Dichotomous Item Response Theory Models Research Articles

An Evaluation of Fit Indices Used in Model Selection of Dichotomous Mixture IRT Models

A Monte Carlo simulation study was conducted to compare fit indices used for detecting the correct latent class in three dichotomous mixture item response theory (IRT) models. Ten indices were considered: Akaike’s information criterion (AIC), the corrected AIC (AICc), Bayesian information criterion (BIC), consistent AIC (CAIC), Draper’s information criterion (DIC), sample size adjusted BIC (SABIC), relative entropy, the integrated classification likelihood criterion (ICL-BIC), the adjusted Lo–Mendell–Rubin (LMR), and Vuong-Lo–Mendell–Rubin (VLMR). The accuracy of the fit indices was assessed for correct detection of the number of latent classes for different simulation conditions including sample size (2,500 and 5,000), test length (15, 30, and 45), mixture proportions (equal and unequal), number of latent classes (2, 3, and 4), and latent class separation (no-separation and small separation). Simulation study results indicated that as the number of examinees or number of items increased, correct identification rates also increased for most of the indices. Correct identification rates by the different fit indices, however, decreased as the number of estimated latent classes or parameters (i.e., model complexity) increased. Results were good for BIC, CAIC, DIC, SABIC, ICL-BIC, LMR, and VLMR, and the relative entropy index tended to select correct models most of the time. Consistent with previous studies, AIC and AICc showed poor performance. Most of these indices had limited utility for three-class and four-class mixture 3PL model conditions.

The Impact of Sample Size and Various Other Factors on Estimation of Dichotomous Mixture IRT Models.

The purpose of this study was to examine the effects of different data conditions on item parameter recovery and classification accuracy of three dichotomous mixture item response theory (IRT) models: the Mix1PL, Mix2PL, and Mix3PL. Manipulated factors in the simulation included the sample size (11 different sample sizes from 100 to 5000), test length (10, 30, and 50), number of classes (2 and 3), the degree of latent class separation (normal/no separation, small, medium, and large), and class sizes (equal vs. nonequal). Effects were assessed using root mean square error (RMSE) and classification accuracy percentage computed between true parameters and estimated parameters. The results of this simulation study showed that more precise estimates of item parameters were obtained with larger sample sizes and longer test lengths. Recovery of item parameters decreased as the number of classes increased with the decrease in sample size. Recovery of classification accuracy for the conditions with two-class solutions was also better than that of three-class solutions. Results of both item parameter estimates and classification accuracy differed by model type. More complex models and models with larger class separations produced less accurate results. The effect of the mixture proportions also differentially affected RMSE and classification accuracy results. Groups of equal size produced more precise item parameter estimates, but the reverse was the case for classification accuracy results. Results suggested that dichotomous mixture IRT models required more than 2,000 examinees to be able to obtain stable results as even shorter tests required such large sample sizes for more precise estimates. This number increased as the number of latent classes, the degree of separation, and model complexity increased.

Assessing Cognitive Abilities Using the WAIS-IV: An Item Response Theory Approach.

Background: The Wechsler Adult Intelligence Scale-Fourth Edition (WAIS-IV) has been adapted to 28 different cultures and there has been considerable interest in examining its structure through exploratory and confirmatory factor analysis. This study investigates item and scale properties of the Egyptian WAIS-IV using item response theory (IRT) models. Methods: The sample consisted of 250 adults from Egypt. The item-level and subtest statistical properties of the Egyptian WAIS-IV were established using a combination of four dichotomous IRT models and four polytomous IRT models. In addition, factor analysis was performed to investigate the dimensionality of each subtest. Results: Factor analysis indicated the unidimensionality of each subtest. Among IRT models, the two-parameter logistic model provided a good fit for dichotomous subtests, while the graded response model fitted the polytomous data. Most items of the Egyptian WAIS-IV showed high discrimination, and the scale was adequately informative across the levels of latent traits (i.e., cognitive variables). However, each subtest included at least some items with limited ability to distinguish between individuals with differing levels of the cognitive variable being measured. Furthermore, most subtests have items that do not follow the difficulty rank they are ascribed in the WAIS-IV manual. Conclusions: Overall, the results suggest that the Egyptian WAIS-IV offers a highly valid assessment of intellectual abilities, despite the need for some improvements.

