The Concept of Configuration of Interpersonal Relations in a Group as a Time-Dependent Stochastic Process

Abstract

To explain changes in the sociometric configuration of a group through time, a problem arises of the extent to which such changes may be viewed as the aggregation of part-processes occurring at the level of two-person choice structures. A possible model is a Markov chain in which three possible states are mutual choice, one-way choice, and indifference, one realization for each pair of choosing individuals in the group. Choice data for an eighth-grade classroom are fitted to this model and are used to answer questions of constancy of transition probabilities, order of the chain, and sex differences.

Estimation in the Mixture Transition Distribution Model

“…The second is a set of 3-steps transitions showing the relationships between 25 students for a total of 300 data. These data were previously presented in Katz & Proctor (1959) and in Bishop et al (1975). The last dataset was used rst in Logan (1981).…”

Investigating purchasing-sequence patterns for financial services using Markov, MTD and MTDg models

“…Sequences have been the subject of research in many disciplines, among which archaeology (McBrearty, 1988), biology (e.g., DNA sequence analysis- Raftery and Tavaré, 1994;Lipman and Pearson, 1984; or even bird songs- Chatfield and Lemon, 1970), chemistry (Xu and Agrawal, 1996), computer sciences (Sabherwal and Robey, 1995), economics (Hopp, 1987), econometrics (Bollerslev et al, 1992), history (Abbott, 1995), linguistics (Jonz, 1989), meteorology (Raftery, 1985a;MacDonald and Zucchini, 1997), psychology (Cohen et al, 1990) and sociology (Abbott and Hrycak, 1990;Katz and Proctor, 1959;Logan, 1981). We define a sequence as a succession of events.…”

Longitudinal Dynamic Network Analysis: Using the Over Time Viewer Feature in ORA

“…Methods for the analysis of over time network data has actually been present in the social sciences literature for quite some time (Katz and Proctor, 1959;Holland and Leinhardt, 1977;Wasserman, 1977;Wasserman and Iacobuccci 1988;Frank, 1991). The dominant methods of longitudinal social network analysis include Markov chain models, multi-agent simulation models, and statistical models.…”