EASY-DIF

: This study reports the analyses of item-level data from the Initial Operational Test and Evaluation (IOT&E) of the Armed Services Vocational Aptitude Battery (ASVAB) Forms 15, 16, and 17 in order to investigate the occurrence of differential item functioning (DIF) on power subtests of the ASVAB, and to examine the effects of sample size on five indices of DIF. This study used the Camilli's Full Chi-Square, the Mantel-Haenszel Chi-Square and Odds Ration, Lord's Chi-Square, and the Modified Sum-of-Squares as indices of DIF. The results of this study indicate that ASVAB Forms 15, 16, and 17 power subtest items are relatively free of DIF. The General Science subtest tended to have the most DIF items, and DIF items tended to occur more often with gender comparisons, although the occurrence of DIF on the Auto-Shop, Mechanical Comprehension, and Electronics information subtests was minimal. The results also indicated that all five indices were consistent for sample sizes of 500, 1, 000 and 2,000. The intercorrelations between the Mantel-Haenszel Chi-Square and Odds Ratio, and the Full Chi-Square were dramatically reduced in the N + 100 sample size. The results indicated that the Mantel-Haenszel Odds Ratio should probably not be used with sample sizes of 100 cases or less. (sdw)

"As estatísticas englobadas sob a denominação métodos Mantel-Haenszel (MH), por suas simplicidades, baixo custo computacional e bons resultados, são os métodos mais empregadas para detectar o funcionamento diferencial dos itens (DIF). Os métodos MH podem ser usados para detectar o DIF tanto em itens dicotômicos como em itens politômicos, permitindo comparar dois ou mais grupos simultaneamente, e aplicam-se tanto no âmbito da Teoria Clássica dos Testes (TCT) como da Teoria da Resposta ao Item (TRI). Este artigo fornece uma visão completa e integrada dos métodos MH e apresenta um programa que permite aplicar essas estatísticas no estudo do DIF. O programa é gratuito e está disponível em Espanhol, Inglês e Português."

This study elaborates the Rasch differential item functioning (DIF) model formulation under the marginal maximum likelihood estimation context. Also, the Rasch DIF model performance was examined and compared with the Mantel–Haenszel (MH) procedure in small sample and short test length conditions through simulations. The theoretically known relationship of the DIF estimators between the Rasch DIF model and the MH procedure was confirmed. In general, the MH method showed a conservative tendency for DIF detection rates compared with the Rasch DIF model approach. When there is DIF, the z test (when the standard error of the DIF estimator is estimated properly) and the likelihood ratio test in the Rasch DIF model approach showed higher DIF detection rates than the MH chi-square test for sample sizes of 100 to 300 per group and test lengths ranging from 4 to 39. In addition, this study discusses proposed Rasch DIF classification rules that accommodate statistical inference on the direction of DIF.

This study compared three procedures—the Mantel- Haenszel (MH), the simultaneous item bias (SIB), and the logistic regression (LR) procedures—with respect to their Type I error rates and power to detect nonuniform dif ferential item functioning (DIF). Data were simulated to reflect a variety of conditions: The factors manipulated included sample size, ability distribution differences between the focal and the reference groups, proportion of DIF items in the test, DIF effect sizes, and type of item. 384 conditions were studied. Both the SIB and LR proce dures were equally powerful in detecting nonuniform DIF under most conditions. The MH procedure was not very effective in identifying nonuniform DIF items that had disordinal interactions. The Type I error rates were within the expected limits for the MH procedure and were higher than expected for the SIB and LR proce dures ; the SIB results showed an overall increase of approximately 1% over the LR results. Index terms: differential item functioning, logistic regression statistic, Mantel-Haenszel statistic, nondirectional DIF, simulta neous item bias statistic, SIBTEST, Type I error rate, unidirectional DIF.

