Online Tutorials on Mathematical Psychology

Dietrich Albert, Rainer Kaluscha
Adapting Knowledge Structures In Dynamic Domains.

For effective processes of knowledge assessment, teaching, information presentation and information use, the information should be presented on basis of a structure which is defined by prerequisite relationships (Which information do I have to know before I'm able to understand and integrate the newly presented information ?). This kind of prerequisite relation for information units has to be determined and tested before using it. A non-numerical theory for representing these structures is already worked out, and several techniques have been suggested to obtain these structures, e.g.

• mass data collection,
• analysis of didactics and curricula,
• querying experts on prerequisite relationships, competence and performance
• analysis of demands
• analysis of competence and performance,

and also techniques are available to test the obtained structures empirically, which - in principle - is a necessary precondition for using them. However, domains and thus the related knowledge nowadays change very fast - an impressive example is the internet. Therefore techniques for convergent structuring, for dynamic testing and for dynamic refinement have to be developed. This article will give an overview of existing techniques in the static case, i.e. the domain doesn't change at all or only very slowly, and discuss advancements towards the use of these techniques in dynamic domains.

Helena Bacelar-Nicolau
Classifying Variables by Hierarchical Clustering Models: Empirical and Probabilistic Approaches

Keywords: cluster analysis, classification, similarity coefficient, hierarchycal clustering, aggregation criterion, random variable, cumulative distribution function.

Hans Colonius
The Analysis of Response Times: Parallel Processing Models With Unlimited Capacity

Unlimited capacity parallel processing models possessing different stopping rules are presented. These stopping rules imply inequalities on the models´ response time distribution functions that can be tested empirically. This generalizes previous results on horse race models (minimum stopping rule) and exhaustive models (maximum stopping rule). Several areas of application are discussed and the results are demonstrated on a numerical example with conditionally independent exponential channel processing times.

Francesca Cristante
Log-Linear Analysis

Log-linear models for the analysis of two-dimensional and multi-dimensional tables are introduced. The subject matter we are dealing with is divided in three chapters. The first chapter is introductory and is designed to present some basic definitions and concepts related to qualitative data analysis (main sources: A84, chapter 3; K92, chapter 1). The second chapter takes into account the log-linear models for the analysis of two-dimensional tables and the hierarchical and non hierarchical log-linear models for the analysis of three-dimensional tables (main sources: A84, chapters 2 and 3; C90, chapters 2 and 3). In the third chapter a graphical interpretation of higher dimensional log-linear models is introduced (main source: C90, chapter 4). Some numerical examples are also presented.

Luc Delbeke
Multidimensional Scaling.

Multidimensional scaling is an exploratory technique used to visualize proximities in a low dimensional space. Interpretation of the dimensions can lead to an understanding of the processes underlying the perceived nearness of entities. Furthermore it is possible to incorporate individual or group differences in the solution. In this paper a general overview of multidimensional scaling is given, explaining the basics and giving a classification of the frequently used models. An example is discussed and the results obtained using the popular ALSCAL algorithm are compared to results obtained using the recent and promising PROXSCAL algorithm.

Gerhard H. Fischer 
Applying the Postulate of Specific Objectivity to the Measurement of Treatment Effects in Clinical Psychology.

K. C. Klauer
A Practical Guide to Multinomial Modeling.

Christof Körner
Introduction to Knowledge Spaces: Theory and Applications.

Eric Maris
Some Examples of The Structural Approach in Psychology

H. C. Micko
Experimental Matrix Games.

This chapter contains a short introduction into the most simple experimental matrix games, their analysis based on elementary principles of normative game theory for rational behavior, findings on subjects' real behavior in such games and applications in the analysis of typical conflicts of interest. It is written for beginners in mathematical psychology without requiring previously acquired knowledge apart from elementary studies in scientific methods of psychology.

H. C. Micko
Introduction to Psychological Decision Theory.