and his contributions to statistics

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

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.*

**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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