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Determinants of artificial DIF – a study based on simulated polytomous data

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Psychological Test and Assessment Modeling, Volume 57, 2015 (3), 342-376 Determinants of artificial DIF – a study based on simulated polytomous data Curt Hagquist1 & David Andrich2 Abstract A general problem in DIF analyses is that some items favouring one group can induce the appearance of DIF in others favouring the other group. Artificial DIF is used as a concept for describing and explaining that kind of DIF which is an artefact of the procedure for identifying DIF, contrasting it to real DIF which is inherent to an item. The purpose of this paper is to elucidate how real both uniform and non-uniform DIF, referenced to the expected value curve, induce artificial DIF, how this DIF impacts on the person parameter estimates and how different factors affect real and artificial DIF, in particular the alignment of person and item locations. The results show that the same basic principles apply to non-uniform DIF as to uniform DIF, but that the effects on person measurement are less pronounced in non-uniform DIF. Similar to artificial DIF induced by real uniform DIF, the size of artificial DIF is determined by the magnitude of the real non-uniform DIF. In addition, in both uniform and non-uniform DIF, the magnitude of artificial DIF depends on the location of the items relative to the distribution of the persons. In contrast to uniform DIF, the direction of non-uniform real DIF (e.g. favouring one group or the other) is affected by the location of the items relative to the distribution of the persons. The results of the simulation study also confirm that regardless of type of DIF, in the person estimates, artificial DIF never balances out real DIF. Keywords: differential item functioning, uniform, non-uniform, artificial, Rasch models 1 Correspondence concerning this article should be addressed to: Curt Hagquist, PhD, Centre for Research on Child and Adolescent Mental Health, Karlstad University, SE-651 88 Karlstad, Sweden; email: curt.hagquist@kau.se 2 The University of Western Australia Determinants of artificial DIF – a study based on simulated polytomous data 343 Introduction Independent work on requirements of invariance of comparisons for measurement by the Danish mathematician Georg Rasch (1961) incorporated ideas of Thurstone (1928) and Guttman (1950) into a probabilistic response model in which invariance is an integral property. Rasch’s requirements implied that any partition of the data should provide invariant comparisons: The comparison between two stimuli should be independent of which particular individuals were instrumental for the comparison; and it should also be independent of which other stimuli within the considered class were or might also have been compared. Symmetrically, a comparison between two individuals should be independent of which particular stimuli within the class considered were instrumental for comparison; and it should also be independent of which other individuals were also compared, on the same or on some other occasion (p.322; Rasch, 1961). It follows that in order to provide meaningful comparisons of different groups, the comparisons of the stimuli of a measuring instrument have to be invariant, not only along the variable of assessment, but also across the groups to be compared. In this paper instruments refer to tests or questionnaires and therefore the stimuli are referred to as items. Because the variable of assessment is inferred from the assessment by the items, it is generally referred to as a latent variable. Further references to a variable in this paper are understood to refer to such a variable. Lack of invariance of the comparisons of item parameters across sample groups is commonly called differential item functioning (DIF). However, DIF may also be used as a generic term to include the lack of the same kind of invariance along the variable. Analysis of DIF in terms of parameter estimates across sample groups has long been used in Rasch model analyses (Andrich & Kline, 1981; Andrich, 1988), although the terminology has changed and new procedures for detecting DIF have been developed. Among the new procedures for detecting DIF with both Rasch measurement theory and item response theory models, which do not estimate and compare item parameters from different groups, the expected value curve (EVC) of the responses of groups to an item is used. DIF across different groups implies that for the same values of the variable, the EVC of the response to an item for members of the groups are different. If the differences along the variable