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Detection of Differential Item/Test Functioning (DIF/DTF) Using IRT

Detection of Differential Item/Test Functioning (DIF/DTF) Using IRT. Implication and example. Why Study DIF/DTF Using IRT. comparing cultural, ethnic, or gender groups. Meaningful comparisons require that measurement equivalence holds .

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Detection of Differential Item/Test Functioning (DIF/DTF) Using IRT

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  1. Detection of Differential Item/Test Functioning (DIF/DTF) Using IRT Implication and example

  2. Why Study DIF/DTF Using IRT • comparing cultural, ethnic, or gender groups. • Meaningful comparisons require that measurement equivalence holds. • Classical test theory methods confound “bias” with true mean differences; IRT does not. • In IRT terminology, item/test bias is referred (relative) to DIF/DTF

  3. Defining DIF and DTF • DIF • DBF • DTF • BIARS and IMPACT

  4. Examples of DIF Reference group favored at all levels Focal favored at low theta Reference favored at high theta

  5. Example of DTF for 50-Item Test Most focal group members expected to score about 3 points higher

  6. Procedures for Detecting DIF/DTF • DIF • Parametric • Lord’s Chi-Square • Likelihood Ratio Test • Signed and Unsigned Area Methods • Nonparametric • SIBTEST • Mantel-Haenszel • DTF • Parametric • Raju’s DFIT Method • Nonparametric • SIBTEST

  7. Detecting DIF Using Lord's Chi-Square vi is a vector of the differences in the estimated item parameters for the ith item between the focal and reference groups Si is the variance-covariance matrix for the differences in item parameter estimates Lord’s Chi-Square is sensitive to both uniform and nonuniform DIF.

  8. Detecting DIF Using Lord's Chi-Square • Estimate item parameters and covariances for focal and reference groups separately. • Obtain linking constants, A and K, for putting the focal and reference parameters on a common metric. • Compute Lord’s chi-square to identify DIF items using the reference and transformed focal group parameters and their covariances. • Once the DIF items have been identified, reequate the focal and reference group metrics using only the non-DIF items. • Repeat steps 2 through 4 until the same items are identified on consecutive trials. • This procedure is implemented in the program ITERLINK.

  9. Detecting DIF Using Mantel-Haenszel(1959) • Detect Dif of Dichotomous items • Statistics S*2 *2 • 0<=aMH<正无穷 (0为无DIF， >1有利于参照组，<1有利于目标组) • 美国ETS公司做了改进。

  10. Detecting DIF Using Mantel-aenszel(1959) ETS公司根据MH方法计算的结果，把项目分成三种，A（negligible） B(Moderate) C(Large)

  11. Detecting DIF Using LOG Model • 假设：如果focal group 及Reference group能力相等，则有： • DIF LOG Model:

  12. Detecting DIF/DTF Using SIBTEST • Nonparametric method that can be used to examine individual items or groups of items • Assumes only monotonicity • Requires only item response data • Works well with fairly small samples (250+) • Several variations exist • Original SIBTEST: Uniform DIF • Crossing SIBTEST: Nonuniform DIF • PolySIB: Uniform DIF, polytomous data • MultiSIB: Uniform DIF, multiple dimensions

  13. Using SIBTEST • SIBTEST consists of two executable files: • SIBIN.EXE : interactive, creates input file • SIBTEST.EXE : performs DIF/DTF analyses • Choose “E” for either, “R” for reference, or “F” for focal group • Detailed discussion of running SIBIN and SIBTEST is presented on the web

  14. LOG Model (SPSS) • 在一个测验中，某道题男女同学(以“1”表示男，以“0”表示女)答对的情况(以“1”表示答对，以“0”表示答错)及其总分如下表。问该题对于性别来说是否存在DIF(以男生为参照组，以女性为目标组)。

  15. Example (LOG Model)

  16. Example (LOG Model)

  17. Example (LOG Model)

  18. Explore DIF Using EZDIF EZDIF measures DIF with the Mantel- Haensael and the Logistic Regression procedures. Output files: the common odds ratio a the M-Hx2 the X2 significance level the Holland & Thayer (1988) MH D-DIF statistic the standard error of MH D-DIF an ETS effect size code indicating A/B/C empirical ICC, Logistic Regression output

