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The present paper introduces a general multidimensional model to measure individual differences in learning within a single administration of a test. Learning is assumed to result from practicing the operations involved in solving the items. The model accounts for the possibility that the ability to learn may manifest differently for correct and incorrect responses, which allows for distinguishing different types of learning effects in the data. Model estimation and evaluation is based on a Bayesian framework. A simulation study is presented that examines the performance of the estimation and evaluation methods. The results show accuracy in parameter recovery as well as good performance in model evaluation and selection. An empirical study illustrates the applicability of the model to data from a logical ability test. [ABSTRACT FROM AUTHOR]

Various methods to detect differential item functioning (DIF) in item response models are available. However, most of these methods assume that the responses are binary, and so for ordered response categories available methods are scarce. In the present article, DIF in the widely used partial credit model is investigated. An item-focused tree is proposed that allows the detection of DIF items, which might affect the performance of the partial credit model. The method uses tree methodology, yielding a tree for each item that is detected as DIF item. The visualization as trees makes the results easily accessible, as the obtained trees show which variables induce DIF and in which way. In the present paper, the new method is compared with alternative approaches and simulations demonstrate the performance of the method. [ABSTRACT FROM AUTHOR]

Previous studies have demonstrated evidence of latent skill continuity even in tests intentionally designed for measurement of binary skills. In addition, the assumption of binary skills when continuity is present has been shown to potentially create a lack of invariance in item and latent ability parameters that may undermine applications. In this article, we examine measurement of growth as one such application, and consider multidimensional item response theory (MIRT) as a competing alternative. Motivated by prior findings concerning the effects of skill continuity, we study the relative robustness of cognitive diagnostic models (CDMs) and (M)IRT models in the measurement of growth under both binary and continuous latent skill distributions. We find CDMs to be a less robust way of quantifying growth under misspecification, and subsequently provide a real-data example suggesting underestimation of growth as a likely consequence. It is suggested that researchers should regularly attend to the assumptions associated with the use of latent binary skills and consider (M)IRT as a potentially more robust alternative if unsure of their discrete nature. [ABSTRACT FROM AUTHOR]

In the literature of modern psychometric modeling, mostly related to item response theory (IRT), the fit of model is evaluated through known indices, such as χ2, M2, and root mean square error of approximation (RMSEA) for absolute assessments as well as Akaike information criterion (AIC), consistent AIC (CAIC), and Bayesian information criterion (BIC) for relative comparisons. Recent developments show a merging trend of psychometric and machine learnings, yet there remains a gap in the model fit evaluation, specifically the use of the area under curve (AUC). This study focuses on the behaviors of AUC in fitting IRT models. Rounds of simulations were conducted to investigate AUC's appropriateness (e.g., power and Type I error rate) under various conditions. The results show that AUC possessed certain advantages under certain conditions such as high-dimensional structure with two-parameter logistic (2PL) and some three-parameter logistic (3PL) models, while disadvantages were also obvious when the true model is unidimensional. It cautions researchers about the dangers of using AUC solely in evaluating psychometric models. [ABSTRACT FROM AUTHOR]

Administering Likert-type questionnaires to online samples risks contamination of the data by malicious computer-generated random responses, also known as bots. Although nonresponsivity indices (NRIs) such as person-total correlations or Mahalanobis distance have shown great promise to detect bots, universal cutoff values are elusive. An initial calibration sample constructed via stratified sampling of bots and humans—real or simulated under a measurement model—has been used to empirically choose cutoffs with a high nominal specificity. However, a high-specificity cutoff is less accurate when the target sample has a high contamination rate. In the present article, we propose the supervised classes, unsupervised mixing proportions (SCUMP) algorithm that chooses a cutoff to maximize accuracy. SCUMP uses a Gaussian mixture model to estimate, unsupervised, the contamination rate in the sample of interest. A simulation study found that, in the absence of model misspecification on the bots, our cutoffs maintained accuracy across varying contamination rates. [ABSTRACT FROM AUTHOR]

Sensitivity analyses encompass a broad set of post-analytic techniques that are characterized as measuring the potential impact of any factor that has an effect on some output variables of a model. This research focuses on the utility of the simulated annealing algorithm to automatically identify path configurations and parameter values of omitted confounders in structural equation modeling (SEM). An empirical example based on a past published study is used to illustrate how strongly related an omitted variable must be to model variables for the conclusions of an analysis to change. The algorithm is outlined in detail and the results stemming from the sensitivity analysis are discussed. [ABSTRACT FROM AUTHOR]

