Differential Item Functioning Detection Research Articles

Detecting Differential Item Functioning Using Response Time

This study investigated uniform differential item functioning (DIF) detection in response times. We proposed a regression analysis approach with both the working speed and the group membership as independent variables, and logarithm transformed response times as the dependent variable. Effect size measures such as Δ[Formula: see text] and percentage change in regression coefficients in conjunction with the statistical significance tests were used to flag DIF items. A simulation study was conducted to assess the performance of three DIF detection criteria: (a) significance test, (b) significance test with Δ[Formula: see text], and (c) significance test with the percentage change in regression coefficients. The simulation study considered factors such as sample sizes, proportion of the focal group in relation to total sample size, number of DIF items, and the amount of DIF. The results showed that the significance test alone was too strict; using the percentage change in regression coefficients as an effect size measure reduced the flagging rate when the sample size was large, but the effect was inconsistent across different conditions; using Δ R2 with significance test reduced the flagging rate and was fairly consistent. The PISA 2018 data were used to illustrate the performance of the proposed method in a real dataset. Furthermore, we provide guidelines for conducting DIF studies with response time.

Enhancing Precision in Predicting Magnitude of Differential Item Functioning: An M-DIF Pretrained Model Approach

Despite numerous studies on the magnitude of differential item functioning (DIF), different DIF detection methods often define effect sizes inconsistently and fail to adequately account for testing conditions. To address these limitations, this study introduces the unified M-DIF model, which defines the magnitude of DIF as the difference in item difficulty parameters between reference and focal groups. The M-DIF model can incorporate various DIF detection methods and test conditions to form a quantitative model. The pretrained approach was employed to leverage a sufficiently representative large sample as the training set and ensure the model’s generalizability. Once the pretrained model is constructed, it can be directly applied to new data. Specifically, a training dataset comprising 144 combinations of test conditions and 144,000 potential DIF items, each equipped with 29 statistical metrics, was used. We adopt the XGBoost method for modeling. Results show that, based on root mean square error (RMSE) and BIAS metrics, the M-DIF model outperforms the baseline model in both validation sets: under consistent and inconsistent test conditions. Across all 360 combinations of test conditions (144 consistent and 216 inconsistent with the training set), the M-DIF model demonstrates lower RMSE in 357 cases (99.2%), illustrating its robustness. Finally, we provided an empirical example to showcase the practical feasibility of implementing the M-DIF model.

The Effectiveness of Mantel Haenszel Log Odds Ratio Method in Detecting Differential Item Functioning Across Different Sample Sizes and Test Lengths Using Real Data Analysis

Objectives: This study aims to determine the effectiveness of the Mantel Haenszel Log Odds Ratio method in detecting Differential Item Functioning (DIF) across gender, while considering variations in sample size and test length. Utilizing real data, the study draws from a sample of tenth-grade students in Jordan who participated in the 2018 PISA International Mathematics Test. Methods: The study employs the experimental methodology, utilizing three levels of sample size and test length: (342, 200, and 100) and (30, 20, and 10), respectively. Nine iterations of the DDFS program were conducted to collect the results, representing nine scenarios resulting from the intersection of sample size and test length levels. Results: The study indicates that variations in sample size and test length significantly affect the Mantel-Hanzel (MH) method. Specifically, it observes an improvement in the MH method’s ability to detect DIF items with larger sample sizes, while maintaining a consistent test length. Conversely, the method’s efficacy declines with longer test lengths, despite maintaining a fixed sample size at a specific level. Conclusion: The study recommends using a large sample size and a short test length for effective detection of DIF items using the MH method.

Differential Item Functioning of the region-based national examination equipment

This research aims to detect Differential Item Functioning (DIF) in the 2014/2015 National Examination Questions in mathematics of junior high schools and equivalent-level schools in the Yogyakarta region as a reference group and the South Kalimantan region as a focus group using the Likelihood Ratio Test (LRT) method, Area Measure Raju, and Lord. A sensitivity analysis was carried out to determine which method was the most sensitive. The data consisted of 5,465 National Examination papers of the students from the two regions, who worked on type A questions. A sample of 1,000 exam papers for each region was established using the simple random sampling (SRS) technique, which was conducted to avoid the effect of sample size. The results of the research showed that by using the LRT method the researchers found 36 items had significant DIF detection, 32 items were significant for Raju Area, and all items had significant DIF detection using Lord. Lord Method is the most sensitive because this method can detect the most DIF items.

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.