NONRESPONSE MODELS FOR SOCIAL NETWORK STOCHASTIC PROCESSES (MARKOV CHAIN)

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.

Social
Systems Simulation GroupP.O. Box 6904San Diego, CA 92166-0904Roland Werner, PrincipalPhone/FAX (619)
660-1603 |

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