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Network Analysis, Longitudinal Methods of

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Encyclopedia of Complexity and Systems Science

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Abbreviations

Actors:

The social actors who are represented by the nodes of the network, and indicated by a label denoted i or j in the set \( { 1, \ldots, n } \).

Behavior:

An umbrella term for changing characteristics of actors, considered as components of the outcome of the stochastic system: e.?g., behavioral tendencies or attitudes of human actors, performance, etc. Each behavior variable Z h is assumed to be measured on an ordinal discrete scale with values \( { 1, 2, \ldots, M_h } \) for some \( { M_h \geq 2 } \). The value of behavior variable Z h for actor i is denoted Z ih .

Change determination process:

The stochastic model defining the probability distribution of changes, conditional on the event that there is an opportunity for change.

Change opportunity model:

The stochastic process defining the moments where tie indicators can change. This can be either tie-based, meaning that an ordered pair of actors \( { (i,j) } \) is chosen and the possibility arises that the tie variable from i to j is changed; or actor-based, meaning that an actor i is chosen and the possibility arises that one of the outgoing tie variables from actor i is changed.

Covariates:

Variables which can depend on the actors (actor covariates) or on pairs of actors (dyadic covariates), and which are considered to be deterministic, or determined outside of the ‘stochastic system’ under consideration.

Effects:

Components of the objective function.

Influence :

The phenomenon that change probabilities for actors' behavior depend on the network positions of the actors, usually in combination with the current behavior of the other actors.

Markov chain :

A stochastic process where the probability distribution of future states, given the present state, does not depend on past states.

Method of moments :

A general method of statistical estimation, where the parameters are estimated in such a way that expected values of a vector of selected statistics are equal to their observed values.

Network :

A simple directed graph representing a relation on the set of actors with binary tie indicators X ij which can be regarded as a state which can change, but will normally change slowly.

Objective function :

Usually denoted by f i ; the informal description is that this is a measure of how attractive it is to go from an old to a new state. More formally, when there is an opportunity for change, the probability of the change is assumed to be proportional to the exponential transform of the objective function.

The objective function has a similar role as the linear predictor in generalized linear models in statistics, and is specified here as a linear combination of effects.

Rate function :

Usually denoted by ?, the expected number of opportunities for change per unit of time.

Selection :

The phenomenon that change probabilities for network ties depend on the behavior of one or both of the two actors involved.

Tie indicator :

A variable X ij indicating by the value \( { X_{ij} =1 } \) that there is a tie \( { i \rightarrow j } \), and by the value 0 that there is no such tie. Also called tie variables.

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Further Reading

  1. For further reading, basic concepts of continuous-time Markov processes can be found in [34]. The basic definition of the model presented here and of the statistical estimation methods for network dynamics based on panel data can be studied in [46,47]. The approach to the co-evolution of networks and behavior is presented in [49,52]. Some examples of the methods presented in this chapter can be found in [6,53,55,56,57].

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Authors and Affiliations

  1. University of Oxford, Oxford, United Kingdom

    Tom A. B. Snijders

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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Snijders, T.A.B. (2009). Network Analysis, Longitudinal Methods of. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_353

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