Some generalizations of p₁: External constraints, interactions and non-binary relations

In 1977, Holland and Leinhardt introduced a new statistical approach to sociometric data analysis. The details of their approach, based on a model termed P₁, were published in 1981 in papers by Holland and Leinhardt, and Fienberg and Wasserman. Since then, many researchers have adopted this model, addressing substantive questions that were unanswerable with existing methodology. The continuing methodological research of Fienberg and Wasserman has allowed this approach to be applied to many different types of sociometric data. We carry on this research by extending p₁ to three new situations: networks of such size that it is impossible for every actor to have contact or knowledge of the other actors; networks in which actor interaction can not be adequately modeled by the simple additive main effects of expansiveness and popularity; and networks in which we measure the strength of the relationship between actors using a non-binary or multivalued relational quantity.