A Machine Learning Approach for the Simultaneous Detection of Preknowledge in Examinees and Items When Both Are Unknown

Pan and Wollack (PW) proposed a machine learning method to detect compromised items. We extend the work of PW to an approach detecting compromised items and examinees with item preknowledge simultaneously and draw on ideas in ensemble learning to relax several limitations in the work of PW. The suggested approach also provides a confidence score, which is based on an autoencoder to represent our confidence that the detection result truly corresponds to item preknowledge. Simulation studies indicate that the proposed approach performs well in the detection of item preknowledge, and the confidence score can provide helpful information for users.     

A Deterministic Gated Lognormal Response Time Model to Identify Examinees with Item Preknowledge

Response times (RTs) have recently attracted a significant amount of attention in the literature as they may provide meaningful information about item preknowledge. In this study, a new model, the Deterministic Gated Lognormal Response Time (DG-LNRT) model, is proposed to identify examinees with item preknowledge using RTs. The proposed model was applied to two different data sets and performance was assessed with false-positive rates, true-positive rates, and precision. The results were compared with another recently proposed Z-statistic. Follow-up simulation studies were also conducted to examine model performance in settings similar to the real data sets. The results indicate that the proposed model is viable and can help detect item preknowledge under certain conditions. However, its performance is highly dependent on the correct specification of the compromised items.     

Digital Module 08: Foundations of Operational Item Analysis https://ncme.elevate.commpartners.com

Item analysis is an integral part of operational test development and is typically conducted within two popular statistical frameworks: classical test theory (CTT) and item response theory (IRT). In this digital ITEMS module, Hanwook Yoo and Ronald K. Hambleton provide an accessible overview of operational item analysis approaches within these frameworks. They review the different stages of test development and associated item analyses to identify poorly performing items and effective item selection. Moreover, they walk through the computational and interpretational steps for CTT‐ and IRT‐based evaluation statistics using simulated data examples and review various graphical displays such as distractor response curves, item characteristic curves, and item information curves. The digital module contains sample data, Excel sheets with various templates and examples, diagnostic quiz questions, data‐based activities, curated resources, and a glossary.     

Investigating the Effect of Item Position in Computer‐Based Tests

Computer‐based tests (CBTs) often use random ordering of items in order to minimize item exposure and reduce the potential for answer copying. Little research has been done, however, to examine item position effects for these tests. In this study, different versions of a Rasch model and different response time models were examined and applied to data from a CBT administration of a medical licensure examination. The models specifically were used to investigate whether item position affected item difficulty and item intensity estimates. Results indicated that the position effect was negligible.     

A Comparison of Item Calibration Procedures in the Presence of Test Speededness

In the presence of test speededness, the parameter estimates of item response theory models can be poorly estimated due to conditional dependencies among items, particularly for end‐of‐test items (i.e., speeded items). This article conducted a systematic comparison of five‐item calibration procedures—a two‐parameter logistic (2PL) model, a one‐dimensional mixture model, a two‐step strategy (a combination of the one‐dimensional mixture and the 2PL), a two‐dimensional mixture model, and a hybrid model‐–by examining how sample size, percentage of speeded examinees, percentage of missing responses, and way of scoring missing responses (incorrect vs. omitted) affect the item parameter estimation in speeded tests. For nonspeeded items, all five procedures showed similar results in recovering item parameters. For speeded items, the one‐dimensional mixture model, the two‐step strategy, and the two‐dimensional mixture model provided largely similar results and performed better than the 2PL model and the hybrid model in calibrating slope parameters. However, those three procedures performed similarly to the hybrid model in estimating intercept parameters. As expected, the 2PL model did not appear to be as accurate as the other models in recovering item parameters, especially when there were large numbers of examinees showing speededness and a high percentage of missing responses with incorrect scoring. Real data analysis further described the similarities and differences between the five procedures.     

Simulation study of item bias detection with restricted factor analysis

Restricted factor analysis (RFA) can be used to detect item bias (also called differential item functioning). In the RFA method of item bias detection, the common factor model serves as an item response model, but group membership is also included in the model. Two simulation studies are reported, both showing that the RFA method detects bias in 7‐point scale items very well, especially when the sample size is large, the mean trait difference between groups is small, the group sizes are equal, and the amount of bias is large. The first study further shows that the RFA method detects bias in dichotomous items at least as well as an established method based on the one‐parameter logistic item response model. The second study concerns various procedures to evaluate the significance of two‐item bias indices provided by the RFA method. The results indicate that the RFA method performs best when it is used in an iterative procedure.     

