Multiplicative Rasch model

Georg Rasch and Benjamin D. Wright: The Early Years

Excerpts from an interview with Benjamin D. Wright taped by David Andrich in Judd 438 during April, 1981, when David was in Chicago for the first International Objective Measurement Workshop, held at the University of Chicago in honor of Georg Rasch (1901-1980).

Benjamin D. Wright speaks:

In 1959, Jimmy Savage, Professor of Statistics at the University of Chicago, ran into Georg at a Biometrics Society meeting in Washington (Georg was a founding member). Jimmy had gotten to know Georg earlier. Georg pressed Jimmy with his need to tell the world of his measurement discoveries.

Shortly afterwards, Jimmy and I talked about Georg's work. Though I taught statistics in the Education Department, this was the first time I had heard of it and I expressed some interest. Jimmy had the money for a visiting professorship, and said: "Well, Ben, if you tell me to have him come, I'll bring him. I don't see a reason for the Statistics Department to have him. But, if you think the people in Psychology or Education will be interested, then I'll bring him." So Georg came in 1960, and because of my promise to Jimmy, I felt obligated to go to Georg's lectures.

Georg's official host was Jimmy, but Georg lived by himself in the Chicago Theological Seminary dormitory. I met him at Jimmy's house for dinner and cocktails. Then I went to the first class, which was heavily attended by the Statistics Department and the statistical people in the Social Science Division. During Georg's opening remarks, I paid more attention to the social situation than to his words. About all I noticed was that he seemed critical of factor analysis.

Georg was bombastic and intolerant, bragging about how smart he was and, so, was truly obnoxious. People stopped coming. The social scientists couldn't understand the math. The statisticians thought he might be insulting them. Jimmy fell asleep about half way through the first lecture and slept all the way through the second. Then he stopped coming. It was a funny and sad situation. Here was this man who cared so much about what he had to say, and he was driving his audience crazy. Gradually everyone thought up reasons why they needn't come.

It wasn't Georg's great ideas that first caught us. What caught Jimmy's interest was that Georg was a good fellow who had been hospitable to him in Denmark, who was fun to talk with, and who was very forward about his need for a forum. I felt obliged to go to Georg's lectures because I promised Jimmy I would. Then, I felt concerned about Georg being deserted by his audience. Although he was a bit overbearing, I didn't feel he had nothing to say. What he was saying was becoming interesting. Yet everyone was deserting him. Under these circumstances, I couldn't desert him. So I stayed on and listened more closely and began to be interested. What got me then was my admiration for Georg's courage. He kept on explaining as though he didn't see there was nobody there. He didn't give-up. He brought in his notebook. He opened it carefully. He gave his lecture, even when there was no one there but me and John Ginther (also in Education). And after awhile, even John Ginther stopped coming. I certainly couldn't leave him then, when I was his last student.

So we made friends. After his lecture we had lunch at his CTS apartment. He got out his cans of sardines, his brown bread, his pepper and his beer. He opened the sardines, put them on the bread, mashed them a little, poured on some oil and added lots of pepper. He enjoyed it all so much. He even enjoyed opening the can. He was really into it. His pleasure in something as simple as a sardine sandwich was an inspiration to me. I thought, "That's the way life should be. I like this man and the way he does things. I want to be like him."

As we chatted over lunch I began to show him some of the semantic differential data that I was using factor analysis on. He took some of it and spent hours and hours copying it into various formats, making tables and graphs, trying to do something with pencil and paper to analyze it. I was fascinated that he could work so hard to see whether he could do something with my data, since I myself, at that moment, doubted whether much could be done with them (see RMT 2:3 p. 25ff.). But he threw himself into it and, as a result of these efforts on his part, I reread his book more carefully and began to appreciate it much more deeply.

After that spring, however, as far as I was concerned, the whole thing disappeared. He went back to Denmark. Later he sent me an autographed copy of his book, long since "borrowed" by someone. I didn't see him again for some time. He called me on the phone once when he was in Washington to ask what I was doing. But I was working on something quite different and didn't think I needed his ideas.

It wasn't until I came to the end of my research on teacher development, from which I had lots of semantic differentials to analyze, that I thought about him again. Then, mostly as an excuse to take a trip, I decided to go and see him, and see if he had anything to say. I really didn't think he could do anything about my semantic differentials, but I did think it would be fun to go to Denmark to visit him.

When Claire and I, with our four little children, finally got to Denmark in the Spring of 1964, however, I began by being annoyed with Georg because he was so unhelpful to our coming there. He said he was going to help, but he ended up not finding us any place to live. It was by the skin of our teeth that we finally figured something out. So, I arrived feeling that he was even less interested in my coming than I was. At that moment I thought the whole visit was going to be a disaster. But the fact is that Georg spent a great deal of time with me. He began by treating me to a splendid, three hour, highly alcoholic Danish Anretning (meaning "everything on the menu") at The Little Prince, his favorite Copenhagen restaurant. Then he had me come out to his rather imposing home in Holte, just outside Copenhagen, three or four mornings a week.

