Examination items in financial mathematics: A Bayesian analysis of Differential Item Functioning (DIF) using Item-Response Theory (IRT)
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Differential item functioning
Item analysis
Classical test theory
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Researchers are commonly interested in group comparisons such as comparisons of group means, called impact, or comparisons of individual scores across groups. A meaningful comparison can be made between the groups when there is no differential item functioning (DIF) or differential test functioning (DTF). During the past three decades, much progress has been made in detecting DIF and DTF. However, little research has been conducted on what researchers can do after such detection. This study presents and evaluates a confirmatory multigroup multidimensional item response model to obtain the purified item parameter estimates, person scores, and impact estimates on the primary dimension, controlling for the secondary dimension due to DIF. In addition, the item response model approach was compared with current practices of DIF treatment such as deleting and ignoring DIF items and using multigroup item response models through simulation studies. The authors suggested guidelines for DIF treatment based on the simulation study results.
Differential item functioning
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Polytomous Rasch model
Classical test theory
Item analysis
Test theory
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A differential item functioning (DIF) detection method for testlet-based data was proposed and evaluated in this study. The proposed DIF model is an extension of a bifactor multidimensional item response theory (MIRT) model for testlets. Unlike traditional item response theory (IRT) DIF models, the proposed model takes testlet effects into account, thus estimating DIF magnitude appropriately when a test is composed of testlets. A fully Bayesian estimation method was adopted for parameter estimation. The recovery of parameters was evaluated for the proposed DIF model. Simulation results revealed that the proposed bifactor MIRT DIF model produced better estimates of DIF magnitude and higher DIF detection rates than the traditional IRT DIF model for all simulation conditions. A real data analysis was also conducted by applying the proposed DIF model to a statewide reading assessment data set.
Differential item functioning
Local independence
Item analysis
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Differential item functioning
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Differential item functioning
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The purpose of this study was to determine the three parametric logistic IRT methods in dichotomous and ordinal test items due to differential item functioning using statistical DIF detection methods of SIBTEST, GMH, and LDFA. The study adopted instrumentation research design. The sample consisted of an intact class of 457 Part 3 undergraduate students who registered for EDU 304 (Tests and Measurement). Two research instruments were used to collect data. Data collected were analysed using three statistical DIF detection methods. The result showed that there was a significant difference in the three parameters logistic models in dichotomous and ordinal test items due to differential item functioning. Hence, there existed a high degree of correspondence among the three parameter models in identifying psychometric properties of dichotomous and ordinal test items. Thus, the three parameters logistic models should be used in test development processes to enhance validity of tests. Keywords :Item response theory (IRT), item parameters, dichotomous test, ordinal test, and differential item functioning (DIF)
Differential item functioning
Ordered logit
Ordinal Scale
Item analysis
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This study aims to compare parametric and nonparametric methods based on Item Response Theory in determining differential item functioning in polytomous scales. DIF analysis based on parametric IRT was conducted by using parameters comparison method. For nonparametric IRT analysis, DIF is determined by comparison of area indices pertaining to ICC obtained for reference and focal groups. The Comparisons were conducted on data sets from TIMSS 2011 8th Class students survey where data set pertaining to responses of students to "Attitudes Toward Mathematics" composing of samplings from Turkey and South Korea and it was determined if it incorporated DIF according to country and sex differences. It is observed that parametric and nonparametric methods produce generally similar results for DIF analysis in terms of countries. Nevertheless, DIF analysis results for country based sex groups differed according to techniques based on parametric and nonparametric IRT. Results of the study showed that items incorporating DIF differed as to preferred technique. This indicated importance of choosing the best technique in studies to detect whether scale items incorporates DIF or not.
Polytomous Rasch model
Differential item functioning
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Differential item functioning
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This chapter contains sections titled: Introduction Item characteristic curves Logistic models Fitting item response theory models: tips Test design IRT versus traditional and Guttman scales Polytomous item response theory models Differential item functioning Quantifying differential item functioning Exploring differential item functioning: tips Conclusions Further reading, and software
Differential item functioning
Guttman scale
Polytomous Rasch model
Classical test theory
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