The acquisition of formal operational schemata during adolescence: The role of the biconditional

To test the hypothesis that the basic “logic” utilized by individuals in scientific hypothesis testing is the biconditional (if and only if), and that the biconditional is a precondition for the development of formal operations, a sample of 387 students in grades eight, ten, twelve, and college were administered eight reasoning items. Five of the items involved the formal operational schemata of probability, proportions and correlations. Two of the items involved propositions and correlations. Two of the items involved propositional logic. One item involved the biconditional. Percentages of correct responses on most of the items increased with age. A principal-component analysis revealed three factors, two of which were identified as involving operational thought, one of which involved propositional logic. As predicted, the biconditional reasoning item loaded on one of the operational thought factors. A Guttman scale analysis of the items failed to reveal a unidimensional scale, yet the biconditional reasoning item ordered first supporting the hypothesis that it is a precondition for formal operational reasoning. Implications for teaching science students how to test hypotheses are discussed.     

Meta‐evaluation in clinical anatomy: A practical application of item response theory in multiple choice examinations

The nature of anatomy education has changed substantially in recent decades, though the traditional multiple‐choice written examination remains the cornerstone of assessing students' knowledge. This study sought to measure the quality of a clinical anatomy multiple‐choice final examination using item response theory (IRT) models. One hundred seventy‐six students took a multiple‐choice clinical anatomy examination. One‐ and two‐parameter IRT models (difficulty and discrimination parameters) were used to assess item quality. The two‐parameter IRT model demonstrated a wide range in item difficulty, with a median of ?1.0 and range from ?2.0 to 0.0 (25th to 75th percentile). Similar results were seen for discrimination (median 0.6; range 0.4–0.8). The test information curve achieved maximum discrimination for an ability level one standard deviation below the average. There were 15 items with standardized loading less than 0.3, which was due to several factors: two items had two correct responses, one was not well constructed, two were too easy, and the others revealed a lack of detailed knowledge by students. The test used in this study was more effective in discriminating students of lower ability than those of higher ability. Overall, the quality of the examination in clinical anatomy was confirmed by the IRT models. Anat Sci Educ 3:17–24, 2010. © 2009 American Association of Anatomists.     

A Stepwise Test Characteristic Curve Method to Detect Item Parameter Drift

An important assumption of item response theory is item parameter invariance. Sometimes, however, item parameters are not invariant across different test administrations due to factors other than sampling error; this phenomenon is termed item parameter drift. Several methods have been developed to detect drifted items. However, most of the existing methods were designed to detect drifts in individual items, which may not be adequate for test characteristic curve–based linking or equating. One example is the item response theory–based true score equating, whose goal is to generate a conversion table to relate number‐correct scores on two forms based on their test characteristic curves. This article introduces a stepwise test characteristic curve method to detect item parameter drift iteratively based on test characteristic curves without needing to set any predetermined critical values. Comparisons are made between the proposed method and two existing methods under the three‐parameter logistic item response model through simulation and real data analysis. Results show that the proposed method produces a small difference in test characteristic curves between administrations, an accurate conversion table, and a good classification of drifted and nondrifted items and at the same time keeps a large amount of linking items.     

Psychometric Aspects of Maintaining Standards of Examinations

Through pilot studies and regular examination procedures, the National Institute for Educational Measurement (CITO) in The Netherlands has gathered experience with different methods of maintaining the standards of examinations. The present paper presents an overview of the psychometric aspects of the various approaches that can be chosen for the maintenance of standards. Generally speaking, the approaches to the problem, can be divided into two classes. In the first approach the examinations are a fixed factor, i.e. the examination is already constructed and cannot be changed, and the link between the standards of both examinations is created by some test equating design. In the second approach the items of both examinations are selected from a pre‐tested pool of items, in such a way that two equivalent examinations are constructed. In both approaches the statistical problems of simultaneously modelling possible differences in the ability level of different groups of examinees and differences in the difficulty of the items are solved within the framework of item response theory. It is shown that applying the Rasch model for dichotomous and polytomous items results in a variety of possible test‐equating designs which adequately deal with the restrictions imposed by the practical conditions related to the fact that the equating involves examinations. Especially the requirement of secrecy of the content of new examinations must be taken into account. Finally it is shown that, given a pool of pre‐tested items, optimisation techniques can be used to construct equivalent examinations.     

