DIF: Graphical Diagnosis

Perhaps you have measured a group of people on a certain scale and you measure them again with the same instrument at a later time. Did the instrument function the same way both times? Perhaps some people took two alternate forms of the same test. Are the forms equivalent? Perhaps two tests share common items. Do the items function the same way in each test (DIF: Differential Item Functioning)? Or perhaps you have two groups of people that took the same test. Are any items biased?

A glance at a simple graph can give you the answer. Merely plot the pairs of person measures or pairs of item calibrations against each other, draw in the identity line, and construct control lines for the confidence interval you want. If all data points lie within the control lines - joy and bliss! If many data points lie without the control lines - sorrow and think again!

Plot of measures with confidence intervals

Plotting is simple to do by hand. But it is neater, and more accurate to have your computer do it for you. Here's the idea: call a typical matching pair of measures from the two analyses D1 and D2, with standard errors SE1 and SE2.

1. Calculate the mean of the set of D1's = MEAN1, and the mean of D2's set = MEAN2.

2. Look up the Z-score for the confidence interval you want, e.g. Z=1.96 for 95%; Z=2.6 for 99%.

3. For each matching pair of measures, calculate the joint standard error: SE12 = sqrt(SE1^2 + SE2^2)

4. For each matching pair of measures, calculate points on the two control lines:
UPPER1 = (D1+D2)/2 + MEAN1 - Z*SE12/2
UPPER2 = (D1+D2)/2 + MEAN2 + Z*SE12/2
LOWER1 = (D1+D2)/2 + MEAN1 + Z*SE12/2
LOWER2 = (D1+D2)/2 + MEAN2 - Z*SE12/2

5. Plot D1 against D2, as points, for the data points.

6. For the identity line, draw a line from (MEAN1-5,MEAN2-5) to (MEAN1+5,MEAN2+5).

7. Sort the (UPPER1,UPPER2) pairs into ascending order, and plot UPPER1 against UPPER2, as lines (smoothed if possible), for the upper control line.

8. Sort the (LOWER1,LOWER2) pairs into ascending order, and plot LOWER1 against LOWER2, as lines (smoothed if possible), for the lower control line.

9. Now get to work on those rascally data points lying outside the control lines!

Graphical Diagnosis, S Luppescu … Rasch Measurement Transactions, 1991, 5:1 p. 136

Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang	Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene	Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver	Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone	Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Statistical Analyses for Language Testers (Facets), Rita Green	Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind	Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind	Rasch Measurement: Applications, Khine	Winsteps Tutorials - free Facets Tutorials - free	Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre	Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
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Rasch Measurement Transactions & Rasch Measurement research papers - free	An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse	Rasch Measurement Theory Analysis in R, Wind, Hua	Applying the Rasch Model in Social Sciences Using R, Lamprianou	El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Rasch Models for Measurement, David Andrich	Constructing Measures, Mark Wilson	Best Test Design - free, Wright & Stone Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias	Diseño de Mejores Pruebas - free, Spanish Best Test Design	A Course in Rasch Measurement Theory, Andrich, Marais	Rasch Models in Health, Christensen, Kreiner, Mesba	Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen

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