﻿ SVDFILE= singular-value decomposition file

SVDFILE= singular-value decomposition file

Singular-value decomposition (SVD) is a technique for factoring a data matrix. Here it is used to look for patterns in the Rasch residuals which may indicate multidimensionality. SVD values are estimated by iterating through the residual data matrix. Each residual is explained, as much as possible, by a value attributed to the person (row) and a value attributed to the item (column). These values are multiplied.

SVDFILE=? opens a Browse window

The general form of the Rasch-SVD model is:

Xni = Eni + Vn*Ui ± ε

where Xni is the observation when person n meets item i. Eni is the Rasch-expected value. Vn is the SVD value for the person. Ui is the SVD value for the item. ε is the unexplained part of the residual.

After the first set of SVD values have been estimated, the process can be continued deeper down to further levels:

Xni = Eni + V1n*U1i + V2n*U2i  ... ± ε

SVD control settings. These can be in the control file, or from the Output file menu, SVDFILE option.

 SVDFACTORS= is the number of SVD terms (factors) to be estimated for each residual. SVD computation can be concluded with Ctrl+F. SVDEPOCHS= is the maximum number of epochs (iterations through the data) for estimating each SVD factor SVDMIN= is the minimum improvement of the root-mean-square residuals based on the current SVD estimates at the end of an SVD iteration (epoch) through the data matrix of residuals in order for SVD estimation to finish for that SVD factor. SVDTYPE= is the type of residual to be decomposed. R = the raw residual or S = the standardized residual. SVDFILE= name of the output file for the SVD values.

SVD file format:

The first four lines are heading lines. To omit them, specify HLINES=NO or in the Output Files specifications dialog box.

RMSR = Root-mean-square-residual corresponding to the column of Rasch measures or SVD factors.

RMSS = Root-mean-square-standardized-residual corresponding to the column of Rasch measures or SVD factors.

MEASURE = Rasch measure in Table 14 etc.

1 2 3 4 ... are the columns of SVD values. For each SVD factor, every person and every item has an SVD value.

SVD factors corresponding to extreme scores have 0 values.

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Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez
Winsteps Tutorials Facets Tutorials Rasch Discussion Groups

Coming Rasch-related Events
Jan. 5 - Feb. 2, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 10-16, 2018, Wed.-Tues. In-person workshop: Advanced Course in Rasch Measurement Theory and the application of RUMM2030, Perth, Australia (D. Andrich), Announcement
Jan. 17-19, 2018, Wed.-Fri. Rasch Conference: Seventh International Conference on Probabilistic Models for Measurement, Matilda Bay Club, Perth, Australia, Website
Jan. 22-24, 2018, Mon-Wed. In-person workshop: Rasch Measurement for Everybody en español (A. Tristan, Winsteps), San Luis Potosi, Mexico. www.ieia.com.mx
April 10-12, 2018, Tues.-Thurs. Rasch Conference: IOMW, New York, NY, www.iomw.org
April 13-17, 2018, Fri.-Tues. AERA, New York, NY, www.aera.net
May 22 - 24, 2018, Tues.-Thur. EALTA 2018 pre-conference workshop (Introduction to Rasch measurement using WINSTEPS and FACETS, Thomas Eckes & Frank Weiss-Motz), https://ealta2018.testdaf.de
May 25 - June 22, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 27 - 29, 2018, Wed.-Fri. Measurement at the Crossroads: History, philosophy and sociology of measurement, Paris, France., https://measurement2018.sciencesconf.org
June 29 - July 27, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
July 25 - July 27, 2018, Wed.-Fri. Pacific-Rim Objective Measurement Symposium (PROMS), (Preconference workshops July 23-24, 2018) Fudan University, Shanghai, China "Applying Rasch Measurement in Language Assessment and across the Human Sciences" www.promsociety.org
Aug. 10 - Sept. 7, 2018, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Sept. 3 - 6, 2018, Mon.-Thurs. IMEKO World Congress, Belfast, Northern Ireland www.imeko2018.org
Oct. 12 - Nov. 9, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com

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