Response data containing an excessive number of zeros are referred to as zero-inflated data. When differential item functioning (DIF) detection is of interest, zero-inflation can attenuate DIF effects in the total sample and lead to underdetection of DIF items. The current study presents a DIF detection procedure for response data with excess zeros due to the existence of unobserved heterogeneous subgroups. The suggested procedure utilizes the factor mixture modeling (FMM) with MIMIC (multiple-indicator multiple-cause) to address the compromised DIF detection power via the estimation of latent classes. A Monte Carlo simulation was conducted to evaluate the suggested procedure in comparison to the well-known likelihood ratio (LR) DIF test. Our simulation study results indicated the superiority of FMM over the LR DIF test in terms of detection power and illustrated the importance of accounting for latent heterogeneity in zero-inflated data. The empirical data analysis results further supported the use of FMM by flagging additional DIF items over and above the LR test. [ABSTRACT FROM AUTHOR]

A number of psychometricians have suggested that parallel analysis (PA) tends to yield more accurate results in determining the number of factors in comparison with other statistical methods. Nevertheless, all too often PA can suggest an incorrect number of factors, particularly in statistically unfavorable conditions (e.g., small sample sizes and low factor loadings). Because of this, researchers have recommended using multiple methods to make judgments about the number of factors to extract. Implicit in this recommendation is that, when the number of factors is chosen based on PA, uncertainty nevertheless exists. We propose a Bayesian parallel analysis (B-PA) method to incorporate the uncertainty with decisions about the number of factors. B-PA yields a probability distribution for the various possible numbers of factors. We implement and compare B-PA with a frequentist approach, revised parallel analysis (R-PA), in the contexts of real and simulated data. Results show that B-PA provides relevant information regarding the uncertainty in determining the number of factors, particularly under conditions with small sample sizes, low factor loadings, and less distinguishable factors. Even if the indicated number of factors with the highest probability is incorrect, B-PA can show a sizable probability of retaining the correct number of factors. Interestingly, when the mode of the distribution of the probabilities associated with different numbers of factors was treated as the number of factors to retain, B-PA was somewhat more accurate than R-PA in a majority of the conditions. [ABSTRACT FROM AUTHOR]

We investigated by means of a simulation study how well methods for factor rotation can identify a two-facet simple structure. Samples were generated from orthogonal and oblique two-facet population factor models with 4 (2 factors per facet) to 12 factors (6 factors per facet). Samples drawn from orthogonal populations were submitted to factor analysis with subsequent Varimax, Equamax, Parsimax, Factor Parsimony, Tandem I, Tandem II, Infomax, and McCammon's minimum entropy rotation. Samples drawn from oblique populations were submitted to factor analysis with subsequent Geomin rotation and a Promax-based Tandem II rotation. As a benchmark, we investigated a target rotation of the sample loadings toward the corresponding faceted population loadings. The three conditions were sample size (n = 400, 1,000), number of factors (q = 4-12), and main loading size (l =.40,.50,.60). For less than six orthogonal factors Infomax and McCammon's minimum entropy rotation and for six and more factors Tandem II rotation yielded the highest congruence of sample loading matrices with faceted population loading matrices. For six and more oblique factors Geomin rotation and a Promax-based Tandem II rotation yielded the highest congruence with faceted population loadings. Analysis of data of 393 participants that performed a test for the Berlin Model of Intelligence Structure revealed that the faceted structure of this model could be identified by means of a Promax-based Tandem II rotation of task aggregates corresponding to the cross-products of the facets. Implications for the identification of faceted models by means of factor rotation are discussed. [ABSTRACT FROM AUTHOR]

This study compares automated methods to develop short forms of psychometric scales. Obtaining a short form that has both adequate internal structure and strong validity with respect to relationships with other variables is difficult with traditional methods of short-form development. Metaheuristic algorithms can select items for short forms while optimizing on several validity criteria, such as adequate model fit, composite reliability, and relationship to external variables. Using a Monte Carlo simulation study, this study compared existing implementations of the ant colony optimization, Tabu search, and genetic algorithm to select short forms of scales, as well as a new implementation of the simulated annealing algorithm. Selection of short forms of scales with unidimensional, multidimensional, and bifactor structure were evaluated, with and without model misspecification and/or an external variable. The results showed that when the confirmatory factor analysis model of the full form of the scale was correctly specified or had only minor misspecification, the four algorithms produced short forms with good psychometric qualities that maintained the desired factor structure of the full scale. Major model misspecification resulted in worse performance for all algorithms, but including an external variable only had minor effects on results. The simulated annealing algorithm showed the best overall performance as well as robustness to model misspecification, while the genetic algorithm produced short forms with worse fit than the other algorithms under conditions with model misspecification. [ABSTRACT FROM AUTHOR]