are homogeneous, then the DIF is referred to as uniform; otherwise it is referred to as non-uniform. Although DIF can be referenced and studied to multiple groups (e.g. DIF across countries), it has generally been focused on two groups (e.g. DIF across genders). In addition, in some cases one of the groups is considered the standard and dominant group, and the other a focal or minority group. In this paper we focus on two groups of equal standing. Although the data are simulated, to simplify the presentation of the results of the study, we refer to one group as Boys, and the other as Girls. For items consisting of only two ordered categories, the expected value is the same as the probability of a positive response. In that case the expected value curve (EVC) is known as the item characteristic curve (ICC). In the context of an analysis of multiple items of a 344 C. Hagquist & D. Andrich test or questionnaire, and as elaborated further in the ICCs of an item for different groups can be estimated by resolving the item so that an item is created in which persons from only one group respond (Andrich and Hagquist, 2012). For consistency with the literature, we continue to use the term ICC for the expected value curve in the case of dichotomous items. However, in the context of polytomous items, and because of its specific relevance to the particular DIF investigated, the more general term EVC will be used. In the dichotomous Rasch model, which has only an item location parameter, the ICCs of all items are parallel. Therefore a difference between ICCs for an item for two groups implies only a difference between the locations of the ICCs. In that case it is possible for responses to fit the ICC for each group statistically even though the locations of the item for the two groups are different. Because the ICCs are parallel, if the responses fit the ICC the differences between the groups are homogeneous across the variable and therefore the DIF is uniform and can be quantified by the difference in the locations for the item between the two groups. On the other hand, it is possible that even after resolving an item and estimating a separate location for the item for each group, the responses do not fit the parallel ICCs. In that case the differences are not homogeneous across the variable and the DIF is non-uniform. Thus, in contrast to uniform DIF, items with nonuniform DIF cannot be resolved while retaining statistical fit to the model. Real and artificial DIF The emphasis in the study of DIF has been on uniform DIF with dichotomous items especially in the context of educational assessment. Over the years a number of different procedures have been used for detecting DIF with dichotomous items of which the Mantel-Haenszel (MH) procedure seems to be the most popular one (Holland & Thayer, 1988; Holland & Wainer, 1993; Osterlind & Everson, 2009). A general problem observed in various DIF analyses, including the MH method, is that some items favouring one group can induce the appearance of DIF in others favouring the other group when in fact no DIF is present. Referring to outcomes based on simulated data, Tennant & Pallant (2007) reported that: “Although not significant, all items showed some level of DIF, indicating how the presence of two items favouring males forced other items to favor females” (p. 1083). They also noted that “ the compensatory DIF may lead the analyst to presume that DIF is cancelling out, but clearly there is a significant impact on individual estimates, and some impact on group estimates” (Tennant & Pallant, 2007, p. 1083). This confusion was compellingly described, but not explained, by Wang & Su (2004) for the MH procedure: “ the M-H-1 tends to declare mistakenly those DIF-free items as DIF items favouring the focal group and to declare mistakenly those DIF items as DIFfree items under these conditions. This tendency makes the total DIF yielded via M-H-1 more or less balanced between groups, when in fact all or most of the DIF items are simulated to favour the reference group” (p. 141). Summarizing the state of the art of DIF Osterlind & Everson (2009) reported similar observations: ‘‘Sometimes, for reasons unknown, calculations of a DIF detection strategy may suggest DIF, where none truly exists’’ (p. 21). Determinants of artificial DIF – a study based on simulated polytomous data 345 Recently these kinds of observations have been explained. Andrich & Hagquist (2012) used the Rasch model for dichotomous responses as the theoretical basis for the MH procedure for the detection of DIF to introduce the concept of artificial DIF: artificial DIF is an artefact of the procedure for identifying it. Contrasting artificial DIF with real DIF which is