Network Analysis, Longitudinal Methods of 2029 Network Analysis, Longitudinal Methods of TOM A. B. SNIJDERS University of Oxford, Oxford, United Kingdom Article Outline Glossary Definition of the Subject Introduction Stochastic Models for Network Dynamics Statistical Estimation and Testing Example: Dynamics of Adolescent Friendship Models for the Co-evolution of Networks and Behavior Example: Co-evolution of Adolescent Friendship and Alcohol Use Extensions Future Directions Bibliography Glossary 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;:::; 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 be- havior variable Z h is assumed to be measured on an or- dinal discrete scale with values 1; 2;:::; M h for some M h  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, con- ditional 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 possi- bility arises that one of the outgoing tie variables from actor i is changed. Covariates Variables which can depend on the actors (ac- tor covariates) or on pairs of actors (dyadic covariates), and which are considered to be deterministic, or deter- mined outside of the ‘stochastic system’ under consid- eration. 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 be- havior of the other actors. Markov chain A stochastic process where the probabil- ity distribution of future states, given the present state, does not depend on past states. Method of moments A general method of statistical es- timation, where the parameters are estimated in such a way that expected values of a vector of selected statis- tics 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 probabil- ity 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 num- ber 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 D 1 that there is a tie i ! j, and by the value 0 that there is no such tie. Also called tie variables. Definition of the Subject Social networks represent the patterns of ties between so- cial actors. To analyze empirically the mechanisms that determine creation and termination of ties, especially if several mechanisms that may be complementary are stud- ied simultaneously, statistical methods are needed. This chapter is aimed at the case that network panel data are available to the researcher, and treats recently developed statistical models for such data, with corresponding esti- mation methods. To represent the feedback processes in- herent in network dynamics, it is helpful to regard such panel data as momentary observations on a continuous- time stochastic process on the space of directed graphs. Tie-oriented and actor-oriented stochastic models are pre- sented, which can reflect endogenous network dynamics as well as effects of exogenous variables. These models can