Item response theory as a feature selection and interpretation tool in the context of machine learning.

Optimizing the number and utility of features to use in a classification analysis has been the subject of many research studies. Most current models use end-classifications as part of the feature reduction process, leading to circularity in the methodology. The approach demonstrated in the present research uses item response theory (IRT) to select features independent of the end-classification results without the biased accuracies that this circularity engenders. Dichotomous and polytomous IRT models were used to analyze 30 histological breast cancer features from 569 patients using the Wisconsin Diagnostic Breast Cancer data set. Based on their characteristics, three features were selected for use in a machine learning classifier. For comparison purposes, two machine learning-based feature selection protocols were run-recursive feature elimination (RFE) and ridge regression-and the three features selected from these analyses were also used in the subsequent learning classifier. Classification results demonstrated that all three selection processes performed comparably. The non-biased nature of the IRT protocol and information provided about the specific characteristics of the features as to why they are of use in classification help to shed light on understanding which attributes of features make them suitable for use in a machine learning context.

Use of item response theory in marketing research

There are three purposes of this paper. The first is to present a brief introduction to item response theory in conjunction with marketing research. The second is to present a review of the current uses of item response theory in representative marketing research journals. The third is to present an example that illustrate and contrasts classical test theory and item response theory approaches to item and scale analysis. Several item response theory relevant papers were recently published in various marketing research journals. Because models under item response theory, from simple to complex, were used without any systematic introduction in marketing research, this paper briefly presents the main concepts in item response theory. A content analysis was done for the second purpose with 30 item response theory relevant articles in marketing research journals. Articles were sorted based on the taxonomy of item response theory models. Many articles reviewed relied on some type of unidimensional dichotomous item response theory models. Articles published recently within the past 10 years used more complicated item response theory models, both mathematically and statistically, than other previously published articles in marketing research journals. Lastly, data from a scale with three Likert-type items of four response categories were analysed using a traditional approach based on item statistics and coefficient alpha as well as using an item response theory approach by employing the graded response model. Main concepts of item response theory were explicated with figures.

A Short Note on Obtaining Item Parameter Estimates of IRT Models with Bayesian Estimation in Mplus

Parameter estimation of Item Response Theory (IRT) models can be applied using both Bayesian and non-Bayesian methods. Although maximum likelihood estimation (MLE), a non-Bayesian method, has predominated since the 1970s, there is an increasing use of Bayesian methods, due to their capability for estimating complex models and for their implementation in commercially available software. In view of the recent increase in the popularity of these methods, a comparison between model parameter estimates from the two types of methods would be useful for practitioners. In this study, we compare MLE and Bayesian estimation, two popular methods for obtaining parameter estimates for dichotomous IRT models, using the MLE and Bayes estimator options as implemented in the Mplus software package. Results indicated Bayesian and MLE estimates differed only slightly, clearly demonstrating the consistency between estimates from the two methods. Further, Bayes estimator option in Mplus can be a viable and relatively easy to use tool for calibrations of IRT models.

Novel Feature Selection for Artificial Intelligence Using Item Response Theory for Mortality Prediction.

Feature selection is a critical component in supervised machine learning classification analyses. Extraneous features introduce noise and inefficiencies into the system leading to a need for feature reduction techniques. Many feature reduction models use the end-classification results in the feature reduction process, committing a circular error. Item Response Theory (IRT) examines the characteristics of features independent of the end-classification results, and provides high levels of information regarding feature utility. A two-parameter dichotomous IRT model was used to analyze 18 features from an intensive care unit data set with 2520 cases. The classification results showed that the features selected via IRT were comparable to that using more traditional machine learning approaches. Strengths and limitations of the IRT selection protocol are discussed.

