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1

Spray, Judith A. Performance of three conditional DIF Statistics in detecting differential item functioning on simulated tests. Iowa City, Iowa: American College Testing Program, 1989.

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2

T, Everson Howard, and Osterlind Steven J, eds. Differential item functioning. 2nd ed. Thousand Oaks: SAGE, 2009.

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3

Osterlind, Steven, and Howard Everson. Differential Item Functioning. 2455 Teller Road, Thousand Oaks California 91320 United States of America: SAGE Publications, Inc., 2009. http://dx.doi.org/10.4135/9781412993913.

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4

Hamilton, Laura S. Exploring differential item functioning on science achievement tests. Los Angeles, CA: Center for the Study of Evaluation, National Center for Research on Evaluation, Standards, and Student Testing, Graduate School of Education & Information Studies, University of California, Los Angeles, 1998.

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5

Schnipke, Deborah L. A comparison of Mantel-Haenszel differential item functioning parameters. Newtown, PA: Law School Admission Council, 2000.

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6

McLeod, Lori Davis. A polynomial logistic regression approach to graphical differential item functioning. Newtown, PA: Law School Admission Council, 2006.

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7

Le, Vi-Nhuan. Identifying differential item functioning on the NELS:88 history achievement test. Los Angeles, CA: Center for the Study of Evaluation, National Center for Research on Evaluation, Standards, and Student Testing, Graduate School of Education & Information Studies, University of California, Los Angeles, 1999.

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8

Roussos, Louis A. A generalized formula for the Mantel-Haenszel differential item functioning parameter. Newtown, PA: Law School Admission Council, 1998.

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9

Roussos, Louis A. A formulation of the Mantel-Haenszel differential item functioning parameter with practical implications. Newtown, PA: Law School Admission Council, 2000.

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10

Lawrence, Ida M. Differential item functioning for males and females on SAT-verbal reading subscore items. New York (Box 886, New York 10101-0886): College Entrance Examination Board, 1988.

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11

Nandakumar, Ratna. CATSIB: A modified SIBTEST procedure to detect differential item functioning in computerized adaptive tests. Newtown, PA: Law School Admission Council, 2001.

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12

Hanson, Bradley A. Application of a polynomial loglinear model to assessing differential item functioning for common items in the common-item equating design. Iowa City, Iowa: ACT, Inc., 1997.

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13

Gamerman, Dani, Tufi M. Soares, and Flávio Gonçalves. Bayesian analysis in item response theory applied to a large-scale educational assessment. Edited by Anthony O'Hagan and Mike West. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198703174.013.22.

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This article discusses the use of a Bayesian model that incorporates differential item functioning (DIF) in analysing whether cultural differences may affect the performance of students from different countries in the various test items which make up the OECD’s Programme for International Student Assessment (PISA) test of mathematics ability. The PISA tests in mathematics and other subjects are used to compare the educational attainment of fifteen-year old students in different countries. The article first provides a background on PISA, DIF and item response theory (IRT) before describing a hierarchical three-parameter logistic model for the probability of a correct response on an individual item to determine the extent of DIF remaining in the mathematics test of 2003. The results of Bayesian analysis illustrate the importance of appropriately accounting for all sources of heterogeneity present in educational testing and highlight the advantages of the Bayesian paradigm when applied to large-scale educational assessment.
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14

W, Holland Paul, Wainer Howard, and Educational Testing Service, eds. Differential item functioning. Hillsdale: Lawrence Erlbaum Associates, 1993.

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15

Holland, Paul W., and Howard Wainer. Differential Item Functioning. Taylor & Francis Group, 2015.

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16

Holland, Paul W. Differential Item Functioning. Routledge, 2012. http://dx.doi.org/10.4324/9780203357811.

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17

W, Holland Paul, Wainer Howard, and Educational Testing Service, eds. Differential item functioning: Theory and practice. Hillsdale, N.J: Lawrence Erlbaum Associates, 1992.

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18

L, Linn Robert, Air Force Human Resources Laboratory., and Universal Energy Systems Inc, eds. Armed Services Vocational Aptitude Battery: Differential item functioning on the high school form. Brooks Air Force Base, Tex: Air Force Human Resources Laboratory, Air Force Systems Command, 1988.

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19

Huang, Chih-hsiang David. Detection of differential item functioning across cultures: Comparing parameter equating, model-based, and Mantel-Haenszel methods with the neo personality inventory. 1995.

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20

Proctor, Kim. Measuring Group Consciousness. Edited by Lonna Rae Atkeson and R. Michael Alvarez. Oxford University Press, 2016. http://dx.doi.org/10.1093/oxfordhb/9780190213299.013.33.

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Although group consciousness is an important concept in explaining political behavior, both theoretical guidance on how to measure group consciousness and empirical consensus regarding its operationalization are lacking. This has the potential to lead to both diverging results and inaccurate empirical conclusions, which greatly limits the ability to understand the role that group consciousness plays in politics. Using data from Pew’s 2013 “Survey of LGBT Americans,” this analysis provides a foundation for measuring group consciousness using item response theory (IRT). Through an examination of dimensionality, monotonicity, model fit, and differential item functioning, the results demonstrate that many assumptions about measuring group consciousness have been incorrect. Further, the findings suggest that previous conclusions about subgroup differences may be the result of survey bias, rather than actual between-group differences. Moving forward, scholars of political behavior should use IRT to measure latent constructs.
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