Essays on Georg Rasch
and his contributions to statistics

Ph.D. thesis
Lina Wøhlk Olsen
Institute Of Economics, University of Copenhagen

Summary

This PhD thesis consists of six self-contained articles. All of them are connected to Georg Rasch and his contributions to statistics.

Chapter 1 is a biography of Georg Rasch covering the years 1901 to the late 1940s. Special attention is paid Rasch's road from being a mathematician to becoming a statistician. His life in the late 1940s is also described at some length. He was a statistical consultant, but he also lectured on mathematics and statistics at the University of Copenhagen. This way, and especially by influencing his young assistants, Rasch was a prominent figure in the progress of statistics in Denmark.

Chapter 2 rediscovers Rasch's work on Growth. We shall see the theory that Rasch developed and explore the events that inspired him to analyze growth. The Growth Model had it's origin in an empirical analysis of calves, but afterwards Rasch used it to model the growth of other animals. By time, Rasch became intrigued by developing a theoretical frame for the Growth Model. Chapter 2 also includes an empirical example of using the Growth Model on recent data.

Chapter 3 is an account of how Rasch developed the Rasch models. Rasch was triggered by an empirical analysis and in the course of some ten years he gained the insight that the idea underlying this particular analysis was a special case of something much more general, namely specific objectivity. Chapter 3 also supplies background information on Rasch prior to his development of the Rasch model, but the main focus stays at the late 1940s and the 1950s. [Parts published elsewhere are not available here.]

Chapter 4 describes Rasch as professor of Statistics. It would be wrong to say that Rasch's professorship was a indisputable success. First of all, Rasch had hoped to be professor at another faculty. Second, some of the scientists at the faculty where he became professor had hoped for somebody else in Rasch's place. As professor, Rasch developed the course in statistics. This change was very welcome to a segment of students and scientists, namely the sociologists. But a larger segment of people, namely the economists, found that the course in statistics had become next to useless. Towards his colleagues Rasch was at the same time very generous and very domineering. He was good at initiating projects and successful in creating a fruitful working environment.

Chapter 5 departures from Georg Rasch's ideas on specific testing. Specific testing is combined with exact testing and the existing results on specific testing are generalized. The main idea of exact Rasch testing is the test statistics used to check the fit of the model is a both necessary and sufficient condition for the model in question. This implies that the observed value of the test statistic is extreme if and only if the observation is extreme as distributed according to the model. The article discloses a class of exponential families for m-dimensional contingency tables for which it is possible to make an exact Rasch test of the goodness of fit of the model. Furthermore, an exact Rasch test of Rasch's multidimensional Rasch model with multidimensional parameters is derived.

Appendix A, Pharmaceutical Prices in Europe: A Linear Structure, derives a pharmaceutical price index. An overall structure in the data is identified and modelled by a two sided analysis of variance. The estimates constitute the price index. This approach is fundamentally different from the commonly used Laspeyres and Paasche index formulas. The connection of this paper to the work of Rasch is stated in the introduction.

Copyright © 2003 Lina Wøhlk Olsen. Reprinted with kind permission.

Link to the full text of Lina Wøhlk Olsen's Ph.D. thesis, a 5 MB PDF file. Parts published elsewhere are not available.

Contents

Introduction

1 Georg Rasch prior to the Rasch models
1 Introduction
2 Childhood
3 Student
4 The time as a mathematician
5 Turning to statistics
6 Rasch's training in statistics
7 Statistical consultant
8 Private life
9 Rasch; an engaged scientist with stature
10 Communicator of Fisher's ideas
11 Summa Summarum
12 Appendix A. Interviews
13 Appendix B. Quotes in Danish
14 References

2 Georg Rasch's Growth Model
1 Introduction
2 Presentation of the sources
3 The Growth Model. Deterministic version
4 Rasch initial development of the Growth Model
5 Growth as a stochastic process
6 Work with growth after 1954
7 The Growth Model and specific objectivity
8 Conclusion
9 Appendix A. Example
10 Appendix B. Interviews
11 Appendix C. Quotes
12 References

3 The life of Georg Rasch as a mathematician and as a statistician
[not available] 1 Introduction
[not available] 2 Early life (1901-1945)
[not available] 3 Rasch's first analysis of an intelligence test [not available] (1945-1948)
[not available] 4 The analysis of slow readers (1952)
[not available] 5 Measuring intelligence (1952-1953)
[not available] 6 The discovery of the dichotomous Rasch model (1952-1958)
[not available] 7 Work on the models (1953-1958)
[not available] 8 The conversation with Ragnar Frisch in 1959
[not available] 9 Two important publications (1960 and 1961)
[not available] 10 Last years (1962-1980)
[not available] 11 Epilogue
[not available] 12 References
13 After word by L.W.O
14 Appendix A. Translations of selected pages of the draft

4 Georg Rasch. Professor of Statistics at the Faculty of Social Sciences, 1962 to 1971
1 Introduction
2 Background
3 The appointment
4 The curriculum of Rasch's predecessor
5 Taking over the Statistical Institute
6 The Models for Measurement
7 Empirical approach and tailored methods
8 Dislike of 'standard methods'
9 The students
10 The economists
11 The sociologist
12 Rasch's scheme for the Statistical Institute
13 Projects and working climate at the Statistical Institute
14 Consulting and further developing the Models for Measurement
15 Approaching retirement
16 Retirement
17 Summa summarum
18 Appendix A. Outline of the contents of Rasch's textbooks
19 Appendix B. List of personnel
20 Appendix C. List of guests at the Statistical Institute
21 Appendix D. Interviews
22 Appendix E. Quotes
23 References

5 Exact Rasch Testing
1 Introduction
2 Exact Rasch Testing
3 Test of Parametric Structures
4 Exact Rasch tests in m dimensional contingency tables
5 Summary
6 Appendix A. An exact Rasch test of the multidimensional Rasch model
7 Appendix B. Proof of Theorem 1
8 References

6 Appendix A. Pharmaceutical Prices in Europe: A Linear Structure.
1 Introduction
2 Data and methods
3 A Linear Structure of Pharmaceutical Drugs Prices
4 Indices of pharmaceutical drugs prices
5 Theories of oligopolistic pricing and the linear price structure
6 Discussion
7 Concluding remarks
8 References

7 Appendix B. List of Rasch's publications and important papers.


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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 2nd. 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

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April 21-22, 2015, Tues.-Wed. IOMC 2015: International Outcomes Measurement Conference, Chicago IL www.jampress.org
May 13-15, 2015, Wed.-Fri. In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
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