Differential Item Functioning Detection Research Articles

Differential Item Functioning via Robust Scaling.

This paper proposes a method for assessing differential item functioning (DIF) in item response theory (IRT) models. The method does not require pre-specification of anchor items, which is its main virtue. It is developed in two main steps: first by showing how DIF can be re-formulated as a problem of outlier detection in IRT-based scaling and then tackling the latter using methods from robust statistics. The proposal is a redescending M-estimator of IRT scaling parameters that is tuned to flag items with DIF at the desired asymptotic type I error rate. Theoretical results describe the efficiency of the estimator in the absence of DIF and its robustness in the presence of DIF. Simulation studies show that the proposed method compares favorably to currently available approaches for DIF detection, and a real data example illustrates its application in a research context where pre-specification of anchor items is infeasible. The focus of the paper is the two-parameter logistic model in two independent groups, with extensions to other settings considered in the conclusion.

Validation of the Barthel Index in Chinese nursing home residents: an item response theory analysis.

The Barthel Index (BI) is used to standardize the grading of assessments for clinical needs, insurance support, and long-term care resource allocation in China. However, its psychometric properties among nursing home residents remain unclear. Therefore, this study aims to assess and modify the psychometric properties of BI in nursing home residents. A total of 1,402 individuals undergoing evaluation in a nursing home facility in China were included in this study from November 2021 to November 2022. Correlations between items were examined to identify the potential multicollinearity concerns. The unidimensional item response theory (IRT) was used to validate and modify the single structure of BI. Furthermore, the logistic regression/IRT hybrid DIF detection method was conducted to assess differential item functioning (DIF) between the dementia group and the normal group. The pairing of items 5 ("bowl control") and 6 ("bladder control") revealed a local dependence issue, leading to their consolidation. Items 56 (bowel and bladder control) and 9 (mobility) both displayed poor fit indices and underwent category collapsing. Through the application of the generalized partial credit model, the adjusted scale displayed better fit indices, demonstrating a robust discriminative power (DC >1.5) and orderly thresholds. Furthermore, non-uniform DIF was identified in item 2 (bathing) between the dementia group and the normal group. The modified BI demonstrated favorable psychometric properties and proved to be suitable for evaluating nursing home residents experiencing moderate functional impairment, which may provide a precise evaluation for long-term care resource allocation. Future studies could explore integrating supplementary measurements, such as objective indices, to assess a broader spectrum of functional statuses to potentially enhance the limited precision width observed in BI.

Detecting differential item functioning in presence of multilevel data: do methods accounting for multilevel data structure make a DIFference?

Assessment practices are, among other things, concerned with issues of fairness and appropriate score interpretation, in particular when making claims about subgroup differences in performance are of interest. In order to make such claims, a psychometric concept of measurement invariance or differential item functioning (DIF) ought to be considered and met. Over the last decades, researchers have proposed and developed a plethora of methods aimed at detecting DIF. However, DIF detection methods that allow multilevel data structures to be modeled are limited and understudied. In the current study, we evaluated the performance of four methods, including the model-based multilevel Wald and the score-based multilevel Mantel–Haenszel (MH), and two well-established single-level methods, the model-based single-level Lord and the score-based single-level MH. We conducted a simulation study that mimics real-world scenarios. Our results suggested that when data were generated as multilevel, mixed results regarding performances were observed, and not one method consistently outperformed the others. Single-level Lord and multilevel Wald yielded best control of the Type I error rates, in particular in conditions when latent means were generated as equal for the two groups. Power rates were low across all four methods in conditions with small number of between- and within-level units and when small DIF was modeled. However, in those conditions, single-level MH and multilevel MH yielded higher power rates than either single-level Lord or multilevel Wald. This suggests that current practices in detecting DIF should strongly consider adopting one of the more recent methods only in certain contexts as the tradeoff between power and complexity of the method may not warrant a blanket recommendation in favor of a single method. Limitations and future research directions are also discussed.

Investigating Differential Item Functioning of an International Mathematics Competition Items across Gender Groups

Mathematical problem-solving competitions have existed for over a century. Scholars report the gender gap in these competitions. As a result, it is necessary to determine whether any score difference between gender groups is attributable to a genuine difference or is the result of the exam itself. Thus, the current study specifically examined bias in one of the well-known mathematics competitions: the Kangaroo Mathematics competition. Determining the fairness of Kangaroo mathematics competition items across gender groups is crucial for creating accurate comparisons and avoiding unintended construct irrelevant bias. To examine the bias, Differential Item Functioning (DIF) analyses were conducted using Logistic Regression, Mantel-Haenszel, and Item Response Theory Likelihood Ratio Test DIF detection methods. After a series of investigations, out of 336 items, it was concluded that these mathematics items were free of DIF and bias across the gender groups. Further implications were discussed in detail regarding the validity and bias.

