Analysis of School Context Effects on Differential Item Functioning Using Hierarchical Generalized Linear Models

This article considers and illustrates a strategy to study effects of school context on differential item functioning (DIF) in large-scale assessment. The approach employs a hierarchical generalized linear modeling framework to (a) detect DIF, and (b) identify school-level correlates of the between-group differences in item performance. To illustrate, I investigated (a) whether any of the civic skills items used in the U.S. Civic Education Study of the International Association for the Evaluation of Educational Achievement displayed ethnic–racial DIF, and (b) the extent to which the ethnic–racial DIF was related to teacher-reported opportunity to learn (OTL) major civic-related topics. The results indicated that 3 of the 13 items displayed ethnic–racial DIF. After adjusting for OTL, two of the three flagged items ceased to exhibit DIF. Implications of this approach are discussed.     

Illustration of MIMIC-Model DIF Testing with the Schedule for Nonadaptive and Adaptive Personality

This research provides an example of testing for differential item functioning (DIF) using multiple indicator multiple cause (MIMIC) structural equation models. True/False items on five scales of the Schedule for Nonadaptive and Adaptive Personality (SNAP) were tested for uniform DIF in a sample of Air Force recruits with groups defined by gender and ethnicity. Uniform DIF exists when an item is more easily endorsed for one group than the other, controlling for group mean differences on the variable under study. Results revealed significant DIF for many SNAP items and some effects were quite large. Differentially-functioning items can produce measurement bias and should be either deleted or modeled as if separate items were administered to different groups. Future research should aim to determine whether the DIF observed here holds for other samples.     

Improvement in Detection of Differential Item Functioning Using a Mixture Item Response Theory Model

Usually, methods for detection of differential item functioning (DIF) compare the functioning of items across manifest groups. However, the manifest groups with respect to which the items function differentially may not necessarily coincide with the true source of the bias. It is expected that DIF detection under a model that includes a latent DIF variable is more sensitive to this source of bias. In a simulation study, it is shown that a mixture item response theory model, which includes a latent grouping variable, performs better in identifying DIF items than DIF detection methods using manifest variables only. The difference between manifest and latent DIF detection increases as the correlation between the manifest variable and the true source of the DIF becomes smaller. Different sample sizes, relative group sizes, and significance levels are studied. Finally, an empirical example demonstrates the detection of heterogeneity in a minority sample using a latent grouping variable. Manifest and latent DIF detection methods are applied to a Vocabulary test of the General Aptitude Test Battery (GATB).     

A new approach for differential item functioning detection using Mantel-Haenszel methods. The GMHDIF program

To date, the statistical software designed for assessing differential item functioning (DIF) with Mantel-Haenszel procedures has employed the following statistics: the Mantel-Haenszel chi-square statistic, the generalized Mantel-Haenszel test and the Mantel test. These statistics permit detecting DIF in dichotomous and polytomous items, although they limit the analysis to two groups. On the contrary, this article describes a new approach (and the related software) that, using the generalized Mantel-Haenszel statistic proposed by Landis, Heyman, and Koch (1978), permits DIF assessment in multiple groups, both for dichotomous and polytomous items. The program is free of charge and is available in the following languages: Spanish, English and Portuguese.     

题组项目功能差异（DIF）检验方法的应用探索

篇章形式的阅读测验是一种典型的题组测验,在进行项目功能差异（DIF）检验时需要采用与之匹配的DIF检验方法.基于题组反应模型的DIF检验方法是真正能够处理题组效应的DIF检验方法,能够提供题组中每个项目的DIF效应测量,是题组DIF检验方法中较有理论优势的一种,主要使用的方法是Rasch题组DIF检验方法.该研究将Rasch题组DIF检验方法引入篇章阅读测验的DIF检验中,对某阅读成就测验进行题组DIF检验,结果显示,该测验在内容维度和能力维度的部分子维度上出现了具有显著DIF效应的项目,研究从测验公平的角度对该测验的进一步修改及编制提出了一定的建议.研究中进一步将Rasch题组DIF检验方法与基于传统Rasch模型的DIF检验方法以及变通的题组DIF检验方法的结果进行比较,研究结果体现了进行题组DIF检验的必要性与优越性.研究结果表明,在篇章阅读测验中,能够真正处理题组效应的题组DIF检验方法更加具有理论优势且对于阅读测验的编制与质量的提高具有更重要的意义.     

