Rasch Dimensional Analysis

Rasch dimensional analysis. Moulton MH. … 1995, 8:4 p.398

The greater part of measurement is taken up with identifying a variable to be measured and then gathering data dominated by that variable. When, as generally occurs, the data reflect the influence of additional variables, those data show misfit to the Rasch model. When misfit becomes substantial, Rasch analysis of the data becomes increasingly ambiguous. To reduce the difficulty of dealing with such data, "Rasch Dimensional Analysis" (RDA) has been developed to filter out the effects of unwanted dimensions in order to expedite the analysis of a particular variable.

Suppose you have a set of interviews and want to measure the respondents on a liberal/conservative dimension. One approach is to read the interviews and identify a set of liberal and conservative indicators chosen to define an approximately unidimensional variable. But this requires finding the indicators in the interview. You must make multiple separate decisions on which respondent statements reflect liberal or conservative positions, and each of those decisions must be reconciled with your intended variable.

RDA takes a different approach. Instead of seeking multiple indicators that mark a particular dimension, you simply choose two respondents (or items) that you decide represent opposite poles of your target dimension. Then two measurements are estimated for each other respondent (or item). These measures are the distances between that respondent's interview and the interviews of the two polar respondents. Simple geometry converts these distances into measures along the dimension defined by the chosen poles.

There are three steps:
1. Choose two persons (A,B) to define the opposite poles of your dimension of interest using your judgement. These persons should differ dramatically on your target dimension, e.g., liberal/conservative, but otherwise be similar.

2. Estimate the absolute logit distances (R,S) between each respondent (C) and the two polar respondents (A,B) by any convenient method, e.g., for dichotomous coding of interview items, a "Poisson" distance between a pair of respondents is [log_e(1+disagreements)]. Similarly estimate the distance (T) between polar persons (A, B).

3. Use Pythagoras' theorem to project each person onto your dimension of interest. The result is a measure of the liberality (or conservativeness) of each respondent along the dimension defined by your choice of A and B.

The measure, x, from pole A toward pole B of respondent C is:
x = (T*T + R*R - S*S)/2T

I applied RDA to interviews of 15 political figures influential in Chicago school governance. Respondents were coded according to their opinions on a number of educational issues, but were not asked about their political philosophies. To define a liberal/conservative dimension, I chose as polar reference points a well-known liberal Democrat from the House of Representatives and a staff member of a well-known conservative Republican Senator. A conventional Rasch analysis of these data was unable to separate respondents along any useful dimension.

The results from RDA, however, were clear-cut, as the plot testifies. In the plot, A marks the polar liberal and B the polar conservative. L marks respondents previously thought to be liberal, M respondents previously thought to be moderate, and C respondents previously thought to be conservative. RDA has succeeded in measuring along my bipolar dimension.

Rasch dimensional analysis. Moulton MH. … Rasch Measurement Transactions, 1995, 8:4 p.398

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
Other Rasch-Related Resources: Rasch Measurement YouTube Channel
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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