38 6 Vol 38 No 6 2014 11 Journal of Jiangxi Normal UniversityNatural Science Nov 2014 1000-5862201406-0593-07 1 2* 1 1001912 100875 i ii DSF DIF DIF B 841 7TP 301 6 A 0 DIF differential item functioning DIF DIF 20 60 DIF 2 3-5 DIF 2 i MH SIBTEST LRDIF STND ii IRT Lord AERA Raju IRT APA NCMELRDIF 4 i 2 ii DIF iii Mantel Mantel- Haenszel SIBTEST iv 1 DIF DIF DIF DIF 2 DIF 20 60 DIF DIF DIF 2014-06-19 31100759 GFA111001 019-105812 2012 CHA12109 1972-
594 2014 DIF a θ DIF D 1 7 G = 0 G = 1 DIF a b j 0 5 DIF GRM b j DIF PCM DIF ω j = 0 DSF ω j > 0 DSF ω j < 0 1 3 DSF DSF DIF DSF DSF DSF j DSF DSF j 1 DSF DSF 2 DIF 1 1 DIF DSF a DSF 2 a DIF DSF 2 DIF DIF IRT DSF 1 2 DSF GRM PCM DSF 2 r J = r - 1 4 0 1 2 DSF 2 3 r = 4 J = 3 Y i 0 1 1 Y 1 ii 1 2 2 Y 2 iii 2 3 Y = 2 iii 2 3 Y = 3 1 2 2 7 DSF DSF j DSF 8 DIF DSF 2 IRT odds Logistic 2 DIF Y = 3 i j i 0 1 ii Y = 1 ii 1 2 2 1 9 GPCM 10 AC-LOR Logistic GRM CU-LOR 2 DSF 2 DSF PY j θ= expdαθ - b j + Gω j DIF 1 + expdαθ - b j + Gω j 2 DSF b j j
6 595 DSF 7 odds ratio DSF 2 11 DSF DSF 1 zλ^ j= λ^ j SEλ^ j DSF SEλ^ DSF DSF SEλ^ 2 j j= m T -2 K A jk D jk + α jb jk C jk A jk + D jk + k = 1 DSF 1 α jb jk + α jc jk 2 m A jk D jk T k 2 1 /2 K = 1 2 2 14 IRT DSF ETS λ j < 0 43 8 DSF 0 43 λ j 0 63 Δb j = b jf - b jr Δb j = 0 DSF DSF λ j > 0 63 Δb j > 0 DSF 2 3 2 Logistic Δb j j DSF 12 Logistic 8 Raju 2 DIF expβ DSF j0 + β j1 X + β j2 G PY j X= 1 + expβ j0 + β j1 X + β j2 G Raju Y j X Δb j < 0 25 G DSF Δb j < 0 50 G = 0 G = 1 β j2 j DSF Δb j > 0 50 DSF DSF β j2 = 0 j IRT DSF DSF β j2 > 0 j DSF 2 Δb j β j2 < 0 j DSF 2 X G 2 DSF 2 3 DSF β j2 G β j2 G β - 2 2 3 1 odds ratio odds DSF ΔR 2 ΔR 2 < 0 10 ratio j DSF 0 10 ΔR 2 0 20 λ DSF ΔR 2 > 0 20 λ 13 λ DSF 15 λ j = ln [ m A jk D jk k = 1 T k m B jk C jk 2 4 3 k = 1 T ] k IRT A jk k j B jk k j BILOGMG3 IRTLRDIF 16 MULTILOG7 DIFAS C jk k j λj zλj 17 D jk k IRT j λ j = 0j 3 DSFλ j > 0 j Logistic odds λ j < 0j ratio β λ j 18 2 2
596 2014 16 DSF 3 DSF DIF 3 1 DSF DIF DSF DSF R D Penfield 19 global DIF DSF global IRT DSF DSF DSF MH DSF DIF SSL 7 DSF DSF net DIF net DSF DIF DSF DSF DIF net Mantel DSF DSF DSF DSF 3 DSF SIBTEST DSF DSF Liu-Aresti common DSF DSF DSF 1 DIF 1 DSF DIF DIF DIF global DIF global DSF odds ratio DIF net DSF DIF global DSF 21 3 3 DSF DIF DIF DSF DSF DSF DIF DIF DSF DIF DSF DSF DIF DIF j DSF DSF DIF DSF DSF DIF DIF DSF DSF DIF DIF DIF net global DSF DSF idsf DIF DSFglobal iidsf DSF DSF net DSF DIF DSF 20 DIF DSF DIF DSF DIF 3 2 DSF DIF DIF net global DSF DIF R D Penfield DSF 19 3 DIF SSLDIF DSF 6 SSL
6 597 4 48% 1 152 52% Logistic IRT 10 DSF 2 2 2 DIFAS 17 DSF common log-ratio λ j λ j Ralf Schwarzer DSF DIF 21 10 4 global net DIF global 1 167 DSF Bonfereoni-adjusted Typed I error rate0 05 /J DIF net Liu-Agresti common Log-odds rationla Z 22 DSF Item step λ i SEλ i Zλ i DSF SIZE DSF FORM DIF EFFECT Item2 Item3 Item4 Item5 Item7 Item8 Item9 Item10 1 0 677 0 225 45 3 003 * 2 0 833 0 124 83 6 673 * 3 1 173 0 213 58 5 492 * 1-1 116 0 160 77-6 942 * 2-0 500 0 124 03-4 031 * 3-0 053 0 263 02-0 0202 LA = 0 873 ZLA= 8 009 * LA = - 0 665 ZLA= - 6 065 * 1-0 599 0 227 96-2 628 * 2-0 415 0 132 98-3 121 * LA = - 0 496 ZLA= - 4 55 * 3-0 614 0 234 26-2 621 * 1-0 686 0 219 43-3 126 * 2-0 442 0 135 86-3 253 * 3-0 070 0 237 58-0 295 1 1 268 0 233 24 5 436 * 2 0 956 0 137 04 6 976 * 3 0 875 0 180 61 4 845 * LA = - 0 430 ZLA= - 3 839 * LA = 0 984 ZLA= 8 708 * 1 0 207 0 249 54 0 830 2 0 269 0 123 48 2 178 * LA = 0 304 ZLA= 2 951 * 3 0 430 0 179 36 2 397 * 1 0 644 0 339 59 1 896 2 0 489 0 139 56 3 504 * 3 0 547 0 176 65 3 097 * 1-1 852 0 283 52-6 532 * 2-1 649 0 142 25-11 592 * 3-1 319 0 248 34-5 311 * LA = 0 522 ZLA= 4 619 * LA = - 1 614 ZLA= - 12 709 * 2 1 2 3 λ i 4 λ i 5 Bonfereoni-adjusted typed I error rate0 05 /J 8 global DSF global 6 net DSF DSF 7 DSF 8 DSF net 3 Logistic SPSSIRT Multilog 10 DSF Logistic DSF DSF 2 7 10 net DIF DSF DIF 2 7 λ 2 IRT 7 10 IRT 9 DSF DIF
598 2014 j λ j j λ j λ 3 4 5 8 DSF λ j 3 Logistic IRT DSF Logistic IRT Item step β j sig ΔR 2 b j FSE b j RSE Δb j SE Z Item1 Item2 Item3 Item4 Item5 Item6 Item7 Item8 Item9 Item10 1-0 023 0 964 0-4 400 23-4 300 44-0 100 35-0 29 2 0 109 0 441 0 01-1 500 07-1 570 10 0 070 09 0 81 3 0 078 0 556 0 01 0 520 09 0 500 07-0 020 08 0 25 1 0 721 0 001 0 52 3 360 14-2 880 19 6 240 17 37 43 * 2 0 835 0 0 70 0 460 09 0 100 08 0 360 09 4 23 * 3 1 260 0 1 59 1 640 15 2 670 13-1 030 14-7 34 * 1-1 070 0 1 14-1 340 08-2 190 13 0 850 11 7 89* 2-0 513 0 0 26 0 510 10 0 060 07 0 450 09 5 21* 3 0 080 0 756 0 01 2 340 22 2 170 11 0 170 17 0 98 1-0 548 0 016 0 30-1 850 05-1 900 10 0 050 08 0 63 2-0 441 0 001 0 19-0 400 05-0 460 05 0 060 05 1 20 3-0 499 0 023 0 25 0 940 10 1 860 04-0 920 08-12 05 * 1-0 658 0 002 0 43-1 760 05-1 860 10 0 100 08 1 27 2-0 427 0 002 0 18-0 310 05 0 370 04-0 680 05-15 01 * 3-0 025 0 914 0 0 990 10 1 080 05-0 090 08-1 14 1 0 120 0 794 0 01-3 860 17-3 830 38-0 030 29-0 10 2 0 046 0 726 0-1 580 07-1 670 10 0 090 09 1 04 3 0 418 0 002 0 17 0 200 08 0 400 37-0 200 27-0 75 1 1 392 0 1 94-2 610 08 1 870 11-4 480 10-46 63 * 2 0 981 0 0 96-0 810 06 0 280 05-1 090 06-19 73 * 3 0 915 0 0 84 0 620 08 1 110 06-0 490 07-6 92 * 1 0 179 0 467 0 03-2 700 09-2 680 18-0 020 14-0 14 2 0 276 0 025 0 08-0 660 07-0 520 07-0 140 07-2 00 * 3 0 471 0 007 0 22-1 080 11 1 340 07-2 420 09-26 21 * 1 0 647 0 058 0 42-3 130 10-2 650 19-0 480 15-3 17 * 2 0 516 0 0 27-0 990 05-0 750 06-0 240 06-4 35 * 3 0 636 0 0 40 0 640 08 0 950 06-0 310 07-4 38 * 1-1 851 0 3 43-1 630 05-2 410 15 0 780 11 6 99 * 2-1 656 0 2 74 0 040 06-0 670 05 0 710 06 12 85 * 3-1 318 0 1 74 1 400 12 0 840 05 0 560 09 6 08 * 23 5 DSF DSF i DSF DIF iidsf DSF DIF DSF 2 DSF DIF DSF DSF DIF 4 2 DIF DSF 2 2 18 iii
