Modeling effects of differential item functioning in polytomous items

Conventional two-group DIF analysis for dichotomous items is extended to factorial DIF analysis for polytomous items where multiple grouping factors with multiple groups in each are jointly analyzed. By adopting the formulation of general linear models, item parameters across all possible groups are treated as a dependent variable and the grouping factors as independent variables. These item parameters are then reparameterized as a set of grand item parameters and sets of DIF parameters representing main and interaction effects of the factors on the items. Results of simulation studies show that the parameters of the proposed modeling could be satisfactorily recovered. A real data set of 10 polytomous items and 1924 subjects was analyzed. Applications and implications of the proposed modeling are addressed.     

A bibliometric study of differential item functioning

Summary This study presents a bibliometric analysis of scientific output in the area of Differential Item Functioning (DIF), the aim being to offer an overview of research activity in this field and characterise its most important aspects and their evolution over the last quarter of the 20th century, thus providing data regarding the basis on which this activity is being developed at the beginning of the 21st century. The analysis makes use of the Web of Science database, the search being restricted to articles published between 1975 and 2000 and which contain the terms differential item functioning, DIF or item bias. The various analyses focus on the presentation of publication frequencies and percentages, as well as on the application of Bradfords law of scattering and Lotkas law.     

Exploring differential item functioning (DIF) with the Rasch model: a comparison of gender differences on eighth grade science items in the United States and Spain

Traditionally, women and minorities have not been fully represented in science and engineering. Numerous studies have attributed these differences to gaps in science achievement as measured by various standardized tests. Rather than describe mean group differences in science achievement across multiple cultures, this study focused on an in-depth item-level analysis across two countries: Spain and the United States. This study investigated eighth-grade gender differences on science items across the two countries. A secondary purpose of the study was to explore the nature of gender differences using the many-faceted Rasch Model as a way to estimate gender DIF. A secondary analysis of data from the Third International Mathematics and Science Study (TIMSS) was used to address three questions: 1) Does gender DIF in science achievement exist? 2) Is there a relationship between gender DIF and characteristics of the science items? 3) Do the relationships between item characteristics and gender DIF in science items replicate across countries. Participants included 7,087 eight grade students from the United States and 3,855 students from Spain who participated in TIMSS. The Facets program (Linacre and Wright, 1992) was used to estimate gender DIF. The results of the analysis indicate that the content of the item seemed to be related to gender DIF. The analysis also suggests that there is a relationship between gender DIF and item format. No pattern of gender DIF related to cognitive demand was found. The general pattern of gender DIF was similar across the two countries used in the analysis. The strength of item-level analysis as opposed to group mean difference analysis is that gender differences can be detected at the item level, even when no mean differences can be detected at the group level.     

Use of cognitive diagnostic model to study differential item functioning in accommodations

This study explored potential sources of differential item functioning (DIF) among accommodated and nonaccommodated groups by examining skills and cognitive processes hypothesized to underlie student performance on the National Assessment for Educational Progress (NAEP). Out of 53 released NAEP items in 2007 for grade 8, a total of 25 items were flagged as DIF among the four studied groups (nonaccommodated, accommodated with extra time, accommodated with read aloud, and accommodated with small groups) by a generalized logistic regression method. The Reparameterized Unified Model was fit to the same data using a Q-matrix containing 25 skills that included content-, process-, and item-type attributes. The nonaccommodated group yielded the highest averages of attribute mastery probabilities as well as the largest proportion of mastered examinees among all the groups. The three accommodated groups tended to have similar attribute mastery means, with the group accommodated with small groups yielding a larger proportion of mastery examinees when compared to the other two accommodated groups.

     

Substance use disorder symptoms: evidence of differential item functioning by age

This study examined the applicability of substance abuse diagnostic criteria for adolescents, young adults, and adults using the Global Appraisal of Individual Need's Substance Problems Scale (SPS) from 7,408 clients. Rasch analysis was used to: 1) evaluate whether the SPS operationalized a single reliable dimension, and 2) examine the extent to which the severity of each symptom and the overall test functioned the same or differently by age. Rasch analysis indicated that the SPS was unidimensional with a person reliability of .84. Eight symptoms were significantly different between adolescents and adults. Young adult calibrations tended to fall between adolescents and adults. Differential test functioning was clinically negligible for adolescents but resulted in about 7% more adults being classified as high need. These findings have theoretical implications for screening and treatment of adolescents vs. adults. SPS can be used across age groups though age-specific calibrations enable greater precision of measurement.     