认知诊断测验中基于信息矩阵的多群组DIF检验

基于改进的Wald统计量,将适用于两群组的DIF检测方法拓展至多群组的项目功能差异（DIF）检验;改进的Wald统计量将分别通过计算观察信息矩阵（Obs）和经验交叉相乘信息矩阵（XPD）而得到。模拟研究探讨了此二者与传统计算方法在多个群组下的DIF检验情况,结果表明：（1）Obs和XPD的一类错误率明显低于传统方法,DINA模型估计下Obs和XPD的一类错误率接近理论水平;（2）样本量和DIF量较大时,Obs和XPD具有与传统Wald统计量大体相同的统计检验力。     

Modeling and Testing Differential Item Functioning in Unidimensional Binary Item Response Models with a Single Continuous Covariate: A Functional Data Analysis Approach

Differential item functioning (DIF), referring to between-group variation in item characteristics above and beyond the group-level disparity in the latent variable of interest, has long been regarded as an important item-level diagnostic. The presence of DIF impairs the fit of the single-group item response model being used, and calls for either model modification or item deletion in practice, depending on the mode of analysis. Methods for testing DIF with continuous covariates, rather than categorical grouping variables, have been developed; however, they are restrictive in parametric forms, and thus are not sufficiently flexible to describe complex interaction among latent variables and covariates. In the current study, we formulate the probability of endorsing each test item as a general bivariate function of a unidimensional latent trait and a single covariate, which is then approximated by a two-dimensional smoothing spline. The accuracy and precision of the proposed procedure is evaluated via Monte Carlo simulations. If anchor items are available, we proposed an extended model that simultaneously estimates item characteristic functions (ICFs) for anchor items, ICFs conditional on the covariate for non-anchor items, and the latent variable density conditional on the covariate—all using regression splines. A permutation DIF test is developed, and its performance is compared to the conventional parametric approach in a simulation study. We also illustrate the proposed semiparametric DIF testing procedure with an empirical example.     

Uncovering Substantive Patterns in Student Responses in International Large-Scale Assessments—Comparing a Latent Class to a Manifest DIF Approach

In this study, we contrast results from two differential item functioning (DIF) approaches (manifest and latent class) by the number of items and sources of items identified as DIF using data from an international reading assessment. The latter approach yielded three latent classes, presenting evidence of heterogeneity in examinee response patterns. It also yielded more DIF items with larger effect sizes and more consistent item response patterns by substantive aspects (e.g., reading comprehension processes and cognitive complexity of items). Based on our findings, we suggest empirically evaluating the homogeneity assumption in international assessments because international populations cannot be assumed to have homogeneous item response patterns. Otherwise, differences in response patterns within these populations may be under-detected when conducting manifest DIF analyses. Detecting differences in item responses across international examinee populations has implications on the generalizability and meaningfulness of DIF findings as they apply to heterogeneous examinee subgroups.     

Random Item IRT Models

It is common practice in IRT to consider items as fixed and persons as random. Both, continuous and categorical person parameters are most often random variables, whereas for items only continuous parameters are used and they are commonly of the fixed type, although exceptions occur. It is shown in the present article that random item parameters make sense theoretically, and that in practice the random item approach is promising to handle several issues, such as the measurement of persons, the explanation of item difficulties, and trouble shooting with respect to DIF. In correspondence with these issues, three parts are included. All three rely on the Rasch model as the simplest model to study, and the same data set is used for all applications. First, it is shown that the Rasch model with fixed persons and random items is an interesting measurement model, both, in theory, and for its goodness of fit. Second, the linear logistic test model with an error term is introduced, so that the explanation of the item difficulties based on the item properties does not need to be perfect. Finally, two more models are presented: the random item profile model (RIP) and the random item mixture model (RIM). In the RIP, DIF is not considered a discrete phenomenon, and when a robust regression approach based on the RIP difficulties is applied, quite good DIF identification results are obtained. In the RIM, no prior anchor sets are defined, but instead a latent DIF class of items is used, so that posterior anchoring is realized (anchoring based on the item mixture). It is shown that both approaches are promising for the identification of DIF.     