6 599 DSF DSF refine the analysis of DIF in polytomous items J Educational MeasurementIssues and Practice 2009 281 38-3 4 49 9Muraki E A generalized partial credit modelapplication of an EM algorithm J Applied Psychological Measurement 1992 162 159-176 DSFj j DIF j 10Wim J van der Linden Ronald K Hambleton Handbook of j j + 1 modern item response theory M New YorkSpringer- DIF Verlag New York Inc 199785-100 j j + 1 11Gattamorta K A A comparison of adjacent categories and cumulative DSF effect estimators D MiamiUniversity of Miami 2009 12Cohen A S Kim S H Baker F B Detection of differential item functioning in the graded response model J Applied Psychological Measurement 1993 174 335-350 DSF DSF DSF 13Penfield R D A nonparametric method for assessing differential step functioning in polytomous items C San Fran- DIF DSF DIF ciscoca 2006 14Hauck W W The large sample variance of the Mantel- Haenszel estimator of a common odds ratio J Biometrics 1979 354 817-819 15Jodoin M G Gierl M J Evaluating type I error and power rates using an effect size measure with the logistic regres- 6 3Holland P W Thayer D T Differential item performance and the Mantel-Haenszel procedure C NJErlbaum 1998129-145 4Penfield R D Camilli G Differential item functioning and item bias C New YorkElsevier 2007125-167 5Zumbo B D Three generations of DIF analysesconsidering where it has been where it is now and where it is going J Language Assessment Quarterly 2007 4 2 223-233 6Penfield R D Assessing differential step functioning in polytomous items using a common odds ratio estimator J Journal of Educational Measurement 2007 44 3 187-210 7Penfield R D Three classes of nonparametric differential step functioning effect estimators J Applied Psychological Measurement 2008 326 480-501 8Penfield R D Gattamorta K Childs R A An NCME instructional module on using differential step functioning to sion procedure for DIF detection J Applied Measure- 1American Educational Research AssociationAmerican ment in Education 2001 144 329-349 Psychological AssociationNational Council on Measure- 16Thissen D IRTLRDIF v 2 0 bsoftware for the computation of the statistics involved in item response theory likement in Education Standards for educational and psychological testing M Washington D CAmerican Psychological Association 1999 Unpublished ms 2 17Penfield R D Computer program exchange DIFASdifferlihood-ratio tests for differential item functioning 2001 J 2003 12 19 ential item functioning analysis system J Applied Psychological Measurement 2005 292 150-151 18Alvarez K Penfield R D Using differential step functioningdsfto refine the analysis of DIF in polytomous i- temsan illustration C Washington D C 2007 19Penfield R D Alvarez K Lee O Using a taxonomy of differential step functioning to improve the interpretation of DIF in polytomous itemsan illustration J Applied Measurement in Education 2009 221 61-78 20Penfield R D Distinguishing between net and global DIF in polytomous items J Journal of Educational Measurement 2010 472 129-149 21Schwarzer R Jerusalem M Generalized self-efficacy scale EB /OL 2014-05-16 www thefindingsgroup com 22Penfield R D Algina J Applying the Liu-Agresti estimator of the cumulative common odds ratio to DIF detection in polytomous items J Journal of Educational Measurement 2003 404 353-370 609
