Exploring differential item functioning in the SF-36 by demographic, clinical, psychological and social factors in an osteoarthritis population

The SF-36 is a very commonly used generic measure of health outcome in osteoarthritis (OA). An important, but frequently overlooked, aspect of validating health outcome measures is to establish if items work in the same way across subgroup of a population. That is, if respondents have the same 'true' level of outcome, does the item give the same score in different subgroups or is it biased towards one subgroup or another. Differential item functioning (DIF) can identify items that may be biased for one group or another and has been applied to measuring patient reported outcomes. Items may show DIF for different conditions and between cultures, however the SF-36 has not been specifically examined in an osteoarthritis population nor in a UK population. Hence, the aim of the study was to apply the DIF method to the SF-36 for a UK OA population. The sample comprised a community sample of 763 people with OA who participated in the Somerset and Avon Survey of Health. The SF-36 was explored for DIF with respect to demographic, social, clinical and psychological factors. Well developed ordinal regression models were used to identify DIF items. Results: DIF items were found by age (6 items), employment status (6 items), social class (2 items), mood (2 items), hip v knee (2 items), social deprivation (1 item) and body mass index (1 item). Although the impact of the DIF items rarely had a significant effect on the conclusions of group comparisons, in most cases there was a significant change in effect size. Overall, the SF-36 performed well with only a small number of DIF items identified, a reassuring finding in view of the frequent use of the SF-36 in OA. Nevertheless, where DIF items were identified it would be advisable to analyse data taking account of DIF items, especially when age effects are the focus of interest

Nonlocal Hardy type inequalities with optimal constants and remainder terms

Using a groundstate transformation, we give a new proof of the optimal Stein-Weiss inequality of Herbst [\int_{\R^N} \int_{\R^N} \frac{\varphi (x)}{\abs{x}^\frac{\alpha}{2}} I_\alpha (x - y) \frac{\varphi (y)}{\abs{y}^\frac{\alpha}{2}}\dif x \dif y \le \mathcal{C}_{N,\alpha, 0}\int_{\R^N} \abs{\varphi}^2,] and of its combinations with the Hardy inequality by Beckner [\int_{\R^N} \int_{\R^N} \frac{\varphi (x)}{\abs{x}^\frac{\alpha + s}{2}} I_\alpha (x - y) \frac{\varphi (y)}{\abs{y}^\frac{\alpha + s}{2}}\dif x \dif y \le \mathcal{C}_{N, \alpha, 1} \int_{\R^N} \abs{\nabla \varphi}^2,] and with the fractional Hardy inequality [\int_{\R^N} \int_{\R^N} \frac{\varphi (x)}{\abs{x}^\frac{\alpha + s}{2}} I_\alpha (x - y) \frac{\varphi (y)}{\abs{y}^\frac{\alpha + s}{2}}\dif x \dif y \le \mathcal{C}_{N, \alpha, s} \mathcal{D}_{N, s} \int_{\R^N} \int_{\R^N} \frac{\bigabs{\varphi (x) - \varphi (y)}^2}{\abs{x-y}^{N+s}}\dif x \dif y] where (I_\alpha) is the Riesz potential, (0 < \alpha < N) and (0 < s < \min(N, 2)). We also prove the optimality of the constants. The method is flexible and yields a sharp expression for the remainder terms in these inequalities.Comment: 9 page

Anchor selection strategies for DIF analysis: Review, assessment, and new approaches

Differential item functioning (DIF) indicates the violation of the invariance assumption for instance in models based on item response theory (IRT). For item-wise DIF analysis using IRT, a common metric for the item parameters of the groups that are to be compared (e.g. for the reference and the focal group) is necessary. In the Rasch model, therefore, the same linear restriction is imposed in both groups. Items in the restriction are termed the anchor items. Ideally, these items are DIF-free to avoid artificially augmented false alarm rates. However, the question how DIF-free anchor items are selected appropriately is still a major challenge. Furthermore, various authors point out the lack of new anchor selection strategies and the lack of a comprehensive study especially for dichotomous IRT models. This article reviews existing anchor selection strategies that do not require any knowledge prior to DIF analysis, offers a straightforward notation and proposes three new anchor selection strategies. An extensive simulation study is conducted to compare the performance of the anchor selection strategies. The results show that an appropriate anchor selection is crucial for suitable item-wise DIF analysis. The newly suggested anchor selection strategies outperform the existing strategies and can reliably locate a suitable anchor when the sample sizes are large enough