A Framework for Detecting Both Main Effect and Interactive DIF in Multidimensional Forced-Choice Assessments

In recent decades, multidimensional forced-choice (MFC) tests have gained widespread popularity in organizational settings due to their effectiveness in reducing response biases. Detecting differential item functioning (DIF) is crucial in developing MFC tests, as it relates to test fairness and validity. However, existing methods appear insufficient for detecting DIF induced by the interaction between multiple covariates. Furthermore, for multi-category, ordered or continuous covariates, existing approaches often dichotomize them using a-priori cutoffs, commonly using the median of the covariates. This may lead to information loss and reduced power in detecting MFC DIF. To address these limitations, we propose a method to identify both main effect DIF and interactive DIF. This method can automatically search for the optimal cutoffs for ordered or continuous covariates without pre-defined cutoffs. We introduce the rationale behind the proposed method and evaluate its performance through three Monte Carlo simulation studies. Results demonstrate that the proposed method effectively identifies various DIF forms in MFC tests, thereby increasing detection power. Finally, we provide an empirical application to illustrate the practical applicability of the proposed method.

A Bayesian Moderated Nonlinear Factor Analysis Approach for DIF Detection under Violation of the Equal Variance Assumption

AbstractResearch has shown that multiple‐indicator multiple‐cause (MIMIC) models can result in inflated Type I error rates in detecting differential item functioning (DIF) when the assumption of equal latent variance is violated. This study explains how the violation of the equal variance assumption adversely impacts the detection of nonuniform DIF and how it can be addressed through moderated nonlinear factor analysis (MNLFA) model via Bayesian estimation approach to overcome limitations from the restrictive assumption. The Bayesian MNLFA approach suggested in this study better control Type I errors by freely estimating latent factor variances across different groups. Our experimentation with simulated data demonstrates that the BMNFA models outperform the existing MIMIC models, in terms of Type I error control as well as parameter recovery. The results suggest that the MNLFA models have the potential to be a superior choice to the existing MIMIC models, especially in situations where the assumption of equal latent variance assumption is not likely to hold.

Bayesian Adaptive Lasso for the Detection of Differential Item Functioning in Graded Response Models

The detection of differential item functioning (DIF) is important in psychological and behavioral sciences. Standard DIF detection methods perform an item-by-item test iteratively, often assuming that all items except the one under investigation are DIF-free. This article proposes a Bayesian adaptive Lasso method to detect DIF in graded response models (GRMs), where the DIF effects for all items can be identified simultaneously. The multiple-group GRMs are specified, and the possible DIF effects for each item are reparameterized using the increment components. Then, a Bayesian adaptive Lasso procedure is developed for parameter estimation, in which DIF effects can be automatically obtained. Our method is evaluated and compared with the commonly used likelihood ratio test method in a simulation study. The results show that our method can recover most model parameters well and has better control of false positive rates in almost all conditions. An application is presented using data from the National Longitudinal Study of Adolescent to Adult Health (Add Health).

Using Regularization to Identify Measurement Bias Across Multiple Background Characteristics: A Penalized Expectation–Maximization Algorithm

Testing for differential item functioning (DIF) has undergone rapid statistical developments recently. Moderated nonlinear factor analysis (MNLFA) allows for simultaneous testing of DIF among multiple categorical and continuous covariates (e.g., sex, age, ethnicity, etc.), and regularization has shown promising results for identifying DIF among many covariates. However, computationally inefficient estimation methods have hampered practical use of the regularized MNFLA method. We develop a penalized expectation–maximization (EM) algorithm with soft- and firm-thresholding to more efficiently estimate regularized MNLFA parameters. Simulation and empirical results show that, compared to previous implementations of regularized MNFLA, the penalized EM algorithm is faster, more flexible, and more statistically principled. This method also yields similar recovery of DIF relative to previous implementations, suggesting that regularized DIF detection remains a preferred approach over traditional methods of identifying DIF.

