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Fellow (1 September 2004 - 30 June 2005)
During my year at NIAS, I worked on three different projects. The first one was to set up the structure of a monograph called "Distance models of Relational Data". My aim with this book was to bring together several quite different approaches for analysing psychological data by showing that they all fit into a consistent geometrical framework. My major task was to make an extended summary, in which I ordered all my notes and all topics by formulating a new classification of relational data, which distinguishes five aspects. The geometrical framework follows from the consideration that we can translate each combination of these relational aspects into spatial relations between points and vectors in some model space. It indeed proved to be possible to integrate five major areas of psychometrics: factor analysis, paired comparison scaling, item response theory, multidimensional scaling, and hierarchical clustering.
The second project concerned a monograph with the working title "Classification, Prediction, and Visualization in Nonlinear Data Analysis". This book is a joint work with my Leiden colleague Jacqueline Meulman. It covers procedures that can be used to study the association between the rows and columns of a multivariate data matrix through a joint graphical representation. It is the natural successor of the Gifi (1990) book, called Nonlinear Multivariate Analysis, but it will be less programmatic and more practical, and it will include recent extensions and a more comprehensive framework for these techniques as well. We now have a contract for this book with a major international publisher. I have started sorting out all existing materials, and worked on the second draft of one of the chapters.
Finally, I produced a series of refereed journal articles and chapters in books. I have been able to clean up many of the unfinished projects that were still on my desk when starting at NIAS. Among other things, I did most of the write-up of my Presidential Address to the Psychometric Society (Heiser, 2004), worked on an invited contribution to a handbook (Warrens and Heiser, 2006), and finished a paper on the statistical aspects of the distinctive features model (Frank and Heiser, 2005). One of the problems that I mentioned in my NIAS research plan was to figure out all special cases of feature models, and I wrote the first draft of a journal article on this topic during the last two months of my stay.
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