A CROSS-VALIDATION STUDY OF THE ITEM ORDERING OF THE PEABODY PICTURE VOCABULARY TEST1

A subset of the items of both forms of the Peabody Picture Vocabulary Test (PPVT) was administered to a sample of 452 fourth-, fifth- and sixth-grade students. This sample of students was randomly divided into two equal subgroups. Item difficulty indices were calculated for each of the two subsamples for each of the two forms of the test. Data obtained from the first subsample were used to evaluate the published ordering of items of Forms A and B of the PPVT and to reorder the items according to the empirically derived item difficulties. The second subsample was used as a cross-validation sample to evaluate the empirically derived reordering of items. The results of the cross-validation of the reordering indicate a substantial and significant increase in the validity of the item orderings for this subset of items on both forms of the PPVT. Therefore, this new ordering may yield a more accurate estimate of the intelligence of average and above students in the fourth-, fifth-, and sixth-grades than the present, published ordering of items.     

Assessing Preknowledge Cheating via Innovative Measures: A Multiple-Group Analysis of Jointly Modeling Item Responses,Response Times,and Visual Fixation Counts

Many approaches have been proposed to jointly analyze item responses and response times to understand behavioral differences between normally and aberrantly behaved test-takers. Biometric information, such as data from eye trackers, can be used to better identify these deviant testing behaviors in addition to more conventional data types. Given this context, this study demonstrates the application of a new method for multiple-group analysis that concurrently models item responses, response times, and visual fixation counts collected from an eye-tracker. It is hypothesized that differences in behavioral patterns between normally behaved test-takers and those who have different levels of preknowledge about the test items will manifest in latent characteristics of the different data types. A Bayesian estimation scheme is used to fit the proposed model to experimental data and the results are discussed.     

Detecting Differential Item Discrimination (DID) and the Consequences of Ignoring DID in Multilevel Item Response Models

Cross‐level invariance in a multilevel item response model can be investigated by testing whether the within‐level item discriminations are equal to the between‐level item discriminations. Testing the cross‐level invariance assumption is important to understand constructs in multilevel data. However, in most multilevel item response model applications, the cross‐level invariance is assumed without testing of the cross‐level invariance assumption. In this study, the detection methods of differential item discrimination (DID) over levels and the consequences of ignoring DID are illustrated and discussed with the use of multilevel item response models. Simulation results showed that the likelihood ratio test (LRT) performed well in detecting global DID at the test level when some portion of the items exhibited DID. At the item level, the Akaike information criterion (AIC), the sample‐size adjusted Bayesian information criterion (saBIC), LRT, and Wald test showed a satisfactory rejection rate (>.8) when some portion of the items exhibited DID and the items had lower intraclass correlations (or higher DID magnitudes). When DID was ignored, the accuracy of the item discrimination estimates and standard errors was mainly problematic. Implications of the findings and limitations are discussed.     

Unidimensional Interpretations for Multidimensional Test Items

This article considers potential problems that can arise in estimating a unidimensional item response theory (IRT) model when some test items are multidimensional (i.e., show a complex factorial structure). More specifically, this study examines (1) the consequences of model misfit on IRT item parameter estimates due to unintended minor item‐level multidimensionality, and (2) whether a Projection IRT model can provide a useful remedy. A real‐data example is used to illustrate the problem and also is used as a base model for a simulation study. The results suggest that ignoring item‐level multidimensionality might lead to inflated item discrimination parameter estimates when the proportion of multidimensional test items to unidimensional test items is as low as 1:5. The Projection IRT model appears to be a useful tool for updating unidimensional item parameter estimates of multidimensional test items for a purified unidimensional interpretation.     