Detecting uniform differential item functioning for continuous response computerized adaptive testing

Evaluating items for potential differential item functioning (DIF) is an essential step to ensuring measurement fairness. In this article, we focus on a specific scenario, namely, the continuous response, severely sparse, computerized adaptive testing (CAT). Continuous responses items are growingly used in performance-based tasks because they tend to generate more information than traditional dichotomous items. Severe sparsity arises when many items are automatically generated via machine learning algorithms. We propose two uniform DIF detection methods in this scenario. The first is a modified version of the CAT-SIBTEST, a non-parametric method that does not depend on any specific item response theory model assumptions. The second is a regularization method, a parametric, model-based approach. Simulation studies show that both methods are effective in correctly identifying items with uniform DIF. A real data analysis is provided in the end to illustrate the utility and potential caveats of the two methods.

Purification procedures used for the detection of gender DIF: Item bias in a foreign language test

Differential item functioning (DIF) detection was handled based on “Mantel-Haenszel (MH)”, “Simultaneous item bias test (SIBTEST)”, “Lord's chi-square”, “Raju's area” methods when item purification was performed or item purification was not performed using real data in current study. After detecting gender-related DIF, expert opinions were taken for bias study. It is important to conduct the gender bias research in the English test when purification is performed and when purification is not performed, as there were DIF studies, but there were not completely similar bias studies in the literature. The sample of the research consists of 7389 students who took the “Transition from Primary to Secondary Education Exam (TPSEE, referred to as “TEOG” in Turkey)” administered in April 2017. When gender-related DIF analysis was performed with the four methods, the results were found to differ partially. DIF analysis results differed in the different conditions item purification was performed or not. Detection of DIF was indicative of possible bias. In the second stage of the study, the opinions of seven experts were taken for item 11, for which DIF was detected at least at B level based on MH, SIBTEST. As a result of expert opinion, it was found that there was no item bias according to gender in any item in the English test. It is recommended that similar bias studies can be conducted for test developers to be aware of the features that may lead to item bias and to construct unbiased items.

Bayesian inference with spike-and-slab priors for differential item functioning detection in a multiple-group IRT tree model

Group differences have practical implications in analysing data from achievement tests or questionnaires. In the current study, we develop a model that accounts for between-group differences, differential item functioning (DIF), latent factors, and missing item response data simultaneously. Different from most of the present DIF studies where one has to iteratively select anchor items and detect DIF items, we achieve DIF detection and parameter estimation simultaneously by properly reparameterizing model parameters and applying some spike-and-slab priors (Ishwaran & Rao, Spike and slab variable selection: frequentist and Bayesian strategies. Ann Stat. 2005a;33:730–773; Ročková & George, The spike-and-slab LASSO. J Am Stat Assoc. 2018;113:431–444) in Bayesian estimation. Simulation studies are conducted to illustrate the validation of the proposed estimation procedure and the efficiency of DIF detection. The proposed method is further applied to a real dataset for illustration.

Detecting differential item functioning with multiple causes: A comparison of three methods

Differential item functioning (DIF) often arises from multiple sources. Within the context of multidimensional item response theory, this study examined DIF items with varying secondary dimensions using the three DIF methods: SIBTEST, Mantel-Haenszel, and logistic regression. The effect of the number of secondary dimensions on DIF detection rates was investigated with several test conditions such as the percentage of DIF items, item loadings, the correlation between primary and secondary dimensions, and DIF magnitude. Results indicate that both the Mantel–Haenszel and logistic regression procedures performed effectively in detecting DIF when multiple secondary dimensions were present.

Uncovering Differential Item Functioning effects using MIMIC and mediated MIMIC models.

The aim of this study was twofold: first, to examine the presence of bias across gender in a scholastic achievement test named the Academic Achievement Test (AAT) for the Science Track. Second, to understand the underlying mechanism that causes these bias effects by examining the effect of general cognitive ability as a mediator. The sample consisted of 1,300 Saudi high school students randomly selected from a larger pool of 173,133 participants to reduce the effects of excessive power. To examine both goals, the Multiple Indicators Multiple Causes (MIMIC) approach for detecting Differential Item Functioning (DIF) items was used. The results showed that 13 AAT items exhibited DIF effects for different gender groups. In most of these items, male participants were more likely to answer them correctly than their female counterparts. Next, the mediated MIMIC approach was applied to explore possible underlying mechanisms that explain these DIF effects. The results from this study showed that general cognitive ability (i.e., General Aptitude Test - GAT) seems to be a factor that could explain why an AAT item exhibits DIF across gender. It was found that GAT scores fully explain the DIF effect in two AAT items (full mediation). In most other cases, GAT helps account for only a proportion of the DIF effect (partial mediation). The results from this study will help experts improve the quality of their instruments by identifying DIF items and deciding how to revise them, considering the mediator's effect on participants' responses.