An item response theory model of matching test performance

In a matching test, a test taker is presented with a list of test items and a list of response alternatives and asked to match each response alternative with a test item. The response alternatives can be given as a response to at most one test item. As a result, the response a test taker offers to one test item depends on his or her responses to all of the other test items. This violates the “local independence” assumption underlying most existing item response theory (IRT) methods, such as the Rasch model. Here we develop a framework for extending dichotomous IRT models to account for test taking behavior on matching tests. This model separates an individual’s knowledge of the correct responses to the items of a matching test from his or her responses to those items. In addition to developing the matching framework, we derive a number of important properties, including its item response function and score distribution. Finally, we demonstrate through an empirical example that our matching test framework provides a good account of behavior on matching tests.

Online Calibration of Polytomous Items Under the Graded Response Model.

Computerized adaptive testing (CAT) is an efficient testing mode, which allows each examinee to answer appropriate items according his or her latent trait level. The implementation of CAT requires a large-scale item pool, and item pool needs to be frequently replenished with new items to ensure test validity and security. Online calibration is a technique to calibrate the parameters of new items in CAT, which seeds new items in the process of answering operational items, and estimates the parameters of new items through the response data of examinees on new items. The most popular estimation methods include one EM cycle method (OEM) and multiple EM cycle method (MEM) under dichotomous item response theory models. This paper extends OEM and MEM to the graded response model (GRM), a popular model for polytomous data with ordered categories. Two simulation studies were carried out to explore online calibration under a variety of conditions, including calibration design, initial item parameter calculation methods, calibration methods, calibration sample size and the number of categories. Results show that the calibration accuracy of new items were acceptable, and which were affected by the interaction of some factors, therefore some conclusions were given.

Statistical Foundations for Computerized Adaptive Testing with Response Revision.

The compatibility of computerized adaptive testing (CAT) with response revision has been a topic of debate in psychometrics for many years. The problem is to provide test takers opportunities to change their answers during the test, while discouraging deceptive strategies from their side and preserving the statistical efficiency of the traditional CAT. The estimating approach proposed in Wang et al. (Stat Sin 27(4):1987-2010, 2017), based on the nominal response model, allows test takers to provide more than one answer to each item during the test, which they all contribute to the interim and final ability estimation. This approach is here reformulated, extended to incorporate a larger class of polytomous and dichotomous item response theory models, and investigated with simulation studies under different test-taking strategies.

A Posterior Predictive Model Checking Method Assuming Posterior Normality for Item Response Theory.

This study investigated the violation of local independence assumptions within unidimensional item response theory (IRT) models. Bayesian posterior predictive model checking (PPMC) methods are increasingly being used to investigate multidimensionality in IRT models. The current work proposes a PPMC method for evaluating local dependence in IRT models that are estimated using full-information maximum likelihood. The proposed approach, which was termed as "PPMC assuming posterior normality" (PPMC-N), provides a straightforward method to account for parameter uncertainty in model fit assessment. A simulation study demonstrated the comparability of the PPMC-N and the Bayesian PPMC approach in the detection of local dependence in dichotomous IRT models.

Item level diagnostics and model - data fit in item response theory (IRT) using BILOG - MG v3.0 and IRTPRO v3.0 programmes