inherent to an item, Andrich & Hagquist state: “The reason that the MH procedure, as analysed through the Rasch model, generates artificial DIF can be traced to the substitution of the estimates of the person locations for unknown values. In the Rasch model, the person total score is a sufficient statistic for the person parameter estimate, and therefore grouping persons by total scores is equivalent to grouping persons according to their estimates.” (Andrich & Hagquist, 2012, p. 413). Distinguishing between real and artificial DIF is decisive for understanding and interpreting correctly outcomes from DIF analyses. Misidentifying artificial DIF items as having real DIF can give the mistaken impression that the effect of DIF among items where some items favour one group and others favour the other group cancels out in comparing mean estimates of groups. Failure to distinguish between real and artificial DIF may also violate the requirement of invariant properties of an instrument, e.g. by removing or resolving artificial DIF items as if they were real DIF items. Andrich & Hagquist (2012) showed algebraically that real DIF in one item is distributed as artificial DIF across all other items, that the magnitude of artificial DIF is a function of the number of items with real DIF, the direction of the DIF, and the total number of items. They also showed that if an item is resolved to an item for each group, then it no longer induces artificial DIF in other items. As a result, Andrich & Hagquist also showed that the magnitude and direction of DIF in an item could be estimated by resolving the item and providing a new unique item for each group. In addition, they showed that the logical process for identifying all items with real DIF required a sequential process of resolving items, beginning with the item which showed the greatest initial DIF. The process continued till no further DIF, at the level of the power of detection, was present, leaving as identified a set of items with no DIF, a “pure” set. Of course, because the DIF identified is relative to the whole set of items analysed, the process presumes that only a minority of items have real DIF. Andrich & Hagquist (2014) generalised the concept of artificial DIF to polytomous items using the polytomous Rasch model (PRM), a generalisation of the dichotomous Rasch model. However, instead of using the MH procedure to identify items with DIF, which may be real or artificial, they used a two way analysis of variance (ANOVA) of personitem residuals classified by class intervals on the variable and by groups. This procedure has the advantage that it immediately, and simultaneously, provides evidence of general fit of the responses of each item to the model across the variable together with evidence for both uniform and non-uniform DIF. Because the expected values of responses used to calculate residuals from the observed responses are obtained using parameter estimates from the data for each person and item, then as in the MH procedure, the procedure will induce artificial DIF. Andrich and Hagquist demonstrated that the same principles hold for polytomous responses using the ANOVA method for detecting DIF as with the MH procedure for dichotomous items. In particular, resolving items sequentially, beginning with the item with the apparent greatest DIF, successively eliminates artificial DIF in- 346 C. Hagquist & D. Andrich duced by that item in the remaining items, thus permitting the identification and quantification of items with real DIF. Andrich and Hagquist focussed on uniform DIF with polytomous items. Uniform and non-uniform DIF This paper is concerned with studies of the impact of both uniform and non-uniform real DIF in inducing both uniform and non-uniform artificial DIF when assessed using the PRM and the method of ANOVA of residuals and quantified using the resolution of items which show DIF. However, non-uniform DIF for a polytomous item referenced to the EVC in the PRM is more complex than for dichotomous items and is briefly summarized here. As shown formally later in the paper, an item with m + 1 categories has m threshold parameters at which the probability of a response in two adjacent categories is identical. In the dichotomous Rasch model where m + 1 = 2 , there is only one threshold (the item location), and in proficiency assessment, this threshold is commonly referred to as a difficulty. Then the probability of success at the threshold as a function of the value on the variable is simply the ICC. In the dichotomous Rasch model there is a manifest dichotomous response between the categories located at the threshold which is graphically represented by a probability curve for the item, i.e. the ICC. In