There has been growing use of ideal point models to develop scales measuring important psychological constructs. For meaningful comparisons across groups, it is important to identify items on such scales that exhibit differential item functioning (DIF). In this study, the authors examined several methods for assessing DIF on polytomous items generated by an ideal point process. Two paradigms (i.e., null hypothesis significance testing [NHST] and effect size quantification) were utilized, and three test statistics (i.e., the log-likelihood ratio [LR], the Akaike information criterion [AIC], and Lord’s chi-square) and two approaches to DIF testing (i.e., the constrained and free baseline methods) were evaluated. In addition, the authors investigated three levels of impact. The results revealed that DIF effect sizes were moderately large for the .50 uniform DIF conditions and small for nonuniform DIF; moreover, the LR test in general yielded the best results. When there was small to moderate impact, the free baseline approach combined with an item linking implementation produced the most satisfactory results.

This study analyzes Differential Item Functioning (DIF) with three combined decision rules and compares the results with the variation of the Mantel-Haenszel procedure (vaMH) proposed by Mazor, Clauser, and Hambleton (1994). One decision rule combines the Mantel-Haenszel procedure (MH) with the Breslow-Day test of trend in odds ratio heterogeneity (BDT), having performed the Bonferroni adjustment, as Randall Penfield proposed. The second uses both MH and BDT without the Bonferroni adjustment. The third combines MH with the Breslow-Day test for homogeneity of the odds ratio without the Bonferroni adjustment. The three decision rules yielded satisfactory results, showed similar power, and none of them detected DIF erroneously. The second rule proved to be the most powerful in the presence of nonuniform DIF. Only in the presence of uniform DIF with the smallest difference of difficulty parameters, was there evidence of vaMH’s superiority.

Analyzing examinees’ responses using cognitive diagnostic models (CDMs) has the advantage of providing diagnostic information. To ensure the validity of the results from these models, differential item functioning (DIF) in CDMs needs to be investigated. In this article, the Wald test is proposed to examine DIF in the context of CDMs. This study explored the effectiveness of the Wald test in detecting both uniform and nonuniform DIF in the DINA model through a simulation study. Results of this study suggest that for relatively discriminating items, the Wald test had Type I error rates close to the nominal level. Moreover, its viability was underscored by the medium to high power rates for most investigated DIF types when DIF size was large. Furthermore, the performance of the Wald test in detecting uniform DIF was compared to that of the traditional Mantel‐Haenszel (MH) and SIBTEST procedures. The results of the comparison study showed that the Wald test was comparable to or outperformed the MH and SIBTEST procedures. Finally, the strengths and limitations of the proposed method and suggestions for future studies are discussed.

When there are no personal consequences associated with test performance for examinees, rapid guessing (RG) is a concern and can differ between subgroups. To date, the impact of differential RG on item-level measurement invariance has received minimal attention. To that end, a simulation study was conducted to examine the robustness of the Mantel-Haenszel (MH), standardization index (STD), and logistic regression (LR) differential item functioning (DIF) procedures to type I error in the presence of differential RG. Sample size, test difficulty, group impact, and differential RG rates were manipulated. Findings revealed that the LR procedure was completely robust to type I errors, while slightly elevated false positive rates (< 1%) were observed for the MH and STD procedures. An applied analysis examining data from the Programme for International Student Assessment showed minimal differences in DIF classifications when comparing data in which RG responses were unfiltered and filtered. These results suggest that large rates of differences in RG rates between subgroups are unassociated with false positive classifications of DIF.

Identifying items with differential item functioning (DIF) in an assessment is a crucial step for achieving equitable measurement. One critical issue that has not been fully addressed with existing studies is how DIF items can be detected when data are multilevel. In the present study, we introduced a Lord's Wald test-based procedure for detecting both uniform and non-uniform DIF with polytomous items in the presence of the ubiquitous multilevel data structure. The proposed approach is a multilevel extension of a two-stage procedure, which identifies anchor items in its first stage and formally evaluates candidate items in the second stage. We applied the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm to estimate multilevel polytomous item response theory (IRT) models and to obtain accurate covariance matrices. To evaluate the performance of the proposed approach, we conducted a preliminary simulation study that considered various conditions to mimic real-world scenarios. The simulation results indicated that the proposed approach has great power for identifying DIF items and well controls the Type I error rate. Limitations and future research directions were also discussed.