Item response theory (IRT) is a framework for modeling and analyzing item response data. Item-level modeling gives IRT advantages over classical test theory. The fit of an item score pattern to an item response theory (IRT) models is a necessary condition that must be assessed for further use of item and models that best fit the data. The study investigated item level diagnostic statistics and model- data fit with one-and two- parameter models using IRTPROV3.0 and BILOG- MG V3.0. Ex-post facto design was adopted. The population for the study consisted of 11,538 candidates’ responses who took Type L 2014 Unified Tertiary Matriculation Examination (UTME) Mathematics paper in Akwa Ibom State, Nigeria. The sample of 5,192(45%) responses was randomly selected through stratified sampling technique. BILOG-MG V3.0 and IRTPROV3.0 computer software was used to calibrate the candidates’ responses. Two research questions were raised to guide the study. Pearson’s χ2 and S - χ2 statistics as an item fit index for dichotomous item response theory models were used. The outputs from the two computer software were used to answer the questions. The findings revealed that only 1 item fitted 1- parameter model in BILOG- MG V3.0 and IRTPRO V3.0. Furthermore, the findings revealed that 26 items fitted 2-parameter models when using BILOG-MG V3.0. Five items fitted 2-parameter models in IRTPRO. It was recommended that the use of more than one IRT software programme offers more useful information for the choice of model that fit the data.KEYWORDS: Item Level, Diagnostics, Statistics, Model - Data Fit, Item Response Theory (IRT).

Large Sample Confidence Intervals for Item Response Theory Reliability Coefficients.

In applications of item response theory (IRT), an estimate of the reliability of the ability estimates or sum scores is often reported. However, analytical expressions for the standard errors of the estimators of the reliability coefficients are not available in the literature and therefore the variability associated with the estimated reliability is typically not reported. In this study, the asymptotic variances of the IRT marginal and test reliability coefficient estimators are derived for dichotomous and polytomous IRT models assuming an underlying asymptotically normally distributed item parameter estimator. The results are used to construct confidence intervals for the reliability coefficients. Simulations are presented which show that the confidence intervals for the test reliability coefficient have good coverage properties in finite samples under a variety of settings with the generalized partial credit model and the three-parameter logistic model. Meanwhile, it is shown that the estimator of the marginal reliability coefficient has finite sample bias resulting in confidence intervals that do not attain the nominal level for small sample sizes but that the bias tends to zero as the sample size increases.

The Effects of Test Length and Sample Size on Item Parameters in Item Response Theory

This study investigates the effects of sample size and test length on item-parameter estimation in test development utilizing three unidimensional dichotomous models of item response theory (IRT). For this purpose, a real language test comprised of 50 items was administered to 6,288 students. Data from this test was used to obtain data sets of three test lengths (10, 20, and 30 items) and nine different sample sizes (150, 250, 350, 500, 750, 1,000, 2,000, 3,000 and 5,000 examinees). These data sets were then used to create various research conditions in which test length, sample size, and IRT model variables were manipulated to investigate item parameter estimation accuracy under different conditions. The results suggest that rather than sample size or test length, the combination of these two variables is important and samples of 150, 250, 350, 500, and 750 examinees can be used to estimate item parameters accurately in three unidimensional dichotomous IRT models, depending on test length and model employed.

On the Finiteness of the Weighted Likelihood Estimator of Ability.

The purpose of this note is to focus on the finiteness of the weighted likelihood estimator (WLE) of ability in the context of dichotomous and polytomous item response theory (IRT) models. It is established that the WLE always returns finite ability estimates. This general result is valid for dichotomous (one-, two-, three- and four-parameter logistic) IRT models, the class of polytomous difference models and divide-by-total models, independently of the number of items, the item parameters and the response patterns. Further implications of this result are outlined.

Online Calibration of Polytomous Items Under the Generalized Partial Credit Model.

Online calibration is a technology-enhanced architecture for item calibration in computerized adaptive tests (CATs). Many CATs are administered continuously over a long term and rely on large item banks. To ensure test validity, these item banks need to be frequently replenished with new items, and these new items need to be pretested before being used operationally. Online calibration dynamically embeds pretest items in operational tests and calibrates their parameters as response data are gradually obtained through the continuous test administration. This study extends existing formulas, procedures, and algorithms for dichotomous item response theory models to the generalized partial credit model, a popular model for items scored in more than two categories. A simulation study was conducted to investigate the developed algorithms and procedures under a variety of conditions, including two estimation algorithms, three pretest item selection methods, three seeding locations, two numbers of score categories, and three calibration sample sizes. Results demonstrated acceptable estimation accuracy of the two estimation algorithms in some of the simulated conditions. A variety of findings were also revealed for the interacted effects of included factors, and recommendations were made respectively.

