Dynamic Social Network Modeling and Analysis Workshop Summary and Papers (2003) / Chapter Skim
Currently Skimming:
Session III: Metrics and Models
Session III: Metrics and Models
Sensitivity Analysis of Social Network Data and Methods: Some Preliminary Results
Pages 195-208
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 195... ...
SESSION III Metrics and Models
|
From page 197... ...
Major breakthroughs over the past ten years, both substantive and methodological, have allowed this paradigm to greatly expand its usefulness, especially in comm7,nication, broadly defined (including internet research) , organizational science, and epidemiology.
|
From page 198... ...
~X, O otherwise We will use a variety of graph characteristics and statistics throughout this presentation Distribution theory The first step for any probabilistic model of a network is to construct a dependence graph. Such a device allows us to distinguish among the many possible graph probability distributions, which can often be characterized by considering which relational ties are assumed to be statistically independent.
|
From page 199... ...
, although the primary focus in the mathematics literature is on asymptotic behavior of various graph statistics as the size of the node set increases (whereas typically in social network analysis we wish to analyze social networks on a fixed node set)
|
From page 200... ...
in the form of an exponential family of distributions, as discussed in detail, in for example, Wasserman and Robins (2002~. For our sensitivity analyses, we will postulate various, albeit simple, dependence graphs, and adopt the associated probability distribution, in order to study the effects of node and line removals on graph statistics.
|
From page 201... ...
. , Many analyses of standard social network data sets involve summarizing the relational data with a substantively-meaningful, carefully chosen set of network statistics.
|
From page 202... ...
We term the study of resistance of network statistics sensitivity analysis, as it is often called in the statistical modelling literature. It should be obvious that sensitivity analyses of standard network statistics are desperately needed.
|
From page 203... ...
. Both network sizes indicate the same nonmonotonic relationship between density and degree centralization (Figure 1 indicates that the underlying distribution governing this relationship may be approximated by a binomial distribution)
|
From page 204... ...
Figure 4 indicates the initial inverse exponential relationship that eventually becomes a linear relationship when density is approximately 0.40. The only difference between the 204 DYNAMIC SOCKS HETWO~MODEL~G~D TRYSTS
|
From page 205... ...
0.25 0.2 in 89.15 Q m ° 0.1 C' 0.05 - / o 0.1 0.2 0.4 0.5 0.6 0.7 Density 0.8 0.9 1 Table 3: Mean and Variances of Distributions-Balance . # of Actors # of Lines Mean Balance Variance 10 ~ Mass points 10 15 20 25 30 35 40 9 0.0006 0.0085 0.0319 0.0808 0.1619 0.2847 0.4608 0.6965 0.0000 0.0001 0.0002 0.0003 0.0004 0.0004 0.0003 0.0001 2 4 10 15 18 16 15 9 networks of 10 actors and the networks of 25 actors is the initial inverse exponential relationship is smoother in the larger sociomatrices.
|
From page 206... ...
This observed abnormality Table 4: Mean and Variances of Distributions-Efficiency # of Actors # of Lines Mean EfficiencG ~ .
|
From page 207... ...
This approach will possibly lead to approximating phenomena in the field of social networks with underlying statistical distributions in the saline manner that Is used in several other fields. References Besag, J.E.
|
From page 208... ...
(2002~. Interdependencies and social processes: Dependence graphs and generalized dependence structures.
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.