﻿ Newton-Raphson step size = 0

# Newton-Raphson step size = 0

Facets uses Joint Maximum Likelihood Estimation (JMLE) or a Facets implementation of PMLE to estimate the Rasch measures from ordinal data. This requires an iterative process. Initial estimates are imputed for all the element measures. The expected observations are computed based on these estimates and totaled for each element. Then for each element, the observed and expected total scores are compared, and the element measure re-estimated to a value intended to make the expected total score the same as the observed total score. This process is repeated until the differences between the observed and the expected total scores are too small to matter. This is called convergence.

Initial estimates are obtained using the PROX (normal approximation) algorithm.

More exact estimates are obtained using iterative curve fitting (when Newton=0) or the Newton-Raphson method. Newton= can be set using the Estimation menu.

 Newton=0 specifies iterative curve fitting. The expected scores follow logistic ogives. The improved measure estimates are the locations on the logistic ogives predicted to produce the observed total scores. Newton=0.1 Newton=0.5 Newton=1 Newton= ... specifies Newton-Raphson method. The expected scores follow local curves defined by their first and second derivatives. When Newton=1, the improved measure estimates are the locations predicted to produce the observed scores. When Newton=0.5, the improved estimates are halfway between the current estimates at the Newton=1 estimates, and similarly for other values of Newton=.

Help for Facets Rasch Measurement Software: www.winsteps.com Author: John Michael Linacre.

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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 Winsteps & Facets Events
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
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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