Stepwise Analysis of Differential Item Functioning Based on Multiple-Group Partial Credit Model

Bock, Muraki, and Pfeiffenberger (1988) proposed a dichotomous item response theory (IRT) model for the detection of differential item functioning (DIF), and they estimated the IRT parameters and the means and standard deviations of the multiple latent trait distributions. This IRT DIF detection method is extended to the partial credit model (Masters, 1982; Muraki, 1993) and presented as one of the multiple-group IRT models. Uniform and non-uniform DIF items and heterogeneous latent trait distributions were used to generate polytomous responses of multiple groups. The DIF method was applied to this simulated data using a stepwise procedure. The standardized DIF measures for slope and item location parameters successfully detected the non-uniform and uniform DIF items as well as recovered the means and standard deviations of the latent trait distributions.This stepwise DIF analysis based on the multiple-group partial credit model was then applied to the National Assessment of Educational Progress (NAEP) writing trend data.     

Logistic Regression and Its Use in Detecting Differential Item Functioning in Polytomous Items

A computer simulation study was conducted to determine the feasibility of using logistic regression procedures to detect differential item functioning (DIF) in polytomous items. One item in a simulated test of 25 items contained DIF; parameters' for that item were varied to create three conditions of nonuniform DIF and one of uniform DIF. Item scores were generated using a generalized partial credit model, and the data were recoded into multiple dichotomies in order to use logistic regression procedures. Results indicate that logistic regression is powerful in detecting most forms of DIF; however, it required large amounts of data manipulation, and interpretation of the results was sometimes difficult. Some logistic regression procedures may be useful in the post hoc analysis of DlF for polytomous items.     

Aggregating Polytomous DIF Results Over Multiple Test Administrations

In typical differential item functioning (DIF) assessments, an item's DIF status is not influenced by its status in previous test administrations. An item that has shown DIF at multiple administrations may be treated the same way as an item that has shown DIF in only the most recent administration. Therefore, much useful information about the item's functioning is ignored. In earlier work, we developed the Bayesian updating (BU) DIF procedure for dichotomous items and showed how it could be used to formally aggregate DIF results over administrations. More recently, we extended the BU method to the case of polytomously scored items. We conducted an extensive simulation study that included four “administrations” of a test. For the single‐administration case, we compared the Bayesian approach to an existing polytomous‐DIF procedure. For the multiple‐administration case, we compared BU to two non‐Bayesian methods of aggregating the polytomous‐DIF results over administrations. We concluded that both the BU approach and a simple non‐Bayesian method show promise as methods of aggregating polytomous DIF results over administrations.     

DIF Detection Using Multiple‐Group Categorical CFA With Minimum Free Baseline Approach

The aim of this study is to assess the efficiency of using the multiple‐group categorical confirmatory factor analysis (MCCFA) and the robust chi‐square difference test in differential item functioning (DIF) detection for polytomous items under the minimum free baseline strategy. While testing for DIF items, despite the strong assumption that all but the examined item are set to be DIF‐free, MCCFA with such a constrained baseline approach is commonly used in the literature. The present study relaxes this strong assumption and adopts the minimum free baseline approach where, aside from those parameters constrained for identification purpose, parameters of all but the examined item are allowed to differ among groups. Based on the simulation results, the robust chi‐square difference test statistic with the mean and variance adjustment is shown to be efficient in detecting DIF for polytomous items in terms of the empirical power and Type I error rates. To sum up, MCCFA under the minimum free baseline strategy is useful for DIF detection for polytomous items.     

Assessing Differential Step Functioning in Polytomous Items Using a Common Odds Ratio Estimator

Many statistics used in the assessment of differential item functioning (DIF) in polytomous items yield a single item-level index of measurement invariance that collapses information across all response options of the polytomous item. Utilizing a single item-level index of DIF can, however, be misleading if the magnitude or direction of the DIF changes across the steps underlying the polytomous response process. A more comprehensive approach to examining measurement invariance in polytomous item formats is to examine invariance at the level of each step of the polytomous item, a framework described in this article as differential step functioning (DSF). This article proposes a nonparametric DSF estimator that is based on the Mantel-Haenszel common odds ratio estimator ( Mantel & Haenszel, 1959 ), which is frequently implemented in the detection of DIF in dichotomous items. A simulation study demonstrated that when the level of DSF varied in magnitude or sign across the steps underlying the polytomous response options, the DSF-based approach typically provided a more powerful and accurate test of measurement invariance than did corresponding item-level DIF estimators.     

A Comparison of Lord's Chi-Square,Raju's Area Measures,and the Likelihood Ratio Test on Detection of Differential Item Functioning

This study compares three procedures for the detection of differential item functioning (DIF) under item response theory (IRT): (a) Lord's chi-square, (b) Raju's area measures, and (c) the likelihood ratio test. Relations among the three procedures and some practical considerations, such as linking metrics and scale purification, are discussed. Data from two forms of a university mathematics placement test were analyzed to examine the congruence among the three procedures. Results indicated that there was close agreement among the three DIF detection procedures.     