Factorial Experiments in Life Testing

This paper discusses procedures for analyzing factorial experiments, where the experiment deals with the life testing of components or equipment. These procedures assume an underlying general distribution of “times-to-failure”, of which the exponential, Weibull, and extreme value distributions are special cases. Statistical tests and confidence procedures are outlined, and an example illustrating the procedure for life-test results of glass capacitors is included. Small sample approximations, which are adequate for practical applications, are given for the proposed procedures. This is shown empirically by generating thousands of life-test experiments on an electronic computer. An empirical sampling investigation is given of the robustness of the proposed procedures. From the sampling results, it is concluded that these techniques are sensitive (non-robust) to departures from the original assumptions on the probability distribution of failure-times. An investigation is also given of a transformation which appears to give robust results. These same techniques carry over exactly to the situation where one is analyzing an array of variance estimates from an underlying normal population.     

Rejecting Outliers in Factorial Designs

In [1] C. Daniel proposed a statistic equivalent to the maximum normed residual for detecting a single bad value in an unreplicated factorial design. The following paper gives a general procedure for calculating critical values of the maximum normed residual and contains revised tables for a two-way layout with one observation per cell, which can be used as a replacement of Table 2 in [l].     

Locating Outliers in Factorial Experiments

The development of experimental designs for constrained mixtttre systems in which the response can be described by a qlladratic model is discussed. It is shown that efficient designs can be constructed from a srtbset of the vertices and centroids of the feasible region. For systems with five or more components, it is recommended that the Wynn and exchange algorithms be used to select a design from the available vertires and centroids. Illustrative examples are included.     

Electric arc modeling of the EAF using differential evolution algorithm

?tore Steel Ltd. makes more than 1400 steel grades. The highest costs in steel production from scrap stems from the electric arc furnace electric energy consumption. Electrical energy is used to produce heat energy generated by the burning arc between the graphite electrodes and steel scrap. In general, the balanced heat input of all electrodes is essential. Based on the input of thermal energy from all electrodes, also the possibility of occurrence of hot and cold spots in the electric arc furnace can be determined. Perception of and the elimination of the unequal heat load of electrodes have a major impact on reducing operating costs and increasing the efficiency of the electric arc furnace production. Most authors have modeled the arc furnace as an electrical equivalent circuit, where the electric arc is modeled using the macroscopic approach. In this paper, the microscopic approach to the electric arc model is described, where a set of equations (electrical neutrality, Dalton law, Saha–Eggert) was solved using differential evolution algorithm. The results of modeling were practically confirmed by measuring electric parameters (voltage, current, active power) during the electric arc furnace operation. In November 2016, the investment in a new electrode controller using implemented logic will be carried out.     

Partial Duplication of Factorial Experiments

Two level factorial and fractional factorial designs are described in which a subset of the treatment combinations are duplicated. The duplicate runs provide an unbiased estimate of the experimental error variance and more reliable estimates of the effects. Several analysis procedures are described and a numerical example is given. Designs for partially duplicated two level factorial and fractional factorial designs are proposed for as many as eleven factors.     

Calibration of multiple-choice questionnaires to assess quantitative indicators

The joint use of two latent factor methods is proposed to assess a measurement instrument for an underlying phenomenon. For this purpose, Rasch analysis is initially used to properly calibrate questionnaires, to discard non informative variables and redundant categories. As a second step, an optimal scaling technique, Nonlinear PCA, is applied to quantify variable categories and to compute a continuous indicator. Specifically, the paper deals with the state of decay of Italian buildings of great architectural and historical interest, which function as a case study . The decay level of the buildings is quantified on the basis of a broad set of observed ordinal variables and the final indicator may be independently used for buildings of future inventory. Overall, similarity and diverse potentiality of the techniques are analyzed and discussed with the purpose of exploring the synergic effect of their combined use.     

Decision-Making in the Analysis of Unreplicated Factorial Designs

Economical and technical reasons, as well as time-related constraints, have contributed considerably to the increasing use of unreplicated factorial designs. Various methods have been proposed in the literature to identify location effects in unreplicated factorial designs, but one method that performs well in all cases has not been found. For this reason, this article presents multiple tests that apply computational methods with different forms. The selected methods are reviewed and their application is justified and illustrated with examples, including one original case study.     

An efficient reduced-order modeling approach for non-linear parametrized partial differential equations

For general non-linear parametrized partial differential equations (PDEs), the standard Galerkin projection is no longer efficient to generate reduced-order models. This is because the evaluation of the integrals involving the non-linear terms has a high computational complexity and cannot be pre-computed. This situation also occurs for linear equations when the parametric dependence is nonaffine. In this paper, we propose an efficient approach to generate reduced-order models for large-scale systems derived from PDEs, which may involve non-linear terms and nonaffine parametric dependence. The main idea is to replace the non-linear and nonaffine terms with a coefficient-function approximation consisting of a linear combination of pre-computed basis functions with parameter-dependent coefficients. The coefficients are determined efficiently by an inexpensive and stable interpolation at some pre-computed points. The efficiency and accuracy of this method are demonstrated on several test cases, which show significant computational savings relative to the standard Galerkin projection reduced-order approach. Copyright © 2008 John Wiley & Sons, Ltd.     

