Mitchell Centre Seminar Series
|Starts:||16:00 1 Mar 2017|
|Ends:||17:30 1 Mar 2017|
|What is it:||Seminar|
|Organiser:||School of Social Sciences|
Speaker: Martin Everett, University of Manchester
Title: Dealing with overlapping categorical attribute data.
Suppose you have a network of ties among individuals, along with their participation is various activities. If participation were mutually exclusive, you would have the simple situation of a single categorical variable that identifies which activity each node was associated with. We could, then, for example, look at the degree to which a node’s alters belong to each category. We could also assess the overall heterogeneity of each person’s alters with respect to these activities – are their friends split across many categories, or are most of their friends just one kind?
Consider now the possibility that each alter might be associated with multiple categories. For example, the categories may represent activities, and the alters may both play the piano and play tennis. The question is can we still calculate attribute-based measures such the diversity of activities participated in by ego’s alters?
The question has bearing on a number of related analyses. A staple of ego network analysis is the assessment of ego-alter similarity ie homophily. When choices are mutually exclusive, we can record node choices as categorical variables, and it is easy to construct measures of ego-alter similarity. For example, the simplest measure is the proportion homophilous: what proportion of ego’s alters made the same choice as ego? But again, what if the choices are not mutually exclusive, and an alter (not to mention ego) could have made multiple choices? In this paper, we consider a general approach to adapting measures conceived for categorical variables (i.e., partitions) to the case where we have instead node-by-category indicator matrices, as in the case of participation in multiple activities. We look at the Blau index, E-I, Yules Q and G-F brokerage. In addition we look at a form of Burt’s structural holes which takes account of associations to different categories.
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