the PRM there is a latent dichotomous response between pairs of adjacent categories located at each threshold which is modelled by the dichotomous Rasch model (Andrich, 1978). In this case, the modelled latent dichotomous response is referred to as a threshold probability curve. As with the ICCs in the dichotomous Rasch model, the threshold probability curves within and between items in the PRM are also all parallel. However, in contrast to the dichotomous Rasch model, the EVCs for the PRM do not have to be parallel. The slope of the EVC of a polytomous item is a function of the distances between its thresholds – the closer the thresholds, the steeper the slope. Therefore it is possible for different items in the PRM to have nonparallel EVCs yet still fit the model. As a result of this same feature, there are three different kinds of DIF with polytomous responses modelled by the PRM. First, on resolving an item by groups, it can have parallel EVCs located at different points on the variable for different groups in which the responses fit the model for each group. In this case the DIF is uniform and it is the one studied in Andrich and Hagquist (2014). Because the responses fit the model, it can be inferred that the latent threshold probability curves are parallel as required by the PRM. Thus this case is analogous to that of uniform DIF with dichotomous items. Second, on resolving an item by groups, it may have non-parallel EVCs located at the same or different points on the variable for different groups in which the responses again fit the model for each group. In this case, in relation to the EVC, the DIF is non-uniform. Because the responses fit the model, it can be inferred that the latent threshold probability curves are parallel as required by the PRM. Thus this case of non-uniform DIF is analogous to uniform DIF with dichotomous items but has no counterpart with non- Determinants of artificial DIF – a study based on simulated polytomous data 347 uniform DIF in dichotomous items. This is the case studied in this paper – that is, on the resolution of an item for different groups, the responses fit the model and the nonuniform DIF is a function of the relative locations of the thresholds for each group. Third, on resolving an item by groups, it may have parallel or non-parallel EVCs located at the same or different points on the variable for different groups, despite the resolution because of perceived DIF, the responses still do not fit the model for each group. Because the responses do not fit the model, it can be inferred that the latent threshold probability curves are not parallel as required by the PRM. This case is analogous to that of non-uniform DIF in dichotomous items which inevitably implies misfit to the dichotomous Rasch model. We are not concerned with this case in the paper. In summary, the purpose of this paper is to elucidate how real both uniform and nonuniform DIF, referenced to the EVC, induce artificial DIF, how this DIF impacts on the person parameter estimates and how different factors affect real and artificial DIF, in particular the alignment of person and item locations. All examples involve polytomous items, which on resolution of an item by the group, and irrespective of whether the DIF is uniform or non-uniform DIF, show fit to the model. That is, in the case of non-uniform DIF, it concerns the second case above. The importance of this case is analogous to that with uniform DIF discussed in Andrich and Hagquist (2014). Although on resolution of the items by groups the responses may fit the PRM, the parameters of an item are no longer invariant with respect to the two groups. Thus there is a trade-off between the requirement of model fit and the requirement of the invariance of item parameter estimates between the groups. On resolution of the items which improves the fit, and depending on the magnitude of enfocar la importancia de la producción mediática de los niños en su descubrimiento del mundo, sobre todo utilizando el periódico escolar y la imprenta. Asimismo las asociaciones de profesores trabajaron en esta línea e incluso la enseñanza católica se comprometió desde los años sesenta realizando trabajos originales en el marco de la corriente del Lenguaje Total. Páginas 43-48 45 Comunicar, 28, 2007 En el ámbito de los medios, también desde el principio del siglo XX hay ciertas corrientes de conexión. Pero es a lo largo de los años sesenta cuando se constituyeron asociaciones de periodistas apasionados por sus funciones de mediadores, que fomentaron la importancia ciudadana de los medios como algo cercano a los jóvenes, a los profesores y a las familias. Así se crearon la APIJ (Asociación de Prensa Información para la