Distinguishing between Net and Global DIF in Polytomous Items

In this article, I address two competing conceptions of differential item functioning (DIF) in polytomously scored items. The first conception, referred to as net DIF, concerns between-group differences in the conditional expected value of the polytomous response variable. The second conception, referred to as global DIF, concerns the conditional dependence of group membership and the polytomous response variable. The distinction between net and global DIF is important because different DIF evaluation methods are appropriate for net and global DIF; no currently available method is universally the best for detecting both net and global DIF. Net and global DIF definitions are presented under two different, yet compatible, modeling frameworks: a traditional item response theory (IRT) framework, and a differential step functioning (DSF) framework. The theoretical relationship between the IRT and DSF frameworks is presented. Available methods for evaluating net and global DIF are described, and an applied example of net and global DIF is presented.     

Logistic Discriminant Function Analysis for DIF Identification of Polytomously Scored Items

The purpose of this article is to present logistic discriminant function analysis as a means of differential item functioning (DIF) identification of items that are polytomously scored. The procedure is presented with examples of a DIF analysis using items from a 27-item mathematics test which includes six open-ended response items scored polytomously. The results show that the logistic discriminant function procedure is ideally suited for DIF identification on nondichotomously scored test items. It is simpler and more practical than polytomous extensions of the logistic regression DIF procedure and appears to fee more powerful than a generalized Mantel-Haenszelprocedure.     

Detection of Differential Item Functioning with Nonlinear Regression: A Non‐IRT Approach Accounting for Guessing

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.     

Classification Consistency and Accuracy for Complex Assessments Using Item Response Theory

In this article, procedures are described for estimating single-administration classification consistency and accuracy indices for complex assessments using item response theory (IRT). This IRT approach was applied to real test data comprising dichotomous and polytomous items. Several different IRT model combinations were considered. Comparisons were also made between the IRT approach and two non-IRT approaches including the Livingston-Lewis and compound multinomial procedures. Results for various IRT model combinations were not substantially different. The estimated classification consistency and accuracy indices for the non-IRT procedures were almost always lower than those for the IRT procedures.     

Using a Taxonomy of Differential Step Functioning to Improve the Interpretation of DIF in Polytomous Items: An Illustration

The assessment of differential item functioning (DIF) in polytomous items addresses between-group differences in measurement properties at the item level, but typically does not inform which score levels may be involved in the DIF effect. The framework of differential step functioning (DSF) addresses this issue by examining between-group differences in the measurement properties at each step underlying the polytomous response variable. The pattern of the DSF effects across the steps of the polytomous response variable can assume several different forms, and the different forms can have different implications for the sensitivity of DIF detection and the final interpretation of the causes of the DIF effect. In this article we propose a taxonomy of DSF forms, establish guidelines for using the form of DSF to help target and guide item content review and item revision, and provide procedural rules for using the frameworks of DSF and DIF in tandem to yield a comprehensive assessment of between-group measurement equivalence in polytomous items.     

Effect of Unequal Variances in Proficiency Distributions on Type-I Error of the Mantel-Haenszel Chi-square Test for Differential Item Functioning

Empirical studies demonstrated Type-I error (TIE) inflation (especially for highly discriminating easy items) of the Mantel-Haenszel chi-square test for differential item functioning (DIF), when data conformed to item response theory (IRT) models more complex than Rasch, and when IRT proficiency distributions differed only in means. However, no published study manipulated proficiency variance ratio (VR). Data were generated with the three-parameter logistic (3PL) IRT model. Proficiency VRs were 1, 2, 3, and 4. The present study suggests inflation may be greater, and may affect all highly discriminating items (low, moderate, and high difficulty), when IRT proficiency distributions of reference and focal groups differ also in variances. Inflation was greatest on the 21-item test (vs. 41) and 2,000 total sample size (vs. 1,000). Previous studies had not systematically examined sample size ratio. Sample size ratio of 1:1 produced greater TIE inflation than 3:1, but primarily for total sample size of 2,000.     

An Empirical Comparison of DDF Detection Methods for Understanding the Causes of DIF in Multiple-Choice Items

This study compared and illustrated four differential distractor functioning (DDF) detection methods for analyzing multiple-choice items. The log-linear approach, two item response theory-model-based approaches with likelihood ratio tests, and the odds ratio approach were compared to examine the congruence among the four DDF detection methods. Data from a college-level mathematics placement test were analyzed to understand the causes of differential functioning. Results indicated some agreement among the four detection methods. To facilitate practical interpretation of the DDF results, several possible effect size measures were also obtained and compared.     