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 restrict the theoretical correlation range [−1, 1] such that certain correlation structures may be unfeasible. The direct implication of this result is that coefficient alpha is bounded above depending on the shape of the distributions. A general form of the Fréchet–Hoeffding bounds is derived for discrete random variables. R code and a user-friendly shiny web application are also provided so that researchers can calculate the bounds on their data. [ABSTRACT FROM AUTHOR]

The present study extended the p -optimality method to the multistage computerized adaptive test (MST) context in developing optimal item pools to support different MST panel designs under different test configurations. Using the Rasch model, simulated optimal item pools were generated with and without practical constraints of exposure control. A total number of 72 simulated optimal item pools were generated and evaluated by an overall sample and conditional sample using various statistical measures. Results showed that the optimal item pools built with the p -optimality method provide sufficient measurement accuracy under all simulated MST panel designs. Exposure control affected the item pool size, but not the item distributions and item pool characteristics. This study demonstrated that the p -optimality method can adapt to MST item pool design, facilitate the MST assembly process, and improve its scoring accuracy. [ABSTRACT FROM AUTHOR]

In test security analyses, answer copying, collusion, and the use of a shared brain dump site can be detected by checking similarity between item response strings. The similarity, however, can possibly be contaminated by aberrant data resulted from careless responding or rapid guessing. For example, some test-takers may answer by repeating a pattern (e.g., ABCDABCDABCD or AAAAAAAA). It is crucial for researchers or practitioners to remove these kinds of repeating patterns before conducting any similarity analysis. In this study, a new algorithm for finding repeating patterns is proposed. The application of this algorithm on real and simulated data showed satisfying results; the simulated repeating patterns were identified 100% by the new algorithm with a negligible false positive rate. Although illustrated only in the context of similarity analysis, the proposed algorithm has broad applications: for example, identifying unmotivated test-takers for school intervention or cleaning data before estimating item parameters under an item response theory model. [ABSTRACT FROM AUTHOR]

The chiropractic clinical competency examination uses groups of items that are integrated by a common case vignette. The nature of the vignette items violates the assumption of local independence for items nested within a vignette. This study examines via simulation a new algorithmic approach for addressing the local independence violation problem using a two-level alternating directions testlet model. Parameter values for item difficulty, discrimination, test-taker ability, and test-taker secondary abilities associated with a particular testlet are generated and parameter recovery through Markov Chain Monte Carlo Bayesian methods and generalized maximum likelihood estimation methods are compared. To aid with the complex computational efforts, the novel so-called TensorFlow platform is used. Both estimation methods provided satisfactory parameter recovery, although the Bayesian methods were found to be somewhat superior in recovering item discrimination parameters. The practical significance of the results are discussed in relation to obtaining accurate estimates of item, test, ability parameters, and measurement reliability information. [ABSTRACT FROM AUTHOR]

Automated scoring based on Latent Semantic Analysis (LSA) has been successfully used to score essays and constrained short answer responses. Scoring tests that capture open-ended, short answer responses poses some challenges for machine learning approaches. We used LSA techniques to score short answer responses to the Consequences Test, a measure of creativity and divergent thinking that encourages a wide range of potential responses. Analyses demonstrated that the LSA scores were highly correlated with conventional Consequence Test scores, reaching a correlation of.94 with human raters and were moderately correlated with performance criteria. This approach to scoring short answer constructed responses solves many practical problems including the time for humans to rate open-ended responses and the difficulty in achieving reliable scoring. [ABSTRACT FROM AUTHOR]