He spent the morning lecturing me on math and statistics - just him and me. He had a blackboard installed in his bedroom for the occasion (that being the only room his wife, Nille, would let him hang it in). He lectured and I took notes. I still have those notes. He told me about his book and what one could read in his book, if one cared to.

Georg was unwilling to take traditional cliches for granted. That intrigued me. His impassioned conviction that we are going to think for ourselves, that we are not going to just believe what anybody else says, that we are not going to just do things the way others have done them, but are going to figure things out for ourselves, and only do what makes sense to us, only do what we are able to make sense out of, that really appealed to me. That's the kind of person I am. Georg was a kindred spirit.

At the beginning, however, I didn't really know what he was talking about, or why he was talking about it. I didn't see my own scientific problems in that light. I didn't recognize his ideas as solutions to my problems. I had come to think that what most educational statisticians were doing was screwy. All those correlations computed between all kinds of things, reliability coefficients, validity coefficients, all that gave me a headache. I thought this can never be science. This is a mess. Georg's approach, in contrast, was clean and clear. He didn't get into any of that goofy stuff. He went right to the observation and modelled it. I liked that idea very much. It was clean and clear, fresh and new, sensible and uncluttered. I listened to him and I thought, "This makes sense, in fact, better sense than anything I have heard so far."

He also took me with him on his consultations to various Danish institutions. These consultations took place after an enormous, alcoholic lunch to which Georg always treated me. The consultations were rather amusing. At the military psychology group Georg introduced me to the people there. Major Borking, the "boss", sat at his big desk in command. Georg sat opposite in the "important" chair. Three young fellows sat, one on the couch beside me, and the other two on little chairs along the wall. Georg asked the young fellows to report on what they had been doing. As soon as they began, Georg went to sleep. They reported to the sleeping Georg for forty-five minutes. Towards the end he awoke, told them what to do next and we left.

On the way out, the Major, a bit distressed at an American visitor seeing the famous Danish mathematical consultant sleep through the consultation, took me aside to explain how miraculous it was that, even though Georg always seemed to be sleeping, he nevertheless heard the reports well enough to know exactly what to advise the group to do next. And, I must say, everyone seemed entirely satisfied with Georg's advice. It was a charming and mysterious experience.

Another place we went was the Danish Pedagogical Institute. That's where I met Georg's daughter Lotte's husband, Bo Prien (see RMT 5:3 p.169). Bo showed me the new math test he was working on. At the time it seemed a bit labored to me. Bo was moving at a snail's pace. He had hundreds of multiplication and division items arranged in patterns on sheets of paper to help him think about the order in which they were best done and the effects of digit processions. It was hard for me to see how so much detail could pay off. [Today (1995), however, after Jack Stenner's astonishing success with his Lexile specification equation, I can better appreciate what Bo was trying to do back in 1964.] In spite of my reservations, however, I paid careful attention throughout Bo's lengthy explanations because I wanted to be a good guest and I liked Bo. In addition to Bo's expositions, Rasch's student, Gus Leunbach, took me through his Rasch model computer programs, every step of the way. And there were a lot of steps!

Erik Thomsen, the institute director, was the charming leader and diplomat of the group. He was the one who told me how Georg's book ever got written. Georg's weekly impromptu consultations in Erik's office during 1955-1958 were taped by Erik's secretary. The recordings were then transcribed in Danish by Lotte, the other mathematician in the family. Finally, Gus Leunbach, "transformed" and later "revised" the Danish manuscript into English.

I was quite tentative when I went to Denmark in 1964. But I was sufficiently intrigued and educated by him in 1964 to go back in 1965, which I arranged to do almost immediately. When I returned in 1965 I took Bruce Choppin with me. Bruce was going home to England for the summer. So I got him to come to Denmark for a few weeks. I was already thinking of being his teacher. Bruce had come to Chicago the year before. He had the same kind of physics background that I had, so we had a lot in common. I asked him to stay with us in Denmark so he could come to the lessons with Georg.

Bringing in a student that I valued made a difference. I had tried a few programs on my own between 1964 and 1965. But I did nothing before 1964, except to glance at his book. I wasn't dealing with dichotomous tests at that time and I wasn't the least bit interested in them. But in taking Bruce to Denmark, I must have already had something in mind. When Bruce and I came back to Chicago we got right to work. We wrote FORTRAN programs for all of Georg's algorithms: LOG (the linear log method he applies in Chapter V), PAIR (the pairwise method he proposes on page 171) and SYMFUN (his fully conditional algorithm based on symmetric functions) and we tested them against simulated data to make sure they worked for us.

We must have worked pretty fast because we organized a Mid-West Psychological Association symposium in the fall of 1965 in Chicago. In those days the MWPA had big meetings in Chicago with hundreds of people. Our symposium met in a ballroom and there were at least a hundred people there. I got Jane Loevinger, a fan of Georg's work, to introduce us and David Wallace to discuss the presentations. The papers were by Bruce, me, Gary Ramseyer and Richard Brooks, two students from Iowa State who had been trying Georg's LOG method in their dissertations because their professor had seen his book. Bruce and I showed that all three algorithms always gave the same answers.

