A Stochastic Model for Time Changes in a Binary Dyadic Relation, with Application to Group Dynamics

摘要

This thesis is concerned with the development of a stochastic model for analyzing time changes in a binary dyadic relation over a finite set of points. For purposes of drawing statistical inference in time the total relation R (A) on the set A is looked upon as an aggregate of its subrelations on subsets of the set A. The number of states in which a subrelation may be found, at any time, is very large; consequently three classification schemes are described to obtain a small number of mutually exclusive and exhaustive classes. Methods are presented to enumerate the number of subrelations of R (A) in various states at any time, and to count the number of transitions from one state to another in time. The process of change in the total relation over time is described as a timedependent process, and some statistical tests to determine the nature of the dependence are given. Certain aspects of the probability distributions of the random variables R sub ni (number of n-point subrelations of R (A) in state s'i) are discussed in the second part of the thesis. It is shown that the probability distributions of R sub ni may be approximated by Poisson distributions. Finally an application of the model to group dynamics is described and empirical examination of Markov properties is made for a particular set of data. (Author)