Use of Half-Normal Plots in Interpreting Factorial Two-Level Experiments

Plotting the empirical cumulative distribution of the usual set of orthogonal contrasts computed from a 2 ^p experiment on a special grid may aid in its criticism and interpretation. Bad values, heteroscedasticity, dependence of variance on mean, and some types of defective randomization, all leave characteristic stigmata. The halfnormal plot can be used to estimate the error standard deviation and to make judgments about the reality of the observed effects. An accompanying paper by A. Birnbaum gives some operating characteristics of these judgments. Examples are given of the use of half-normal plots in each of these ways.     

Analysis of Augmented Unreplicated Factorial Designs Repeated in Time

Unreplicated designs are fairly common in industrial applications; however, there is resistance to their use in agricultural science. In the agriculture community, there is still a belief that lack of replication may prevent the experimenter from getting useful conclusions. Nevertheless, sound statistical methods that permit valid comparisons in unreplicated studies are available for many types of designs. The objective of this paper is to present an analysis procedure for unreplicated designs combining typical characteristics found in industrial experimentation (factorial designs augmented with center points) and in agricultural applications (inclusion of control treatments and repeated measurements). We illustrate the method through a real experiment to evaluate the use of sugarcane by‐products in chicken diet. Specifically, it is an unreplicated two‐level factorial design with two additional runs (a center point and a control treatment), with experimental units measured in two periods of time. Replication was initially planned in the case study, but the actual treatment application led to an unreplicated design. The application of the proposed method allows interpretation of the data collected. We conclude that the appropriate use of unreplicated designs in agricultural and biological research may reduce overall costs and lessen the use of in vivo testing. Copyright © 2015 John Wiley & Sons, Ltd.     

Use of Fractional Factorial Designs in Antiviral Drug Studies

Experimental design and analysis is an effective and commonly used tool in scientific investigations and industrial applications. Many successful applications have been reported in engineering domains, such as chemical engineering, electrical engineering, and mechanical engineering. However, few cases have been reported in biological research, particularly in virology study. Antiviral drug combinations are increasingly used to reduce possible drug‐resistant viral mutant and reduce cytotoxicity. Drug combinations have often been reported to have higher efficacy and lower individual drug dosage. However, the combined antiviral drug effect is generally hard to assess. One important reason is due to the complex interactions between biological systems and drug molecules. We report a study using fractional factorial designs to investigate a biological system with Herpes simplex virus type 1 and five antiviral drugs. The experiment uses a novel composite design that consists of a 16‐run fractional factorial design and an 18‐run orthogonal array. The results indicate that two chemical drugs, Ribavirin and Acyclovir, are more effective than three Interferon drugs. Furthermore, significant interactions exist within the Interferon drug group and within the Ribavirin‐Acyclovir chemical drug group, but the interactions between the Interferon group and the chemical group are not significant. These observations have major implications in the understanding of antiviral drug mechanism towards better design of combinatorial antiviral drug therapy. Copyright © 2012 John Wiley & Sons, Ltd.     

Using Individual Factor Information in Fractional Factorial Designs

While literature on constructing efficient experimental designs has been plentiful, how best to incorporate prior information when assigning factors to the columns of a nonregular design has received little attention. Following Li, Zhou, and Zhang (2015 Li, W., Zhou, Q., and Zhang, R. C. (2015), “Effective Designs Based on Individual Word Length Patterns,” Journal of Statistical Planning and Inference, 163, 43–47.[Crossref], [Web of Science ®] , [Google Scholar]), we propose the individual generalized word length pattern (iGWLP) for ranking columns of a nonregular design. Taking examples from the literature of recommended orthogonal arrays, we illustrate how iGWLP helps to identify important differences in the aliasing that is likely otherwise missed. Given the complexity of characterizing partial aliasing for nonregular designs, iGWLP will help practitioners make more informed assignment of factors to columns when using nonregular fractions. We provide theoretical justification of the proposed iGWLP. A theorem is given to relate the proposed iGWLP criterion to the expected bias caused by model misspecifications. We also show that the proposed criterion may lead to designs having better projection properties in the factors considered most likely to be important. Furthermore, we discuss how iGWLP can be used for design selection. We propose a criterion for choosing best designs when the focus is on a small set of important factors, for which the aliasing of effects involving these factors is minimized.