A new method for detecting differential item functioning in the Rasch model

Differential item functioning (DIF) can lead to an unfair advantage or disadvantage for certain subgroups in educational and psychological testing. Therefore, a variety of statistical methods has been suggested for detecting DIF in the Rasch model. Most of these methods are designed for the comparison of pre-specified focal and reference groups, such as males and females. Latent class approaches, on the other hand, allow to detect previously unknown groups exhibiting DIF. However, this approach provides no straightforward interpretation of the groups with respect to person characteristics. Here we propose a new method for DIF detection based on model-based recursive partitioning that can be considered as a compromise between those two extremes. With this approach it is possible to detect groups of subjects exhibiting DIF, which are not prespecified, but result from combinations of observed covariates. These groups are directly interpretable and can thus help understand the psychological sources of DIF. The statistical background and construction of the new method is first introduced by means of an instructive example, and then applied to data from a general knowledge quiz and a teaching evaluation

Anchor methods for DIF detection: A comparison of the iterative forward, backward, constant and all-other anchor class

In the analysis of differential item functioning (DIF) using item response theory (IRT), a common metric is necessary to compare item parameters between groups of test-takers. In the Rasch model, the same restriction is placed on the item parameters in each group in order to define a common metric. However, the question how the items in the restriction - termed anchor items - are selected appropriately is still a major challenge. This article proposes a conceptual framework for categorizing anchor methods: The anchor class to describe characteristics of the anchor methods and the anchor selection strategy to guide how the anchor items are determined. Furthermore, a new anchor class termed the iterative forward anchor class is proposed. Several anchor classes are implemented with two different anchor selection strategies (the all-other and the single-anchor selection strategy) and are compared in an extensive simulation study. The results show that the newly proposed anchor class combined with the single-anchor selection strategy is superior in situations where no prior knowledge about the direction of DIF is available. Moreover, it is shown that the proportion of DIF items in the anchor - rather than the fact whether the anchor includes DIF items at all (termed contamination in previous studies) - is crucial for suitable DIF analysis

The Use of Loglinear Models for Assessing Differential Item Functioning Across Manifest and Latent Examinee Groups

Loglinear latent class models are used to detect differential item functioning (DIF). These models are formulated in such a manner that the attribute to be assessed may be continuous, as in a Rasch model, or categorical, as in Latent Class Mastery models. Further, an item may exhibit DIF with respect to a manifest grouping variable, a latent grouping variable, or both. Likelihood-ratio tests for assessing the presence of various types of DIF are described, and these methods are illustrated through the analysis of a "real world" data set

A new method for detecting differential item functioning in the Rasch model

Differential item functioning (DIF) can lead to an unfair advantage or disadvantage for certain subgroups in educational and psychological testing. Therefore, a variety of statistical methods has been suggested for detecting DIF in the Rasch model. Most of these methods are designed for the comparison of pre-specified focal and reference groups, such as males and females. Latent class approaches, on the other hand, allow to detect previously unknown groups exhibiting DIF. However, this approach provides no straightforward interpretation of the groups with respect to person characteristics. Here we propose a new method for DIF detection based on model-based recursive partitioning that can be considered as a compromise between those two extremes. With this approach it is possible to detect groups of subjects exhibiting DIF, which are not prespecified, but result from combinations of observed ovariates. These groups are directly interpretable and can thus help understand the psychological sources of DIF. The statistical background and construction of the new method is first introduced by means of an instructive example, and then applied to data from a general knowledge quiz and a teaching evaluation.item response theory, IRT, Rasch model, di erential item functioning, DIF, structural change, multidimensionality.

lordif: An R Package for Detecting Differential Item Functioning Using Iterative Hybrid Ordinal Logistic Regression/Item Response Theory and Monte Carlo Simulations

Logistic regression provides a flexible framework for detecting various types of differential item functioning (DIF). Previous efforts extended the framework by using item response theory (IRT) based trait scores, and by employing an iterative process using group--specific item parameters to account for DIF in the trait scores, analogous to purification approaches used in other DIF detection frameworks. The current investigation advances the technique by developing a computational platform integrating both statistical and IRT procedures into a single program. Furthermore, a Monte Carlo simulation approach was incorporated to derive empirical criteria for various DIF statistics and effect size measures. For purposes of illustration, the procedure was applied to data from a questionnaire of anxiety symptoms for detecting DIF associated with age from the Patient--Reported Outcomes Measurement Information System.

MIMIC Models for Uniform and Nonuniform DIF as Moderated Mediation Models.

In this article, the authors describe how multiple indicators multiple cause (MIMIC) models for studying uniform and nonuniform differential item functioning (DIF) can be conceptualized as mediation and moderated mediation models. Conceptualizing DIF within the context of a moderated mediation model helps to understand DIF as the effect of some variable on measurements that is not accounted for by the latent variable of interest. In addition, useful concepts and ideas from the mediation and moderation literature can be applied to DIF analysis: (a) improving the understanding of uniform and nonuniform DIF as direct effects and interactions, (b) understanding the implication of indirect effects in DIF analysis, (c) clarifying the interpretation of the "uniform DIF parameter" in the presence of nonuniform DIF, and (d) probing interactions and using the concept of "conditional effects" to better understand the patterns of DIF across the range of the latent variable