Vol. 38 No Journal of Jiangxi Normal University Natural Science Nov DIF differential item functioning

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1 38 6 Vol 38 No Journal of Jiangxi Normal UniversityNatural Science Nov * i ii DSF DIF DIF B 841 7TP A 0 DIF differential item functioning DIF DIF DIF 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 DIF DIF DIF GFA CHA

2 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 < 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 DSF 2 3 r = 4 J = 3 Y i Y 1 ii Y 2 iii 2 3 Y = 2 iii 2 3 Y = DSF DSF j DSF 8 DIF DSF 2 IRT odds Logistic 2 DIF Y = 3 i j i 0 1 ii Y = 1 ii 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

3 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 = IRT DSF ETS λ j < 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 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 odds ratio odds DSF ΔR 2 ΔR 2 < 0 10 ratio j DSF 0 10 ΔR 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 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

4 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 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

5 % % Logistic IRT 10 DSF DIFAS 17 DSF common log-ratio λ j λ j Ralf Schwarzer DSF DIF global net DIF global 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 Item * * * * * LA = ZLA= * LA = ZLA= * * * LA = ZLA= * * * * * * * LA = ZLA= * LA = ZLA= * * LA = ZLA= * * * * * * * LA = ZLA= * LA = ZLA= * 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 net DIF DSF DIF 2 7 λ 2 IRT 7 10 IRT 9 DSF DIF

6 j λ j j λ j λ 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 Item * * * * * * * * * * * * * * * * * * 23 5 DSF DSF i DSF DIF iidsf DSF DIF DSF 2 DSF DIF DSF DSF DIF 4 2 DIF DSF iii

7 6 599 DSF DSF refine the analysis of DIF in polytomous items J Educational MeasurementIssues and Practice Muraki E A generalized partial credit modelapplication of an EM algorithm J Applied Psychological Measurement 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 j j Gattamorta K A A comparison of adjacent categories and cumulative DSF effect estimators D MiamiUniversity of Miami Cohen A S Kim S H Baker F B Detection of differential item functioning in the graded response model J Applied Psychological Measurement DSF DSF DSF 13Penfield R D A nonparametric method for assessing differential step functioning in polytomous items C San Fran- DIF DSF DIF ciscoca Hauck W W The large sample variance of the Mantel- Haenszel estimator of a common odds ratio J Biometrics Jodoin 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 Penfield R D Camilli G Differential item functioning and item bias C New YorkElsevier Zumbo B D Three generations of DIF analysesconsidering where it has been where it is now and where it is going J Language Assessment Quarterly Penfield R D Assessing differential step functioning in polytomous items using a common odds ratio estimator J Journal of Educational Measurement Penfield R D Three classes of nonparametric differential step functioning effect estimators J Applied Psychological Measurement Penfield 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 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 ential item functioning analysis system J Applied Psychological Measurement Alvarez K Penfield R D Using differential step functioningdsfto refine the analysis of DIF in polytomous i- temsan illustration C Washington D C Penfield 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 Penfield R D Distinguishing between net and global DIF in polytomous items J Journal of Educational Measurement Schwarzer R Jerusalem M Generalized self-efficacy scale EB /OL 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

8 6 Fitz Cui Yang Gang Wei Chen Fangjiong An estimation-range extended autocorrelation-based frequency estimator J EURASIP Journal on Advances in Signal Processing J Fu HKam P Y Sample-autocorrelation-function-based frequency estimation of a single sinusoid in AWGN C/ / IEEE 75th Vehicular Technology Conference Yokohama D J Lank G W Reed I S Pollon G E A semicoherent detection and Doppler estimation statistic J Aerospace and Electronic Systems Ω J 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 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 Leighton 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 The Differential Step Functioning in Polytomous Items LI Mei-juan 1 LIU Hong-yun 2* 1 Beijing Academy of Educational Sciences Beijing School of Psychology Beijing Normal University Beijing 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

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