This article introduces the Quality of Item Pool (QIP) Index, a novel approach to quantifying the adequacy of an item pool of a computerized adaptive test for a given set of test specifications and examinee population. This index ranges from 0 to 1, with values close to 1 indicating the item pool presents optimum items to examinees throughout the test. This index can be used to compare different item pools or diagnose the deficiencies of a given item pool by quantifying the amount of deviation from a perfect item pool. Simulation studies were conducted to evaluate the capacity of this index for detecting the inadequacies of two simulated item pools. The value of this index was compared with the existing methods of evaluating the quality of computerized adaptive tests (CAT). Results of the study showed that the QIP Index can detect even slight deviations between a proposed item pool and an optimal item pool. It can also uncover shortcomings of an item pool that other outcomes of CAT cannot detect. CAT developers can use the QIP Index to diagnose the weaknesses of the item pool and as a guide for improving item pools. [ABSTRACT FROM AUTHOR]

Researchers frequently use machine-learning methods in many fields. In the area of detecting fraud in testing, there have been relatively few studies that have used these methods to identify potential testing fraud. In this study, a technical review of a recently developed state-of-the-art algorithm, Extreme Gradient Boosting (XGBoost), is provided and the utility of XGBoost in detecting examinees with potential item preknowledge is investigated using a real data set that includes examinees who engaged in fraudulent testing behavior, such as illegally obtaining live test content before the exam. Four different XGBoost models were trained using different sets of input features based on (a) only dichotomous item responses, (b) only nominal item responses, (c) both dichotomous item responses and response times, and (d) both nominal item responses and response times. The predictive performance of each model was evaluated using the area under the receiving operating characteristic curve and several classification measures such as the false-positive rate, true-positive rate, and precision. For comparison purposes, the results from two person-fit statistics on the same data set were also provided. The results indicated that XGBoost successfully classified the honest test takers and fraudulent test takers with item preknowledge. Particularly, the classification performance of XGBoost was reasonably good when the response time information and item responses were both taken into account. [ABSTRACT FROM AUTHOR]

With the development of technology-enhanced learning platforms, eye-tracking biometric indicators can be recorded simultaneously with students item responses. In the current study, visual fixation, an essential eye-tracking indicator, is modeled to reflect the degree of test engagement when a test taker solves a set of test questions. Three negative binomial regression models are proposed for modeling visual fixation counts of test takers solving a set of items. These models follow a similar structure to the lognormal response time model and the two-parameter logistic item response model. The proposed modeling structures include individualized latent person parameters reflecting the level of engagement of each test taker and two item parameters indicating the visual attention intensity and discriminating power of each test item. A Markov chain Monte Carlo estimation method is implemented for parameter estimation. Real data are fitted to the three proposed models, and the results are discussed. [ABSTRACT FROM AUTHOR]

Multidimensional item response theory (MIRT) models use data from individual item responses to estimate multiple latent traits of interest, making them useful in educational and psychological measurement, among other areas. When MIRT models are applied in practice, it is not uncommon to see that some items are designed to measure all latent traits while other items may only measure one or two traits. In order to facilitate a clear expression of which items measure which traits and formulate such relationships as a math function in MIRT models, we applied the concept of the Q-matrix commonly used in diagnostic classification models to MIRT models. In this study, we introduced how to incorporate a Q-matrix into an existing MIRT model, and demonstrated benefits of the proposed hybrid model through two simulation studies and an applied study. In addition, we showed the relative ease in modeling educational and psychological data through a Bayesian approach via the NUTS algorithm. [ABSTRACT FROM AUTHOR]

For item selection in cognitive diagnostic computerized adaptive testing (CD-CAT), ideally, a single item selection index should be created to simultaneously regulate precision, exposure status, and attribute balancing. For this purpose, in this study, we first proposed an attribute-balanced item selection criterion, namely, the standardized weighted deviation global discrimination index (SWDGDI), and subsequently formulated the constrained progressive index (CP_SWDGDI) by casting the SWDGDI in a progressive algorithm. A simulation study revealed that the SWDGDI method was effective in balancing attribute coverage and the CP_SWDGDI method was able to simultaneously balance attribute coverage and item pool usage while maintaining acceptable estimation precision. This research also demonstrates the advantage of a relatively low number of attributes in CD-CAT applications. [ABSTRACT FROM AUTHOR]

