yielded the best results. The preferences of each of these criteria for items with specific patterns of parameter values was also assessed. It was found that the criteria differed mainly in their preferences of items with different patterns of values for their discrimination parameters. [ABSTRACT FROM AUTHOR]

Current modeling of response times on test items has been strongly influenced by the paradigm of experimental reaction-time research in psychology. For instance, some of the models have a parameter structure that was chosen to represent a speed-accuracy tradeoff, while others equate speed directly with response time. Also, several response-time models seem to be unclear as to the level of parametrization they represent. A hierarchical framework for modeling speed and accuracy on test items is presented as an alternative to these models. The framework allows a "plug-and-play approach" with alternative choices of models for the response and response-time distributions as well as the distributions of their parameters. Bayesian treatment of the framework with Markov chain Monte Carlo (MCMC) computation facilitates the approach. Use of the framework is illustrated for the choice of a normal-ogive response model, a lognormal model for the response times, and multivariate normal models for their parameters with Gibbs sampling from the joint posterior distribution. [ABSTRACT FROM AUTHOR]

Two local methods for observed-score equating are applied to the problem of equating an adaptive test to a linear test. In an empirical study, the methods were evaluated against a method based on the test characteristic function (TCF) of the linear test and traditional equipercentile equating applied to the ability estimates on the adaptive test for a population of test takers. The two local methods were generally best. Surprisingly, the TCF method performed slightly worse than the equipercentile method. Both methods showed strong bias and uniformly large inaccuracy, but the TCF method suffered from extra error due to the lower asymptote of the test characteristic function. It is argued that the worse performances of the two methods are a consequence of the fact that they use a single equating transformation for an entire population of test takers and therefore have to compromise between the individual score distributions. [ABSTRACT FROM AUTHOR]

A statistical test for detecting answer copying on multiple-choice tests based on Cohen's kappa is proposed. The test is free of any assumptions on the response processes of the examinees suspected of copying and having served as the source, except for the usual assumption that these processes are probabilistic. Because the asymptotic null and alternative distributions of the kappa statistic are derived under the assumption of common marginal probabilities for all items, a recoding of the item alternatives is proposed to approximate this case. The results from a simulation study in this article show that under this recoding, the test approximates its nominal Type I error rates and has promising power functions [ABSTRACT FROM AUTHOR]

Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of test takers on one version of the test to make them indistinguishable from those on another, equating error should be defined as the degree to which the equated scores realize this goal. Two equivalent definitions of equating error based on this criterion are formulated. It is shown how these definitions allow one to evaluate such key quantities as the bias and mean squared error of any equating method if the tests fit a unidimensional response model. Several alternative applications of the ideas for the case in which the tests do not fit a unidimensional response model are discussed [ABSTRACT FROM AUTHOR]

In test assembly, a fundamental difference exists between algorithms that select a test sequentially or simultaneously. Sequential assembly allows us to optimize an objective function at the examinee's ability estimate, such as the test information function in computerized adaptive testing. But it leads to the non-trivial problem of how to realize a set of content constraints on the test—a problem more naturally solved by a simultaneous item-selection method. Three main item-selection methods in adaptive testing offer solutions to this dilemma. The spiraling method moves item selection across categories of items in the pool proportionally to the numbers needed from them. Item selection by the weighted-deviations method (WDM) and the shadow test approach (STA) is based on projections of the future consequences of selecting an item. These two methods differ in that the former calculates a projection of a weighted sum of the attributes of the eventual test and the latter a projection of the test itself. The pros and cons of these methods are analyzed. An empirical comparison between the WDM and STA was conducted for an adaptive version of the Law School Admission Test (LSAT), which showed equally good item-exposure rates but violations of some of the constraints and larger bias and inaccuracy of the ability estimator for the WDM. [ABSTRACT FROM AUTHOR]

A popular design in large-scale educational assessments as well as any other type of survey is the balanced incomplete block design. The design is based on an item pool split into a set of blocks of items that are assigned to sets of "assessment booklets." This article shows how the problem of calculating an optimal balanced incomplete block design can be formulated as a problem in combinational optimization. Several examples of structural and practical requirements for balanced incomplete block designs are shown to be linear constraints on the optimization problem. In addition, a variety of possible objective functions to optimize the design is discussed. The technique is demonstrated using the 1996 Grade 8 Mathematics National Assessment of Educational Progress (NAEP) as a case study. [ABSTRACT FROM AUTHOR]

Presents a linear programming-based method to stratify an item pool optimally for use in α-stratified adaptive testing. Description of the item pool in stratified approach; Factors needed for the successful implementation of the stratified method; Formulation of the method.

Proposes the use of item cloning technique to increase the number of items available for computerized adaptive testing. Function of the item response theory model in dealing with the consequence of item cloning; Stages of the item-selection procedure; Types of parent items.

Presents a study that evaluated the methods of alpha-stratified adaptive testing and constrained adaptive testing with shadow tests. Application of the shadow test approach which allows the implementation of any type of constraint on item selection in alpha-stratified adaptive testing; Examination of a set of constraints that can be used in any application of the shadow test; Assessment of a Law School Admission Test in order to determine the advantage of the shadow test.

Presents a study that proposed a procedure for empirical initialization of the trait estimator in adaptive testing. Application of item response theory in adaptive testing; Use of collateral data to initialize a computerized adaptive testing; Models and procedure used in the study.

Dichotomous IRT models can be viewed as families of stochastically ordered distributions of responses to test items. This paper explores several properties of such distributions. In particular, it is examined under what conditions stochastic order in families of conditional distributions is transferred to their inverse distributions, from two families of related distributions to a third family, or from multivariate conditional distributions to a marginal distribution. The main results are formulated as a series of theorems and corollaries which apply to dichotomous IRT models. One part of the results holds for unidimensional models with fixed item parameters. The other part holds for models with random item parameters as used, for example, in adaptive testing or for tests with multidimensional abilities. [ABSTRACT FROM AUTHOR]