An item analysis of the Conditional Reasoning Test of Aggression.

This manuscript uses item response theory (IRT) to estimate item characteristics of the Conditional Reasoning Test of Aggression (CRT-A). Using a sample size of 5,511 respondents, the present analysis provides an accurate assessment of the capability of the CRT-A to measure latent aggression. The one-parameter logistic (1PL) model, two-parameter logistic (2PL) model, and three-parameter logistic (3PL) model are compared before the item analysis. Results suggest that the 2PL model is the most appropriate dichotomous IRT model for describing the item characteristics of the CRT-A. Potential multdimensionality in the CRT-A is also examined. Results suggest that CRT-A items work as theoretically intended, with the probability of selecting an aggressive response increasing with latent trait levels. Information curves indicate that the CRT-A is best suited for use with individuals who are high on latent aggression. Exploratory analyses include an examination of polytomous IRT models and DIF comparing student and employee respondents. The results have implications for future research using the CRT-A as well as the identification of populations appropriate for measurement using this assessment tool.

A Note on the Equivalence Between Observed and Expected Information Functions With Polytomous IRT Models

The purpose of this note is to study the equivalence of observed and expected (Fisher) information functions with polytomous item response theory (IRT) models. It is established that observed and expected information functions are equivalent for the class of divide-by-total models (including partial credit, generalized partial credit, rating scale, and nominal response models) but not for the class of difference models (including the graded response and modified graded response models). Yet, observed information function remains positive in both classes. Straightforward connections with dichotomous IRT models and further implications are outlined.

Effect of Item Response Theory (IRT) Model Selection on Testlet‐Based Test Equating

The local item independence assumption underlying traditional item response theory (IRT) models is often not met for tests composed of testlets. There are 3 major approaches to addressing this issue: (a) ignore the violation and use a dichotomous IRT model (e.g., the 2‐parameter logistic [2PL] model), (b) combine the interdependent items to form a polytomous item and apply a polytomous IRT model (e.g., the graded response model [GRM]), and (c) apply a model that explicitly takes into account the dependence at the item level (e.g., the testlet response theory [TRT] model). In this study, a simulation was conducted to compare the performance of these 3 approaches on number‐correct score equating when degrees of testlet effect were manipulated. The traditional equipercentile method was used as an evaluation baseline. The results show that the 2PL and the TRT approaches produce comparable results that more closely agree with the results of the equipercentile method than the GRM does. And the number‐correct equating using the 2PL is robust to the violation of local item independence.

Anchor Selection Strategies for DIF Analysis: Review, Assessment, and New Approaches.

Differential item functioning (DIF) indicates the violation of the invariance assumption, for instance, in models based on item response theory (IRT). For item-wise DIF analysis using IRT, a common metric for the item parameters of the groups that are to be compared (e.g., for the reference and the focal group) is necessary. In the Rasch model, therefore, the same linear restriction is imposed in both groups. Items in the restriction are termed the ``anchor items''. Ideally, these items are DIF-free to avoid artificially augmented false alarm rates. However, the question how DIF-free anchor items are selected appropriately is still a major challenge. Furthermore, various authors point out the lack of new anchor selection strategies and the lack of a comprehensive study especially for dichotomous IRT models. This article reviews existing anchor selection strategies that do not require any knowledge prior to DIF analysis, offers a straightforward notation, and proposes three new anchor selection strategies. An extensive simulation study is conducted to compare the performance of the anchor selection strategies. The results show that an appropriate anchor selection is crucial for suitable item-wise DIF analysis. The newly suggested anchor selection strategies outperform the existing strategies and can reliably locate a suitable anchor when the sample sizes are large enough.