Plausible values can be used to either estimate population-level statistics or compute point estimates of latent variables. While it is well known that five plausible values are usually sufficient for accurate estimation of population-level statistics in large-scale surveys, the minimum number of plausible values needed to obtain accurate latent variable point estimates is unclear. This is especially relevant when an item response theory (IRT) model is estimated with MCMC (Markov chain Monte Carlo) methods in Mplus and point estimates of the IRT ability parameter are of interest, as Mplus only estimates the posterior distribution of each ability parameter. In order to obtain point estimates of the ability parameter, a number of plausible values can be drawn from the posterior distribution of each individual ability parameter and their mean (the posterior mean ability estimate) can be used as an individual ability point estimate. In this note, we conducted a simulation study to investigate how many plausible values were needed to obtain accurate posterior mean ability estimates. The results indicate that 20 is the minimum number of plausible values required to obtain point estimates of the IRT ability parameter that are comparable to marginal maximum likelihood estimation(MMLE)/expected a posteriori (EAP) estimates. A real dataset was used to demonstrate the comparison between MMLE/EAP point estimates and posterior mean ability estimates based on different number of plausible values. [ABSTRACT FROM AUTHOR]

Stan is a new Bayesian statistical software program that implements the powerful and efficient Hamiltonian Monte Carlo (HMC) algorithm. To date there is not a source that systematically provides Stan code for various item response theory (IRT) models. This article provides Stan code for three representative IRT models, including the three-parameter logistic IRT model, the graded response model, and the nominal response model. We demonstrate how IRT model comparison can be conducted with Stan and how the provided Stan code for simple IRT models can be easily extended to their multidimensional and multilevel cases. [ABSTRACT FROM AUTHOR]

The clinical assessment of mental disorders can be a time-consuming and error-prone procedure, consisting of a sequence of diagnostic hypothesis formulation and testing aimed at restricting the set of plausible diagnoses for the patient. In this article, we propose a novel computerized system for the adaptive testing of psychological disorders. The proposed system combines a mathematical representation of psychological disorders, known as the "formal psychological assessment," with an algorithm designed for the adaptive assessment of an individual's knowledge. The assessment algorithm is extended and adapted to the new application domain. Testing the system on a real sample of 4,324 healthy individuals, screened for obsessive-compulsive disorder, we demonstrate the system's ability to support clinical testing, both by identifying the correct critical areas for each individual and by reducing the number of posed questions with respect to a standard written questionnaire. [ABSTRACT FROM AUTHOR]

Application of MIRT modeling procedures is dependent on the quality of parameter estimates provided by the estimation software and techniques used. This study investigated model parameter recovery of two popular MIRT packages, BMIRT and flexMIRT, under some common measurement conditions. These packages were specifically selected to investigate the model parameter recovery of three item parameter estimation techniques, namely, Bock–Aitkin EM (BA-EM), Markov chain Monte Carlo (MCMC), and Metropolis–Hastings Robbins–Monro (MH-RM) algorithms. The results demonstrated that all estimation techniques had similar root mean square error values when larger sample size and higher test length were used. Depending on the number of dimensions, sample size, and test length, each estimation technique exhibited some strengths and weaknesses. Overall, the BA-EM technique was found to have shorter estimation time with all test specifications. [ABSTRACT FROM AUTHOR]

In a pioneering research article, Wollack and colleagues suggested the "erasure detection index'' (EDI) to detect test tampering. The EDI can be used with or without a continuity correction and is assumed to follow the standard normal distribution under the null hypothesis of no test tampering. When used without a continuity correction, the EDI often has inflated Type I error rates. When used with a continuity correction, the EDI has satisfactory Type I error rates, but smaller power compared with the EDI without a continuity correction. This article suggests three methods for detecting test tampering that do not rely on the assumption of a standard normal distribution under the null hypothesis. It is demonstrated in a detailed simulation study that the performance of each suggested method is slightly better than that of the EDI. The EDI and the suggested methods were applied to a real data set. The suggested methods, although more computation intensive than the EDI, seem to be promising in detecting test tampering. [ABSTRACT FROM AUTHOR]

Interest in using Bayesian methods for estimating item response theory models has grown at a remarkable rate in recent years. This attentiveness to Bayesian estimation has also inspired a growth in available software such as WinBUGS, R packages, BMIRT, MPLUS, and SAS PROC MCMC. This article intends to provide an accessible overview of Bayesian methods in the context of item response theory to serve as a useful guide for practitioners in estimating and interpreting item response theory (IRT) models. Included is a description of the estimation procedure used by SAS PROC MCMC. Syntax is provided for estimation of both dichotomous and polytomous IRT models, as well as a discussion on how to extend the syntax to accommodate more complex IRT models. [ABSTRACT FROM AUTHOR]