Identification of sources of DIF using covariates in patient-reported outcome measures: a simulation study comparing two approaches based on Rasch family models.

When analyzing patient-reported outcome (PRO) data, sources of differential item functioning (DIF) can be multiple and there may be more than one covariate of interest. Hence, it could be of great interest to disentangle their effects. Yet, in the literature on PRO measures, there are many studies where DIF detection is applied separately and independently for each covariate under examination. With such an approach, the covariates under investigation are not introduced together in the analysis, preventing from simultaneously studying their potential DIF effects on the questionnaire items. One issue, among others, is that it may lead to the detection of false-positive effects when covariates are correlated. To overcome this issue, we developed two new algorithms (namely ROSALI-DIF FORWARD and ROSALI-DIF BACKWARD). Our aim was to obtain an iterative item-by-item DIF detection method based on Rasch family models that enable to adjust group comparisons for DIF in presence of two binary covariates. Both algorithms were evaluated through a simulation study under various conditions aiming to be representative of health research contexts. The performance of the algorithms was assessed using: (i) the rates of false and correct detection of DIF, (ii) the DIF size and form recovery, and (iii) the bias in the latent variable level estimation. We compared the performance of the ROSALI-DIF algorithms to the one of another approach based on likelihood penalization. For both algorithms, the rate of false detection of DIF was close to 5%. The DIF size and form influenced the rates of correct detection of DIF. Rates of correct detection was higher with increasing DIF size. Besides, the algorithm fairly identified homogeneous differences in the item threshold parameters, but had more difficulties identifying non-homogeneous differences. Over all, the ROSALI-DIF algorithms performed better than the penalized likelihood approach. Integrating several covariates during the DIF detection process may allow a better assessment and understanding of DIF. This study provides valuable insights regarding the performance of different approaches that could be undertaken to fulfill this aim.

DIF Statistical Inference Without Knowing Anchoring Items

Establishing the invariance property of an instrument (e.g., a questionnaire or test) is a key step for establishing its measurement validity. Measurement invariance is typically assessed by differential item functioning (DIF) analysis, i.e., detecting DIF items whose response distribution depends not only on the latent trait measured by the instrument but also on the group membership. DIF analysis is confounded by the group difference in the latent trait distributions. Many DIF analyses require knowing several anchor items that are DIF-free in order to draw inferences on whether each of the rest is a DIF item, where the anchor items are used to identify the latent trait distributions. When no prior information on anchor items is available, or some anchor items are misspecified, item purification methods and regularized estimation methods can be used. The former iteratively purifies the anchor set by a stepwise model selection procedure, and the latter selects the DIF-free items by a LASSO-type regularization approach. Unfortunately, unlike the methods based on a correctly specified anchor set, these methods are not guaranteed to provide valid statistical inference (e.g., confidence intervals and p-values). In this paper, we propose a new method for DIF analysis under a multiple indicators and multiple causes (MIMIC) model for DIF. This method adopts a minimal L_1 norm condition for identifying the latent trait distributions. Without requiring prior knowledge about an anchor set, it can accurately estimate the DIF effects of individual items and further draw valid statistical inferences for quantifying the uncertainty. Specifically, the inference results allow us to control the type-I error for DIF detection, which may not be possible with item purification and regularized estimation methods. We conduct simulation studies to evaluate the performance of the proposed method and compare it with the anchor-set-based likelihood ratio test approach and the LASSO approach. The proposed method is applied to analysing the three personality scales of the Eysenck personality questionnaire-revised (EPQ-R).

Detecting Differential Item Functioning in 2PL Multistage Assessments

The detection of differential item functioning is crucial for the psychometric evaluation of multistage tests. This paper discusses five approaches presented in the literature: logistic regression, SIBTEST, analytical score-based tests, bootstrap score-based tests, and permutation score-based tests. First, using an simulation study inspired by a real-life large-scale educational assessment, we compare the five approaches with respect to their type I error rate and their statistical power. Then, we present an application to an empirical data set. We find that all approaches show type I error rates close to the nominal alpha level. Furthermore, all approaches are shown to be sensitive to uniform and non-uniform DIF effects, with the score-based tests showing the highest power.