Item-focussed Trees for the Identification of Items in Differential Item Functioning

A novel method for the identification of differential item functioning (DIF) by means of recursive partitioning techniques is proposed. We assume an extension of the Rasch model that allows for DIF being induced by an arbitrary number of covariates for each item. Recursive partitioning on the item level results in one tree for each item and leads to simultaneous selection of items and variables that induce DIF. For each item, it is possible to detect groups of subjects with different item difficulties, defined by combinations of characteristics that are not pre-specified. The way a DIF item is determined by covariates is visualized in a small tree and therefore easily accessible. An algorithm is proposed that is based on permutation tests. Various simulation studies, including the comparison with traditional approaches to identify items with DIF, show the applicability and the competitive performance of the method. Two applications illustrate the usefulness and the advantages of the new method.     

汉语词汇测验中的项目功能差异初探

该文运用两种不同的方法对实际的汉语词汇测验中的３６个词汇进行了ＤＩＦ探测。对于１４００多劬的初三学生分别作了男女生与城郊学生间的比较。在男女组分析中检出７个属于一致性ＤＩＦ的项目;对于城郊学生组经两种方法同时确定的ＤＩＦ项目有７个,其中５个是一致性ＤＩＦ,２个是非一致性ＤＩＦ的项目。该文还讨论了产生ＤＩＦ的可能因素。     

Classification of loneliness using the T‐ILS: Is it as simple as it seems?

Student well‐being is a growing issue in higher education, and assessment of the prevalence of conditions as loneliness is therefore important. In higher education and population surveys the Three‐Item Loneliness Scale (T‐ILS) is used increasingly. The T‐ILS is attractive for large multi‐subject surveys, as it consists of only three items (derived from the UCLA Loneliness Scale). Several ways of classifying persons as lonely based on T‐ILS scores exist: dichotomous and trichotomous classification schemes and use of sum scores with rising levels indicating more loneliness. The question remains whether T‐ILS scores are comparable across the different population groups where they are used or across groups of students in the higher education system. The aim was to investigate whether the T‐ILS suffers from differential item functioning (DIF) that might change the loneliness classification among higher education students, using a large sample just admitted to 22 different academy profession degree programs in Denmark (N = 3,757). DIF was tested relative to degree program, age groups and gender. The framework of graphical loglinear Rasch models was applied, as this allows for adjustment of sum scores for uniform DIF, and thus for assessment of whether DIF might change the classification. Two items showed DIF relative to degree program and gender, and adjusting for this DIF changed the classification for some subgroups. The consequences were negligible when using a dichotomous classification and larger when using a trichotomous classification. Therefore, trichotomous classification should be used with caution unless suitable adjustments for DIF are done prior to classification.     

变通的题组项目功能差异检验方法在篇章阅读测验中的应用

篇章形式的阅读测验在语文学科考试与语言能力测试中占有越来越重要的地位。篇章阅读测验是一种典型的题组测验, 因此需要采用能够处理题组效应的统计方法进行分析。在进行项目功能差异(DIF)检验时, 也需要采用与之匹配的DIF检验方法。目前能够处理题组效应的DIF检验方法主要包括变通的题组DIF检验方法和基于题组反应模型的DIF检验方法, 基于题组反应模型的DIF检验方法由于实现过程繁琐, 目前只停留在理论探讨阶段。本研究将变通的题组DIF检验方法及其效应值指标引入篇章阅读测验的DIF检验中, 能够解决篇章阅读测验中DIF检验与测量的问题, 效应值指标能够为如何处理有DIF效应的题组项目提供重要依据。本研究首先选用非题组DIF检验方法与变通的题组DIF检验方法对一份试卷进行DIF检验, 两种方法的比较结果体现了进行题组DIF检验的必要性与优越性, 然后选用变通的题组DIF检验方法中有代表性的四种方法对某阅读成就测验进行题组DIF检验。研究结果表明, 在篇章阅读测验中, 能够处理题组效应的DIF检验方法较传统的DIF检验方法具有较大的优越性。     

ASSESSING THE EFFECT OF COHORT,GENDER, AND RACE ON DIFFERENTIAL ITEM FUNCTIONING (DIF) IN AN ADAPTIVE TEST DESIGNED FOR MULTI-AGE GROUPS

Differential item functioning (DIF) statistics were computed using items from the Peabody Individual Achievement Test (PIAT)-Reading Comprehension subtest for children of the same age group (ages 7 through 12 respectively). The pattern of observed DIF items was determined by comparing each cohort across age groups. Differences related to race and gender were also identified within each cohort. Characteristics of DIF items were identified based on sentence length, vocabulary frequency, and density of a sentence. DIF items were more frequently associated with short sentences than with long sentences. This study explored the potential limitation in the longitudinal use of items in an adaptive test.     