  19. EZDI RESULT • Mantel-Haenszel and Logistic Regression Analysis of • DIFFERENTIAL ITEM FUNCTIONING • Programmed by Niels G. Waller • RFDATA • Reference Group: F:\JANE\rdata • Focal Group: F:\JANE\fdata • Number of Cases in Reference Group: 1000 • Number of Cases in Focal Group: 1000 • Conditioning Levels • 0 5 9 13 16 19 21 24 27 30 33 36 • 4 8 12 15 18 20 23 26 29 32 35 40 • Note: • Alpha > 1.00 favors Reference Group; Alpha < 1.00 favors Focal Group • D-DIF < 0.00 favors Reference Group, D-DIF > 0.00 favors Focal Group

  20. EZDIF RESULT CONT. • Results for Pass Number: 1 • WARNING: Insufficient Data Found in Level: 0 - 4 • SE • ITEM Alpha X^2 P-Value MH D-DIF (MH D-DIF) • CR 1*** 9.734 312.890 0.000 -5.348 0.332 • CR 2*** 10.182 345.163 0.000 -5.453 0.323 • CR 3*** 8.411 225.039 0.000 -5.004 0.363 • CR 4*** 10.235 237.853 0.000 -5.466 0.400 • CR 5*** 10.368 54.170 0.000 -5.496 0.871 • A 6*** 0.697 8.351 0.004 0.848 0.288 • A 7* 0.750 6.431 0.011 0.675 0.260 • A 8 0.858 0.393 0.531 0.361 0.492 • A 9 0.874 0.380 0.538 0.318 3.344 • A 10* 0.747 6.584 0.010 0.686 0.262 • A 11*** 0.715 8.161 0.004 0.788 0.271 • B 12** 0.638 7.256 0.007 1.056 0.381 • A 13 0.799 2.580 0.108 0.526 0.315 • A 14*** 0.689 8.497 0.004 0.874 0.294 • A 15** 0.737 6.668 0.010 0.718 0.272 • A 16** 0.664 7.446 0.006 0.963 0.345 • A 17 0.789 2.795 0.095 0.558 0.320

  21. EZDIF RESULT cont. • Number of Items Purged in Pass 1: 5 • Item Numbers: • 1 • 2 • 3 • 4 • 5 • Results for Pass Number: 2 • WARNING: Insufficient Data Found in Level: 36 - 40 • SE • ITEM Alpha X^2 P-Value MH D-DIF (MH D-DIF) • CR 1*** 11.796 357.628 0.000 -5.799 0.342 • CR 2*** 12.610 394.589 0.000 -5.956 0.337 • CR 3*** 11.565 280.040 0.000 -5.753 0.385 • CR 4*** 14.334 288.049 0.000 -6.257 0.429 • CR 5*** 14.755 74.687 0.000 -6.325 0.897 • A 6 1.000 0.004 0.951 0.000 0.287 • A 7 1.000 0.003 0.956 0.000 0.259 • A 8 1.000 0.010 0.919 0.000 0.478 • A 9 1.000 0.257 0.612 0.000 2.412

  22. EZDIF RESULT cont.

  23. EZDIF RESULT cont. • Empirical Item Characteristic Curves • Item 1 ETS Code = C R • R 0.00 0.10 0.31 0.52 0.78 0.82 0.85 0.95 0.96 1.00 1.00 9.00 • F 0.00 0.00 0.02 0.13 0.21 0.32 0.37 0.52 0.70 0.84 1.00 9.00 • L 0 5 9 13 16 19 21 24 27 30 33 36 • U 4 8 12 15 18 20 23 26 29 32 35 40 • Item 2 ETS Code = C R • R 0.00 0.12 0.25 0.46 0.55 0.64 0.79 0.87 0.96 0.96 1.00 9.00 • F 0.00 0.00 0.00 0.06 0.06 0.22 0.24 0.36 0.58 0.74 0.93 9.00 • L 0 5 9 13 16 19 21 24 27 30 33 36 • U 4 8 12 15 18 20 23 26 29 32 35 40 • Item 3 ETS Code = C R • R 0.00 0.02 0.03 0.15 0.12 0.23 0.40 0.52 0.74 0.84 0.98 9.00 • F 0.00 0.00 0.00 0.01 0.00 0.01 0.06 0.12 0.15 0.37 0.76 9.00 • L 0 5 9 13 16 19 21 24 27 30 33 36 • U 4 8 12 15 18 20 23 26 29 32 35 40

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