Using a Generalized Logistic Regression Method to Detect Differential Item Functioning With Multiple Groups in Cognitive Diagnostic Tests.

Items with the presence of differential item functioning (DIF) will compromise the validity and fairness of a test. Studies have investigated the DIF effect in the context of cognitive diagnostic assessment (CDA), and some DIF detection methods have been proposed. Most of these methods are mainly designed to perform the presence of DIF between two groups; however, empirical situations may contain more than two groups. To date, only a handful of studies have detected the DIF effect with multiple groups in the CDA context. This study uses the generalized logistic regression (GLR) method to detect DIF items by using the estimated attribute profile as matching criteria. A simulation study is conducted to examine the performance of the two GLR methods, GLR-based Wald test (GLR-Wald) and GLR-based likelihood ratio test (GLR-LRT), in detecting the DIF items, the results based on the ordinary Wald test are also reported. Results show that (1) both GLR-Wald and GLR-LRT have more reasonable performance in controlling Type I error rates than the ordinary Wald test in most conditions; (2) the GLR method also produces higher empirical rejection rates than the ordinary Wald test in most conditions; and (3) using the estimated attribute profile as the matching criteria can produce similar Type I error rates and empirical rejection rates for GLR-Wald and GLR-LRT. A real data example is also analyzed to illustrate the application of these DIF detection methods in multiple groups.

Combining Item Purification and Multiple Comparison Adjustment Methods in Detection of Differential Item Functioning

Many of the differential item functioning (DIF) detection methods rely on a principle of testing for DIF item by item, while considering the rest of the items or at least some of them being DIF-free. Computational algorithms of these DIF detection methods involve the selection of DIF-free items in an iterative procedure called item purification. Another aspect is the need to correct for multiple comparisons, which can be done with a number of existing multiple comparison adjustment methods. In this article, we demonstrate that implementation of these two controlling procedures together may have an impact on which items are detected as DIF items. We propose an iterative algorithm combining item purification and adjustment for multiple comparisons. Pleasant properties of the newly proposed algorithm are shown with a simulation study. The method is demonstrated on a real data example.

Comparison of Methods Used in Detection of DIF in Cognitive Diagnostic Models with Traditional Methods: Applications in TIMSS 2011

This study aims to compare the Wald test and likelihood ratio test (LRT) approaches with Classical Test Theory (CTT) and Item Response Theory (IRT) based differential item functioning (DIF) detection methods in the context of cognitive diagnostic models (CDMs), using the TIMSS 2011 dataset as a retrofitting study. CDMs, which have a significant potential when determining the DIF and their contribution to validity, can give confidence under the strong methodological background condition is met. Therefore, it is hoped that this study will contribute to the literature to ensure the correct usage of CDMs and evaluate the compatibility of these new approaches with traditional methods. According to the analysis results, thirty-one items showed differences between the cognitive diagnosis assessments and the traditional methods. The item with the largest DIF was found in the Raju Unsigned Area Measures technique in IRT, whereas the item with the lowest DIF was found in the Wald test technique developed for CDMs. In general, the analyses show that methods not based on CDMs detect more items with DIF, but the Wald test and LRT methods based on CDMs detect fewer items with DIF. This study conducted DIF analyses to determine the test's psychometric properties within the framework of CDMs rather than the source of the bias. Researchers can take the study one step further and make more specific assessments about the items' bias regarding the test structure, test scope, and subgroups. In addition, DIF analyses in this study were carried out using only the gender variable, and researchers can use different variables to conduct studies specific to their purpose.

The Impact of Missing Data on the Performances of DIF Detection Methods

This study analyzed the impact of missing data techniques on performances of two differential item functioning (DIF) detection methods (Mantel Haenszel and Multiple Indicator and Multiple Causes) under missing completely at random missing data mechanism. Percentage of missing data was set at 5% and 15%. Zero imputation, listwise deletion and fractional hot-deck imputation were used to handle missing data. The data set of the study consisted of 17 items in the S12 item cluster of Programme for International Student Assessment (PISA) 2015 science test. Results showed that fractional hot-deck imputation produced the best results in identifying DIF items in all conditions and it had also the closest DIF values to the values obtained from complete data set. It was also found that multiple indicator and multiple causes method was more adversely affected than Mantel Haenszel by the presence of missing data.