Rasch Measurement in America before 1971

University of Chicago, Department of Education
5835 Kimbark Avenue, Chicago 60637

May 27, 1993

Prof. dr. Eddy Roskam
University of Nijmegen
Institute for Cognition and Information
Department of Mathematical Psychology
P.O. Box 9104
6500 HE Nijmegen
The Netherlands

Dear Eddy,

Thanks for your paper. Great references!!

I must protest, however, against the one or two lines in your paper where you assert nothing happened in America before 1971. On that topic you are seriously misinformed.

Jimmie Savage and I brought Rasch to Chicago in March, 1960, because of our already existing knowledge of and interest in his work. Rasch explained and reported on his work for three months in Chicago. He and I worked daily on the problem of how to analyze the bipolar rating scales used in the semantic differential - a problem to which I had been applying factor analysis with - as you know - ambiguous and sample-dependent results. It was during those three months that Rasch developed the m-dimensional model for rating scales with (m 1) categories which he discussed at the Fourth Berkeley Symposium and published in 1961.

In the next four years we organized a program on Rasch measurement in the MESA Special Field at the University of Chicago, got students working, wrote many FORTRAN programs to implement the least squares/LOG, pairwise/PAIR and conditional/FCON algorithms described in Rasch's 1960 book and tested these programs on real and simulated data to see how they worked. The principals in this were Bruce Choppin, Nargis Panchapakesan and myself.

In the course of these investigations we added the unconditional/UCON [now called "Joint Maximum Likelihood Estimation", JMLE] method of estimation. We also attempted a program to estimate an item slope parameter, the infamous item discrimination! No matter what tricks we introduced, some estimates always diverged. There was no unambiguous way to obtain finite values. We consulted our best applied mathematicians to make sure we hadn't missed a trick and, finally did the obvious algebra to prove that, not only in practice, but, more decisive, in principle a second item parameter could NOT be estimated when the observation was a dichotomy.

As you have noticed in the history of American IRT, however, our 1966 result did not deter the foolish adventures by some Americans into two and three item parameter IRT models for dichotomous data. When I showed our results to Fred Lord and Darrell Bock at lunch in December 1967, they merely snickered arrogantly, asserting they would easily, within weeks, have solutions to the problem which I and my students were incompetent to solve. But Lord's three-parameter LOGIST program did not work in 1967 or in 1968 and the lengthy 1989 ETS report on the current functioning of Lord's LOGIST and Bock and Mislevy's BILOG reviews in thorough detail the continuation of the same old problems - failure to recover the generating parameters of data simulated to follow the 3-P model exactly and failure to converge on any data even when the generating values are used to start the iterations.

The 1989 report also explains how LOGIST falls back on a Rasch algorithm every second iteration to keep from exploding and advises would-be users to confine themselves to as few iterations as possible, preferably just four, in order to escape divergence!

Returning to the University of Chicago, our experiences in 1964-1965 with our four ways to obtain Rasch estimates convinced us that, for all practical purposes, it did not matter which method was used. This conclusion and its parts we reported in a well-attended symposium at the September 1965 Annual Meeting of the Midwestern Psychological Association. I still have the program.

Speakers were: my students Bruce Choppin and Nargis Panchapakesan; Washington U. Professor Jane Loevinger (who reviewed Rasch 1960 in 1965); Iowa State U. Professor Paul Blommers, two of his students, Gary Ramsayer and Richard Brooks, who wrote dissertations testing the empirical invariance of Rasch estimates for educational test data; and Chicago Statistics Professor, David Wallace.

The professional attention these activities engendered led to a three year 1965-1968 grant from the National Science Foundation to support Bruce and Nargis and pay for computing to continue our Rasch research.

In 1966 Bruce and I programmed a fully conditional multidimensional pairwise algorithm BIGPAR which estimates an L by (m-1) matrix of item parameters from m category data and expresses this matrix in principal components. I have dated printouts of the FORTRAN coding and a few analyses, if you're interested.

For the Likert rating scale data we analyzed we always got one dominant component specifying a sequence of category values matching the intended direction of the rating scale. We usually also got a minor but distinct second largest component that specified a Guttman 1950 "intensity" effect.

However, as UCON [JMLE] became versatile and we generalized its algorithm from dichotomies to one dimensional rating scales it was easier to enter UCON, first with linear scores like: 1,2,3,4,5,6 for direction, second with quadratic scores like: 3,2,1,1,2,3 for intensity, etc, rather to bother with BIGPAR.

As you might expect, the value and salience of the quadratic form suffered the same fate as Guttman's intensity component - it never mattered enough to bother with.

To finish up, here is a much marked on report I prepared for my Chairman in 1971. The two pages list my Rasch activities during the 1960-1970 period, particularly my explanations and demonstrations of Rasch measurement to the Psychometric Society in June 1967 (Bock, Lord, Tucker, Harris, Angoff and many others were there) and to the enormous audience at the 1967 ETS Invitational Conference on Testing Problems in October 1967.

The list also documents my continuing collaborations with Rasch in 1964, 1965, 1967, 1968-1969 and his participation in the first ever AERA Professional Training Session in February 1969, which was, of all things, on Rasch Measurement.

So you can hardly say with any conviction or a clear conscience that nothing happened in America in the 60's. Indeed almost everything basic had happened in America by the dawn of 1971. What remained were ever widening teaching, training and practice, bigger and better computer programs, Andrich's and Master's filling out and completing the rating scale and partial credit work that Georg and Bruce began and John Michael Linacre's derivation and implementation of the many facet measurement model.

I enjoyed being with you in Atlanta. You are a marvelous talker and a fascinating thinker. I believe you and I agree on a great many important principles. I also believe there are several basic things that you could teach me. I hope you will come again to the New World. You are constantly welcome in Chicago.

Don't forget to send me your next draft.


Benjamin Drake Wright

Professor of Education and Psychology
Director MESA Psychometric Laboratory

cc: George Engelhard

Editor's Note: Prof. Dr. Eddy E.C.I. Roskam of the Katholieke Universiteit of Nijmegen died on May 24th, 1997.

Letter courtesy of George Engelhard, Jr., Emory University.

Wright B.D. (2009) Rasch Measurement in America before 1971, Rasch Measurement Transactions, 2009, 23:1, 1186-7

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: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. 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

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