RUMSEY, DEBORAH JEAN; PHD
THE OHIO STATE UNIVERSITY, 1993
STATISTICS (0463); PSYCHOLOGY, SOCIAL (0451); PSYCHOLOGY, PSYCHOMETRICS (0632)
Social networks are used by biologists, psychologists and sociologists, among
others, to study the
structure of a group of individuals linked by a certain important relationship(s). For example, each
individual in a group of 25 eighth-grade students is asked each month to provide a list of his/her friends.
Here, the social network is the class of students, and the relationship of importance is friendship. A
directed graph is typically used as the mathematical tool for representing a social network. Current
research methods study the evolution of a social network over time, using a Markov-chain model, based
on graph-theoretic properties. We present methods for handling nonresponse in social network data.
We identify two types of nonresponse that can occur in a social network: link nonresponse, where
information regarding any particular link(s) is missing at some time period(s), and node-nonresponse,
where all information regarding the choices of a particular individual are missing at some time period(s).
We consider a model-based approach using a Markov-chain to model the nonresponse. Six models for
each type of nonresponse are presented, in which nonresponse occurs at one time period only, or both
time periods. Both random and nonrandom models are proposed. Two types of nonrandom
nonresponse models are proposed, where nonresponse depends on the state of the social network at
the time of the nonresponse (nonignorable nonresponse), or the other time period (ignorable
nonresponse). Model fitting is illustrated using randomly and nonrandomly generated link nonresponse.
Suggestions for social network data collection methods which include the possibility of nonresponse are
presented. Areas of future research include pooling of data across time periods, the EM algorithm, and
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