Recursive Partitioning to Identify Potential Causes of Differential Item Functioning in Cross-National Data

Differential item functioning (DIF) assessment is key in score validation. When DIF is present scores may not accurately reflect the construct of interest for some groups of examinees, leading to incorrect conclusions from the scores. Given rising immigration, and the increased reliance of educational policymakers on cross-national assessments such as Programme for International Student Assessment, Trends in International Mathematics and Science Study, and Progress in International Reading Literacy Study (PIRLS), DIF with regard to native language is of particular interest in this context. However, given differences in language and cultures, assuming similar cross-national DIF may lead to mistaken assumptions about the impact of immigration status, and native language on test performance. The purpose of this study was to use model-based recursive partitioning (MBRP) to investigate uniform DIF in PIRLS items across European nations. Results demonstrated that DIF based on mother's language was present for several items on a PIRLS assessment, but that the patterns of DIF were not the same across all nations.     

中国少数民族考生与外国考生HSK成绩的公平性分析

该研究利用项目功能差异(Differential Item Functioning,简称DIF)理论,对HSK考生中不同两个群体——外国人和中国国内的少数民族,进行题目的反应分析。考查HSK的题目是否存在不利于某一群体。具体做法：采用MH和SIBTEST方法检测DIF,利用标准化的离散分析方法和SIBTEST的项目束分析法鉴别DIF的真伪,并寻找造成DIF的原因。由数据分析的结果可知,HSK(初、中等)A卷对对外国考生和中国国内的少数民族考生存在一些有DIF的题目。     

Differential item functioning by sex and race in the Hogan Personality Inventory

The authors examined measurement bias in the Hogan Personality Inventory by investigating differential item functioning (DIF) across sex and two racial groups (Caucasian and Black). The sample consisted of 1,579 Caucasians (1,023 men, 556 women) and 523 Blacks (321 men, 202 women) who were applying for entry-level, unskilled jobs in factories. Although the group mean differences were trivial, more than a third of the items showed DIF by sex (38.4%) and by race (37.3%). A content analysis of potentially biased items indicated that the themes of items displaying DIF were slightly more cohesive for sex than for race. The authors discuss possible explanations for differing clustering tendencies of items displaying DIF and some practical and theoretical implications of DIF in the development and interpretation of personality inventories.     

HYPOTHESIZING DIFFERENTIAL ITEM FUNCTIONING IN GLOBAL EMPLOYEE OPINION SURVEYS

Cross-cultural researchers have not used cultural dimensions to predict when differential item functioning (DIF) in attitude survey items is likely to occur. Predictive hypotheses for items related to supervision on a global corporate survey were developed based on 3 of Hofstede's (1991a) dimensions. In some cases, greater DIF was found on hypothesized items between countries differing on cultural dimensions. Implications for the use of this framework and DIF in examining multinational employee opinion surveys are discussed.     

Do Raven's Colored Progressive Matrices function in the same way in typical and clinical populations? Insights from the intellectual disability field

Standardized tests are used widely in comparative studies of clinical populations, either as dependent or control variables. Yet, one cannot always be sure that the test items measure the same constructs in the groups under study. In the present work, 460 participants with intellectual disability of undifferentiated etiology and 488 typical children were tested using Raven's Colored Progressive Matrices (RCPM). Data were analyzed using binomial logistic regression modeling designed to detect differential item functioning (DIF). Results showed that 12 items out of 36 function differentially between the two groups, but only 2 items exhibit at least moderate DIF. Thus, a very large majority of the items have identical discriminative power and difficulty levels across the two groups. It is concluded that RCPM can be used with confidence in studies comparing participants with and without intellectual disability. In addition, it is suggested that methods for investigating internal bias of tests used in cross-cultural, cross-linguistic or cross-gender comparisons should also be regularly employed in studies of clinical populations, particularly in the field of developmental disability, to show the absence of systematic measurement error (i.e. DIF) affecting item responses.