Juventud), la ARPEJ (Asociación Regional de Prensa y Enseñanza para la Juventud), el CIPE (Comité Interprofesional para la Prensa en la Escuela) o la APE (Asociación de Prensa y Enseñanza), todas ellas para la prensa escrita Estas asociaciones fueron precedidas por movimientos surgidos en mayo de 1968, como el CREPAC que, utilizando películas realizadas por periodistas conocidos, aclaraba temas que habían sido manipulados por una televisión demasiado próxima al poder político y realizaba encuentros con grupos de telespectadores. cipio del siglo XX, y nos han legado textos fundadores muy preciados, importantes trabajos de campo y muchos logros educativos y pedagógicos. La educación en medios ha tenido carácter de oficialidad de múltiples maneras, aunque nunca como una enseñanza global. Así la campaña «Operación Joven Telespectador Activo» (JTA), lanzada al final de los años setenta y financiada de manera interministerial para hacer reflexionar sobre las prácticas televisuales de los jóvenes, la creación del CLEMI (Centro de Educación y Medios de Comunicación) en el seno del Ministerio de Educación Nacional en 1983, la creación de la optativa «Cine-audiovisual» en los bachilleratos de humanidades de los institutos en 1984 (primer bachillerato en 1989) y múltiples referencias a la educación de la imagen, de la prensa, de Internet. La forma más visible y rápida de evaluar el lugar de la educación en medios es valorar el lugar que se le ha reservado en los libros de texto del sistema educa- 2. Construir la educación en los medios sin nombrarla El lugar que ocupa la edu- La denominación «educación en medios», que debería cación en los medios es muy ambiguo, aunque las cosas están cambiando recientemente. entenderse como un concepto integrador que reagrupase todos los medios presentes y futuros, es a menudo percibida En principio, en Francia, co- por los «tradicionalistas de la cultura» como una tendencia mo en muchos otros países, la educación en los medios no es hacia la masificación y la pérdida de la calidad. una disciplina escolar a tiempo completo, sino que se ha ido conformado progresivamente a través de experiencias y reflexiones teóricas que han tivo en Francia. Una inmersión sistemática nos permi- permitido implantar interesantes actividades de carác- te constatar que los textos oficiales acogen numerosos ter puntual. Se ha ganado poco a poco el reconoci- ejemplos, citas, sin delimitarla con precisión. miento de la institución educativa y la comunidad es- colar. Podemos decir que ha conquistado un «lugar», 3. ¿Por qué la escuela ha necesitado casi un siglo en el ámbito de la enseñanza transversal entre las dis- para oficilializar lo que cotidianamente se hacía en ciplinas existentes. ella? Sin embargo, la escuela no está sola en esta aspi- Primero, porque las prácticas de educación en me- ración, porque el trabajo en medios es valorado igual- dios han existido antes de ser nombradas así. Recor- mente por el Ministerio de Cultura (campañas de foto- demos que no fue hasta 1973 cuando aparece este grafía, la llamada «Operación Escuelas», presencia de término y que su definición se debe a los expertos del colegios e institutos en el cine ), así como el Minis- Consejo Internacional del Cine y de la Televisión, que terio de la Juventud y Deportes que ha emprendido en el seno de la UNESCO, definen de esta forma: numerosas iniciativas. «Por educación en medios conviene entender el estu- Así, esta presencia de la educación en los medios dio, la enseñanza, el aprendizaje de los medios moder- no ha sido oficial. ¡La educación de los medios no apa- nos de comunicación y de expresión que forman parte rece oficialmente como tal en los textos de la escuela de un dominio específico y autónomo de conocimien- francesa hasta 2006! tos en la teoría y la práctica pedagógicas, a diferencia Este hecho no nos puede dejar de sorprender ya de su utilización como auxiliar para la enseñanza y el que las experiencias se han multiplicado desde el prin- aprendizaje en otros dominios de conocimientos tales Páginas 43-48 46 Comunicar, 28, 2007 como los de matemáticas, ciencias y geografía». A pe- mente en todas las asignaturas. Incluso los nuevos cu- sar de que esta definición ha servido para otorgarle un rrículos de materias científicas en 2006 para los alum- reconocimiento real, los debates sobre lo que abarca y nos de 11 a 18 años hacen referencia a la necesidad no, no están totalmente extinguidos. de trabajar sobre la información científica y técnica y En segundo lugar, porque si bien a la escuela fran- el uso de las imágenes que nacen de ella. cesa le gusta la innovación, después duda mucho en Desde junio de 2006, aparece oficialmente el tér- reflejar y sancionar estas prácticas innovadoras