On the Issue of Item Selection in Computerized Adaptive Testing With Response Times

Many standardized tests are now administered via computer rather than paper‐and‐pencil format. The computer‐based delivery mode brings with it certain advantages. One advantage is the ability to adapt the difficulty level of the test to the ability level of the test taker in what has been termed computerized adaptive testing (CAT). A second advantage is the ability to record not only the test taker's response to each item (i.e., question), but also the amount of time the test taker spends considering and answering each item. Combining these two advantages, various methods were explored for utilizing response time data in selecting appropriate items for an individual test taker. Four strategies for incorporating response time data were evaluated, and the precision of the final test‐taker score was assessed by comparing it to a benchmark value that did not take response time information into account. While differences in measurement precision and testing times were expected, results showed that the strategies did not differ much with respect to measurement precision but that there were differences with regard to the total testing time.     

浅析阅读理解考试中的测试方法效应问题

本文研究的是不同的测试方法-单项选择和信息转移-是否会在阅读理解考试中产生测试方法效应的问题.除对学生的考试成绩(分数)进行分析外,本研究还进一步对试题的难度值进行了分析,而本研究中试题难度是通过项目反应理论(Item Response Theory)计算得到的.结果显示不同测试方法的确会影响题目难度及考生的考试表现,就试题难度而言信息转移比单项选择更难.     

Use of Restricted Item Response Models for Examining Item Difficulty Ordering and Slope Uniformity

This article demonstrates the utility of restricted item response models for examining item difficulty ordering and slope uniformity for an item set that reflects varying cognitive processes. Twelve sets of paired algebra word problems were developed to systematically reflect various types of cognitive processes required for successful performance. This resulted in a total of 24 items. They reflected distance-rate–time (DRT), interest, and area problems. Hypotheses concerning difficulty ordering and slope uniformity for the items were tested by constraining item difficulty and discrimination parameters in hierarchical item response models. The first set of model comparisons tested the equality of the discrimination and difficulty parameters for each set of paired items. The second set of model comparisons examined slope uniformity within the complex DRT problems. The third set of model comparisons examined whether the familiarity of the story context affected item difficulty for two types of complex DRT problems. The last set of model comparisons tested the hypothesized difficulty ordering of the items.     

An Examination of Two Procedures for Identifying Consequential Item Parameter Drift

The purpose of the present study was to develop and evaluate two procedures flagging consequential item parameter drift (IPD) in an operational testing program. The first procedure was based on flagging items that exhibit a meaningful magnitude of IPD using a critical value that was defined to represent barely tolerable IPD. The second procedure was based on flagging items in which the D² statistic was more than two standard deviations from the mean. Both procedures were implemented using an iterative purification approach to detect IPD. A simulation study was implemented to evaluate the effectiveness of both detection procedures in flagging non-negligible IPD. Both procedures were able to identify IPD and the iterative purification method provided useful information regarding the consequences of excluding or including a flagged item. The advantages and disadvantages of both procedures as well as possible modifications intended to improve the procedures’ effectiveness are discussed in the article.     

Effect of the number of scale points on chi‐square fit indices in confirmatory factor analysis

This article investigates the effect of the number of item response categories on chi‐square statistics for confirmatory factor analysis to assess whether a greater number of categories increases the likelihood of identifying spurious factors, as previous research had concluded. Four types of continuous single‐factor data were simulated for a 20‐item test: (a) uniform for all items, (b) symmetric unimodal for all items, (c) negatively skewed for all items, or (d) negatively skewed for 10 items and positively skewed for 10 items. For each of the 4 types of distributions, item responses were divided to yield item scores with 2,4, or 6 categories. The results indicated that the chi‐square statistic for evaluating a single‐factor model was most inflated (suggesting spurious factors) for 2‐category responses and became less inflated as the number of categories increased. However, the Satorra‐Bentler scaled chi‐square tended not to be inflated even for 2‐category responses, except if the continuous item data had both negatively and positively skewed distributions.     

Generalization of the Lord‐Wingersky Algorithm to Computing the Distribution of Summed Test Scores Based on Real‐Number Item Scores

With known item response theory (IRT) item parameters, Lord and Wingersky provided a recursive algorithm for computing the conditional frequency distribution of number‐correct test scores, given proficiency. This article presents a generalized algorithm for computing the conditional distribution of summed test scores involving real‐number item scores. The generalized algorithm is distinct from the Lord‐Wingersky algorithm in that it explicitly incorporates the task of figuring out all possible unique real‐number test scores in each recursion. Some applications of the generalized recursive algorithm, such as IRT test score reliability estimation and IRT proficiency estimation based on summed test scores, are illustrated with a short test by varying scoring schemes for its items.