## Methods for Diagnosis and Interpretation of Stochastic Actor-oriented Models for Dynamic Networks

2014
Dissertation
##### Abstract
The stochastic actor-oriented model (SAOM) is the most established model for the statistical analysis of dynamic social network data. It is designed for network panel data, consisting of two or more observations of a network at discrete moments in time, and has the aim to detect local formation rules, called network effects, that govern the unobserved evolution process between consecutive network observations.
Thereby, the evolution is modeled as a parameterized continuous-time Markov process and is assumed to be a sequence of single relational changes that are consequences of decisions taken by individual actors.

This dissertation provides methodological contributions to support the informative analysis of dynamic networks with SAOMs. The focus is on two aspects:

1. The SAOM is one of the few network models that allow for statistical inference. So far, the interpretation of inferred results has been restricted to statistical significance tests while the importance of effects has usually been ignored. Indeed, there is no established approach or measure to assess the relative importance of effects in a SAOM.

We introduce such a measure based on the influence of effects on decisions of individual actors, in particular, on the idea of comparing the predicted choice distribution of an actor decision in the given model with the predicted choice distribution in a modified model.
The proposed measure is descriptive and relates directly to the analyzed data. Thereby, it reveals time-dependent changes in the data and their consequences for model interpretation. Its major advantage, however, lies in the possibility to compare the relative importance of effects within a model, among different models, and for different data sets which facilitates the communication and interpretation of inferred results beyond significance tests.

2. A main assumption of the SAOM is the assumption of actor homogeneity implying that local formation rules apply to all actors identically. This assumption is unjustified in many cases and may lead to unreliable results. However, allowing individual rules for all actors would inflate the model and obstruct the purpose of finding general evolutionary regularities.

In this dissertation, we develop diagnostic methods for validating the assumption of actor homogeneity or, failing that, for identifying outliers, i.e., actors to which the generalized rules do not apply, and, especially, for detecting influential actors, i.e., outliers with a particularly strong impact on estimation results. The proposed diagnostics are based on two principles. The first corresponds to residual analysis, distinguishing actors based on the quality of model predictions, and the second investigates the sensitivity of models towards small perturbations of the estimation procedure, distinguishing actors based on their influence on parameter estimates. Both require negligible extra computation time so that they lend themselves well to preventive standard usage.
##### Subject (DDC)
004 Computer Science
##### Cite This
ISO 690INDLEKOFER, Natalie, 2014. Methods for Diagnosis and Interpretation of Stochastic Actor-oriented Models for Dynamic Networks [Dissertation]. Konstanz: University of Konstanz
BibTex
@phdthesis{Indlekofer2014Metho-27469,
year={2014},
title={Methods for Diagnosis and Interpretation of Stochastic Actor-oriented Models for Dynamic Networks},
author={Indlekofer, Natalie},
school={Universität Konstanz}
}

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<dcterms:abstract xml:lang="eng">The stochastic actor-oriented model (SAOM) is the most established model for the statistical analysis of dynamic social network data. It is designed for network panel data, consisting of two or more observations of a network at discrete moments in time, and has the aim to detect local formation rules, called network effects, that govern the unobserved evolution process between consecutive network observations.&lt;br /&gt;Thereby, the evolution is modeled as a parameterized continuous-time Markov process and is assumed to be a sequence of single relational changes that are consequences of decisions taken by individual actors.&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;This dissertation provides methodological contributions to support the informative analysis of dynamic networks with SAOMs. The focus is on two aspects:&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;1. The SAOM is one of the few network models that allow for statistical inference. So far, the interpretation of inferred results has been restricted to statistical significance tests while the importance of effects has usually been ignored. Indeed, there is no established approach or measure to assess the relative importance of effects in a SAOM.&lt;br/&gt;&lt;br /&gt;&lt;br /&gt;We introduce such a measure based on the influence of effects on decisions of individual actors, in particular, on the idea of comparing the predicted choice distribution of an actor decision in the given model with the predicted choice distribution in a modified model.&lt;br /&gt;The proposed measure is descriptive and relates directly to the analyzed data. Thereby, it reveals time-dependent changes in the data and their consequences for model interpretation. Its major advantage, however, lies in the possibility to compare the relative importance of effects within a model, among different models, and for different data sets which facilitates the communication and interpretation of inferred results beyond significance tests.&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;2. A main assumption of the SAOM is the assumption of actor homogeneity implying that local formation rules apply to all actors identically. This assumption is unjustified in many cases and may lead to unreliable results. However, allowing individual rules for all actors would inflate the model and obstruct the purpose of finding general evolutionary regularities.&lt;br/&gt;&lt;br /&gt;&lt;br /&gt;In this dissertation, we develop diagnostic methods for validating the assumption of actor homogeneity or, failing that, for identifying outliers, i.e., actors to which the generalized rules do not apply, and, especially, for detecting influential actors, i.e., outliers with a particularly strong impact on estimation results. The proposed diagnostics are based on two principles. The first corresponds to residual analysis, distinguishing actors based on the quality of model predictions, and the second investigates the sensitivity of models towards small perturbations of the estimation procedure, distinguishing actors based on their influence on parameter estimates. Both require negligible extra computation time so that they lend themselves well to preventive standard usage.</dcterms:abstract>
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February 4, 2014
No