Item-Bundle DIF Hypothesis Testing: Identifying Suspect Bundles and Assessing Their Differential Functioning

This article proposes two multidimensional IRT model-based methods of selecting item bundles (clusters of not necessarily adjacent items chosen according to some organizational principle) suspected of displaying DIF amplification. The approach embodied in these two methods is inspired by Shealy and Stout's (1993a, 1993b) multidimensional model for DIF. Each bundle selected by these methods constitutes a DIF amplification hypothesis. When SIBTEST (Shealy & Stout, 1993b) confirms DIF amplification in selected bundles, differential bundle functioning (DBF) is said to occur. Three real data examples illustrate the two methods for suspect bundle selection. The effectiveness of the methods is argued on statistical grounds. A distinction between benign and adverse DIF is made. The decision whether flagged DIF items or DBF bundles display benign or adverse DIF/DBF must depend in part on nonstatistical construct validity arguments. Conducting DBF analyses using these methods should help in the identification of the causes of DIF/DBF.     

An NCME Instructional Module on Using Differential Step Functioning to Refine the Analysis of DIF in Polytomous Items

Traditional methods for examining differential item functioning (DIF) in polytomously scored test items yield a single item‐level index of DIF and thus provide no information concerning which score levels are implicated in the DIF effect. To address this limitation of DIF methodology, the framework of differential step functioning (DSF) has recently been proposed, whereby measurement invariance is examined within each step underlying the polytomous response variable. The examination of DSF can provide valuable information concerning the nature of the DIF effect (i.e., is the DIF an item‐level effect or an effect isolated to specific score levels), the location of the DIF effect (i.e., precisely which score levels are manifesting the DIF effect), and the potential causes of a DIF effect (i.e., what properties of the item stem or task are potentially biasing). This article presents a didactic overview of the DSF framework and provides specific guidance and recommendations on how DSF can be used to enhance the examination of DIF in polytomous items. An example with real testing data is presented to illustrate the comprehensive information provided by a DSF analysis.     

An NCME Instructional Module on Polytomous Item Response Theory Models

A polytomous item is one for which the responses are scored according to three or more categories. Given the increasing use of polytomous items in assessment practices, item response theory (IRT) models specialized for polytomous items are becoming increasingly common. The purpose of this ITEMS module is to provide an accessible overview of polytomous IRT models. The module presents commonly encountered polytomous IRT models, describes their properties, and contrasts their defining principles and assumptions. After completing this module, the reader should have a sound understating of what a polytomous IRT model is, the manner in which the equations of the models are generated from the model's underlying step functions, how widely used polytomous IRT models differ with respect to their definitional properties, and how to interpret the parameters of polytomous IRT models.     

A Note on Three Statistical Tests in the Logistic Regression DIF Procedure

Although logistic regression became one of the well‐known methods in detecting differential item functioning (DIF), its three statistical tests, the Wald, likelihood ratio (LR), and score tests, which are readily available under the maximum likelihood, do not seem to be consistently distinguished in DIF literature. This paper provides a clarifying note on those three tests when logistic regression is applied for DIF detection.     

Assessing Differential Item Functioning in Direct Writing Assessments: Problems and an Example

The recent emphasis on various types of performance assessments raises questions concerning the differential effects of such assessments on population subgroups. Procedures for detecting differential item functioning (DIF) in data from performance assessments are available but may be hindered by problems that stem from this mode of assessment. Foremost among these are problems related to finding an appropriate matching variable. These problems are discussed and results are presented for three methods for DIF detection in polytomous items using data from a direct writing assessment. The purpose of the study is to examine the effects of using different combinations of internal and external matching variables. The procedures included a generalized Mantel-Haenszel statistic, a technique based on meta-analysis methodology, and logistic discriminant function analysis. In general, the results did not support the use of an external matching criterion and indicated that continued problems may be expected in attempts to assess DIF in performance assessments.     

Trace Lines for Classification Decisions

Referral, placement, and retention decisions were analyzed using item response theory (IRT) to investigate whether classification decisions could be placed on the latent continuum of ability normally associated with test items. A second question pertained to the existence of classification differential item functioning (DIF) for the various decisions. When the decisions were calibrated, the resulting "item" parameters were similar to those that might be expected from conventional test items. For classification DIF analyses, referral decisions for ethnicity were found to be functioning differently for Whites versus non-Whites. Analyzing decisions represents a new unit of analysis for IRT and represents a powerful methodology that could be applied to a variety of new problem types.     

Detecting Local Item Dependence in Polytomous Adaptive Data

A rapidly expanding arena for item response theory (IRT) is in attitudinal and health‐outcomes survey applications, often with polytomous items. In particular, there is interest in computer adaptive testing (CAT). Meeting model assumptions is necessary to realize the benefits of IRT in this setting, however. Although initial investigations of local item dependence have been studied both for polytomous items in fixed‐form settings and for dichotomous items in CAT settings, there have been no publications applying local item dependence detection methodology to polytomous items in CAT despite its central importance to these applications. The current research uses a simulation study to investigate the extension of widely used pairwise statistics, Yen's Q₃ Statistic and Pearson's Statistic X², in this context. The simulation design and results are contextualized throughout with a real item bank of this type from the Patient‐Reported Outcomes Measurement Information System (PROMIS).