That was the debut of Rasch work in this country. No other American did anything about it except that professor in Iowa with his two students and they soon disappeared, and then Bruce Choppin did his thesis on something else. If it hadn't been for Nargis Panchapakesan, the work might have stopped right there.

Nargis had a physics Ph.D. from Calcutta and came around to MESA because she was interested in education. She began with Ben Bloom. But he didn't know what to do with a physicist so he sent her to me. I talked her into helping me work on the mathematical side of Rasch estimation and to write some better computer programs. She learnt FORTRAN. She was a good mathematician. Finally, I talked her into getting another Ph.D. She didn't really want to, but she liked the work. That's how the unconditional estimation JMLE (UCON) FORTRAN routine was born.

It was because I had Bruce and Nargis working together that we got so much done so fast. In those days I spent hours at the computation center. I had an office there. I had free computer time. I was one of the few faculty members who used the computers. Most of the other users were physicists, astronomers and meteorologists. This was 1965-67. University computing was just getting started. We had a wonderful IBM 7090. I used to run it myself - the whole thing. It filled an enormous room full of tape drives and memory banks. By today's standards it was crude and primitive. But it had a 32K core! It took 12 engineers to keep the 7090 going. But we were able to do a lot of things fast that people hadn't done before. In particular we could simulate data with known properties and the use them to test our programs. In the spring of 1967 I gave a Rasch paper on conditional estimation at the Psychometric Society in Madison.

In 1965, Georg happened to be sitting next to Ben Bloom on a flight from Stockholm to Copenhagen. He talked Bloom's ear off, impressing him enough to get him interested in what I was doing with the Rasch model back in Chicago. That led Bloom to invite me to give that infamous talk at the 1967 ETS Invitational Conference. I felt that that talk would surely complete my Rasch work.

But I had become obliged to write the Ed. Psych. Measurement paper with Nargis on JMLE (UCON). It seemed sensible to put into a paper what we had been doing, so we did, forgetting to mention that we were unbiasing the UCON estimates so that they would match the conditional ones. So we had many questions after that. "Why does your program have this (L-1)/L factor when it is not in your paper?" Even so, I felt surely that article finished my Rasch work.

But I spent August 1967 at Georg's thatch-roofed cottage on Laeso in order to show him how well our simple, easy-to-use unconditional method (UCON) worked. We had talked about it in 1965. But he insisted then that it would be absolutely wrong. He feared it would not take full advantage of separability and surely that must not be right. When I objected that his LOG method worked exactly that way, he said, "Yes, but I only used the LOG method because I didn't have any way to apply the conditional method then."

When I went in 1967, I took a suitcase full of output -- very heavy to carry. That was when I showed Georg that the only bias produced by UCON was removed by the factor (L-1)/L. He saw that he couldn't win the argument. But he didn't like it.

That was an important point in our relationship because at that moment he and I separated a little bit. Up until then, as far as he was concerned, I was doing everything exactly the way he told me. But UCON was a new something that I did on my own, not to his liking, which seemed to me plainly convenient, practical and useful. So it was a point in our work where I was becoming myself, in spite of, indeed, against his wishes. We continued to be good friends. But from that summer of 1967, there was that bit of difference between us.

Georg came to Chicago for the academic year of 1968-1969. I brought him over in the Fall and he and Nille stayed 9 months.

Then David Farr insisted on my doing that first ever AERA pre-session on the Rasch model (1969). David had heard me talk at the ETS conference and thought it was a great idea. He called me and started persuading. At first, I felt apprehensive about the task and annoyed at being asked. But, again, Ben Bloom said I must do it. It was important to do it, absolutely essential for my career, for the sake of science.

The 5-day pre-session in Los Angeles was attended by lots of big shots: Bill Angoff, Chester Harris, Henry Kaiser and fifty others. Georg gave the final lectures. But it didn't make a dent on them. It did, however, make an impression on Lou Bashaw, Bob Rentz and Charlotte Cox. Rentz and Cox were Bashaw's graduate students. They didn't really understand what was going on. But Bashaw liked it and he pushed them and they finally got a large grant to equate a mass of published test results.

There was a second pre-session in Minneapolis in 1970, the one George Ingebo sent Fred Forster (of Portland Public School and NWEA fame) to. Once again, after those two pre-sessions, I thought, "That's it." I had about signed off on Rasch measurement. I had no more students in the area. I felt I'd done everything I wanted to do. But then David Andrich arrived. So I started again. And then Graham Douglas came, and then Geoff Masters, and then, and then, and then....

"We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that it is not crazy enough." - Niels Bohr to Wolfgang Pauli, 1957

Rasch and Wright: the early years. Wright BD, Andrich DA. … Rasch Measurement Transactions, 1987, Pre-History p.1-4

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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