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
                         variance estimation.


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