en sus mino «educación en medios» al publicar el Ministerio textos oficiales. Nos encontramos con una tradición de Educación los nuevos contenidos mínimos y las sólidamente fundada sobre una transmisión de conoci- competencias que deben adquirir los jóvenes al salir mientos muy estructurados, organizados en disciplinas del sistema educativo. escolares que se dedican la mayor parte a transmitir Este documento pretende averiguar cuáles son los conocimientos teóricos. La pedagogía es a menudo se- conocimientos y las competencias indispensables que cundaria, aunque los profesores disfrutan de una ver- deben dominar para terminar con éxito su escolaridad, dadera libertad pedagógica en sus clases. El trabajo seguir su formación y construir su futuro personal y crítico sobre los medios que estaba aún en elaboración profesional. Siete competencias diferentes han sido te- necesitaba este empuje para hacerse oficial. nidas en cuenta y en cada una de ellas, el trabajo con Aunque el trabajo de educación en los medios no los medios es reconocido frecuentemente. Para citar esté reconocido como disciplina, no está ausente de un ejemplo, la competencia sobre el dominio de la len- gua francesa definen las capa- cidades para expresarse oral- La metodología elaborada en el marco de la educación en mente que pueden adquirirse con la utilización de la radio e, medios parece incluso permitir la inclinación de la sociedad incluso, se propone fomentar de la información hacia una sociedad del conocimiento, como defiende la UNESCO. En Francia, se necesitaría unir el interés por la lectura a través de la lectura de la prensa. La educación en los medios las fuerzas dispersas en función de los soportes mediáticos y orientarse más hacia la educación en medios que al dominio adquiere pleno derecho y entidad en la sección sexta titulada «competencias sociales y cívi- técnico de los aparatos. cas» que indica que «los alum- nos deberán ser capaces de juz- gar y tendrán espíritu crítico, lo que supone ser educados en los las programaciones oficiales, ya que, a lo largo de un medios y tener conciencia de su lugar y de su influencia estudio de los textos, los documentalistas del CLEMI en la sociedad». han podido señalar más de una centena de referencias a la educación de los medios en el seno de disciplinas 4. Un entorno positivo como el francés, la historia, la geografía, las lenguas, Si nos atenemos a las cifras, el panorama de la las artes plásticas : trabajos sobre las portadas de educación en medios es muy positivo. Una gran ope- prensa, reflexiones sobre temas mediáticos, análisis de ración de visibilidad como la «Semana de la prensa y publicidad, análisis de imágenes desde todos los ángu- de los medios en la escuela», coordinada por el CLE- los, reflexión sobre las noticias en los países europeos, MI, confirma año tras año, después de 17 convocato- información y opinión rias, el atractivo que ejerce sobre los profesores y los Esta presencia se constata desde la escuela mater- alumnos. Concebida como una gran operación de nal (2 a 6 años) donde, por ejemplo, se le pregunta a complementariedad source of circulating FGF-21. The lack of association between circulating and muscle-expressed FGF-21 also suggests that muscle FGF-21 primarily works in a local manner regulating glucose metabolism in the muscle and/or signals to the adipose tissue in close contact to the muscle. Our study has some limitations. The number of subjects is small and some correlations could have been significant with greater statistical power. Another aspect is that protein levels of FGF-21 were not determined in the muscles extracts, consequently we cannot be sure the increase in FGF-21 mRNA is followed by increased protein expression. In conclusion, we show that FGF-21 mRNA is increased in skeletal muscle in HIV patients and that FGF-21 mRNA in muscle correlates to whole-body (primarily reflecting muscle) insulin resistance. These findings add to the evidence that FGF-21 is a myokine and that muscle FGF-21 might primarily work in an autocrine manner. Acknowledgments We thank the subjects for their participation in this study. Ruth Rousing, Hanne Willumsen, Carsten Nielsen and Flemming Jessen are thanked for excellent technical help. The Danish HIV-Cohort is thanked for providing us HIV-related data. 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(2010) Serum FGF21 levels are elevated in association with lipodystrophy, insulin resistance and biomarkers of liver injury in HIV-1-infected patients. AIDS 24: 2629–2637. PLOS ONE | www.plosone.org 7 March 2013 | Volume 8 | Issue 3 | e55632
Determinants of artificial DIF – a study based on simulated polytomous data
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