Analysing Differential Item Functioning in the problem video game playing test: A pilot study comparing the Spanish and English versions

In this article we present a general approach not relying on item response theory models (non‐IRT) to detect differential item functioning (DIF) in dichotomous items with presence of guessing. The proposed nonlinear regression (NLR) procedure for DIF detection is an extension of method based on logistic regression. As a non‐IRT approach, NLR can be seen as a proxy of detection based on the three‐parameter IRT model which is a standard tool in the study field. Hence, NLR fills a logical gap in DIF detection methodology and as such is important for educational purposes. Moreover, the advantages of the NLR procedure as well as comparison to other commonly used methods are demonstrated in a simulation study. A real data analysis is offered to demonstrate practical use of the method.

The authors demonstrated the empirical relationship between Cohen's chi-square effect size, w, and differential item functioning (DIF), defined as group differences in item response theory (IRT) item difficulty. In Experiment 1, in which the lower asymptote was 0, the authors argued that Cohen's designation of small, medium, and large effects connotes reasonably well for that definition of DIF. In Experiment 2, the lower asymptote of the item response function was raised from 0 to 0.2 and the item discrimination parameter was held to 1.0. Doing so admitted non-crossing nonuniform DIF to the model, violating an underlying assumption of the Mantel–Haenszel procedure that the odds ratio is constant across studied levels of the matching criterion. Smaller difficulty parameter difference resulted, which produced larger effects with an inflation in effect size of about 15%. In Experiment 3, the authors used the 1-parameter logistic model to examine the effect that group differences in the matching criterion has on the apparent effect size. A 1-standard-deviation difference in group means on the matching criterion resulted in an approximately 30% increase in effect size for a given magnitude of DIF. The implications of the inflation of apparent effect size caused by (a) group differences in the matching criterion and (b) choice of IRT model on studies of DIF are discussed.

Simulated data were used to investigate the performance of modified versions of the Mantel-Haenszel method of differential item functioning (DIF) analysis in computerized adaptive tests (CATs). Each simulated examinee received 25 items from a 75-item pool. A three-parameter logistic item response theory (IRT) model was assumed, and examinees were matched on expected true scores based on their CAT responses and estimated item parameters. The CAT-based DIF statistics were found to be highly correlated with DIF statistics based on nonadaptive administration of all 75 pool items and with the true magnitudes of DIF in the simulation. Average DIF statistics and average standard errors also were examined for items with various characteristics. Finally, a study was conducted of the accuracy with which the modified Mantel-Haenszel procedure could identify CAT items with substantial DIF using a classification system now implemented by some testing programs. These additional analyses provided further evidence that the CAT-based DIF procedures performed well. More generally, the results supported the use of IRT-based matching variables in DIF analysis. Index terms: adaptive testing, computerized adaptive testing, differential item functioning, item bias, item response theory.

A Comparison of IRT-based Methods for Examining Differential Item Functioning in TIMSS 2011 Mathematics Subtest

To detect differential item functioning (DIF), Rasch trees search for optimal splitpoints in covariates and identify subgroups of respondents in a data-driven way. To determine whether and in which covariate a split should be performed, Rasch trees use statistical significance tests. Consequently, Rasch trees are more likely to label small DIF effects as significant in larger samples. This leads to larger trees, which split the sample into more subgroups. What would be more desirable is an approach that is driven more by effect size rather than sample size. In order to achieve this, we suggest to implement an additional stopping criterion: the popular Educational Testing Service (ETS) classification scheme based on the Mantel-Haenszel odds ratio. This criterion helps us to evaluate whether a split in a Rasch tree is based on a substantial or an ignorable difference in item parameters, and it allows the Rasch tree to stop growing when DIF between the identified subgroups is small. Furthermore, it supports identifying DIF items and quantifying DIF effect sizes in each split. Based on simulation results, we conclude that the Mantel-Haenszel effect size further reduces unnecessary splits in Rasch trees under the null hypothesis, or when the sample size is large but DIF effects are negligible. To make the stopping criterion easy-to-use for applied researchers, we have implemented the procedure in the statistical software R. Finally, we discuss how DIF effects between different nodes in a Rasch tree can be interpreted and emphasize the importance of purification strategies for the Mantel-Haenszel procedure on tree stopping and DIF item classification.