6 Fitz 609 12Cui Yang Gang Wei Chen Fangjiong An estimation-range extended autocorrelation-based frequency estimator J EURASIP Journal on Advances in Signal Processing 2009 10961938 13 J 2011 3781030-1033 14Fu HKam P Y Sample-autocorrelation-function-based frequency estimation of a single sinusoid in AWGN C/ / IEEE 75th Vehicular Technology Conference Yokohama 20121-5 15 D 2012 16 J 2013 375492-496 17Lank G W Reed I S Pollon G E A semicoherent detection and Doppler estimation statistic J Aerospace and Electronic Systems 1973 9 2 151-165 18 4 Ω J 2013 37 6561-564 An Improved Fitz Frequency Estimation Algorithm with Fast Speed and High Accuracy WANG Fang CHEN Yong YE Zhi-qing College of Physics and Communication Electronics Jiangxi Normal University Nanchang Jiangxi 330022 China AbstractFitz frequency estimation algorithm frequency estimation variance in the high SNR is higher and there is a big gap between the CRB An improved Fitz frequency estimation algorithm which first defines the modified autocorrelation function weighted by generalized Kay window has been proposed and then calculates the sum of the weighted phases of the modified autocorrelation function finally gets the frequency estimation of the complex sinusoidal signal in AWGN Computer simulation and analysis shows thatthe frequency estimation variance of improved algorithm decreases about 2 db when the data length is 24 and the signal to noise ratio is 20 db while the calculated a- mount of improved algorithm and original algorithm is about the same In the other words the proposed algorithm to meet the real-time requirement achieves a higher frequency estimation precision Key wordsfrequency estimationautocorrelationreal-timecramer-rao bound 599 23Leighton J P Gierl M J Defining and evaluating models of cognition used in educational measurement to make inferences about examinees thinking processes J Educational MeasurementIssues and Practice 2007 2623-16 The Differential Step Functioning in Polytomous Items LI Mei-juan 1 LIU Hong-yun 2* 1 Beijing Academy of Educational Sciences Beijing 1001912 School of Psychology Beijing Normal University Beijing 100875 AbstractThe research mainly introducesdifferential stepfunctioning DSFhow to play a role in the examination and interpretation of differential item functioningdifeffect There are two parts in the research The first part summarizes and reviews models methods patterns applications result interpretation about DSF abroad which aims to provide some reference for domestic test fairness Using DSF analysis methodology by testing actual data the second part verifies the DIF in test items and differentlevel of steps and takes further analysis to the reason for DIF production Therefore it provides more specific and operational basis for the item review and revision Key wordspolytomous itemsdifferential item functioningdifdifferential step functioning DSF