UCInet入门以及社会网络基础

Introduction to social network methods

18. Some statistical tools

This page is part of an on-line text by Robert A. Hanneman (Department of Sociology,

University of California, Riverside) and Mark Riddle (Department of Sociology, University of

Northern Colorado).+ Feel free to use and distribute this textbook, with citation. Your

comments and suggestions are very welcome. Send me e-mail.

Contents of chapter 18:+ Some statistical tools

 Introduction: + Applying statistical tools to network data

o Network regression

 Explaining attributes of networked actors

o Hypotheses about the means of two groups

o Hypotheses about the means of multiple groups

o Regressing position on attributes

 Explaining the relations among actors in a network

o Hypotheses about relations within/between groups

o Homophily models

o Hypotheses about similarity and distance

o The probability of a dyadic tie: + Leinhardt's P1

confidence in the reliability of our observations about the relations among the

actors.+ Most of the tools of social network analysis involve the use of

mathematical functions to describe networks and their sub-structures.

In more recent work, however, some of the focus of social network research

has moved away from these roots.+ Increasingly, the social networks that are

being studied may contain many nodes; and, sometimes our observations

about these very large networks are based not on censuses, but on samples

of nodes.+ Network researchers have come to recognize that the relations that

they study may be constantly evolving, and that the relations observed at one

point in time may not the entirely typical because the pattern of relations is not

provide useful tools for summarizing large amounts of information, and for

treating observations as stochastic, rather than deterministic outcomes of

social processes.

Descriptive statistics have proven to be of great value because they provide

convenient tools to summarize key facts about the distributions of actors,

attributes, and relations; statistical tools can describe not only the shape of

one distribution, but also joint distributions, or "statistical association."+ So,

statistical tools have been particularly helpful in describing, predicting, and

testing hypotheses about the relations between network properties.

Inferential statistics have also proven to have very useful applications to social

network analysis.+ At a most general level, the question of "inference" is:+ how

tuned for the needs of social network analysis is one of the most rapidly

table of contents

Describing one network

Most social scientists have a reasonable working knowledge of basic

univariate and bivariate descriptive and inferential statistics.+ Many of these

tools find immediate application in working with social network data.+ There

are, however, two quite important distinctive features of applying these tools

to network data.

First, and most important, social network analysis is about relations among

actors, not about relations between variables.+ Most social scientists have

learned their statistics with applications to the study of the distribution of the

scores of actors (cases) on variables, and the relations between these

distributions and relations among distributions.+ But, rather than describing

network data, we are concerned the issues like the average strength of the

strength of ties between actors in a network correlated with the centrality of

the actors in the network?"++ Most of the descriptive statistical tools are the

same for attribute analysis and for relational analysis -- but the subject matter

is quite different!

Second, many of tools of standard inferential statistics that we learned from

the study of the distributions of attributes do not apply directly to network

data.+ Most of the standard formulas for calculating estimated standard errors,

computing test statistics, and assessing the probability of null hypotheses that

samplings from populations.+ In attribute analysis, it is often very reasonable

to assume that Fred's income and Fred's education are a "trial" that is

independent of Sue's income and Sue's education.+ We can treat Fred and

Sue as independent replications.

an George), it is probably not reasonable to suppose that these relations are

"independent" because they both involve George.

The standard formulas for computing standard errors and inferential tests on

attributes generally assume independent observations.+ Applying them when

the observations are not independent can be very misleading.+ Instead,

alternative numerical approaches to estimating standard errors for network

statistics are used.+ These "boot-strapping" (and permutations) approaches

calculate sampling distributions of statistics directly from the observed

networks by using random assignment across hundreds or thousands of trials

under the assumption that null hypotheses are true.

table of contents

Univariate descriptive statistics

These particular data happen to be asymmetric and binary.+ Most of the

statistical tools for working with network data can be applied to symmetric

data, and data where the relations are valued (strength, cost, probability of a

tie).+ As with any descriptive statistics, the scale of measurement (binary or

valued) does matter in making proper choices about interpretation and

application of many statistical tools.

The data that are analyzed with statistical tools when we are working with

network data are the observations about relations among actors.+ So, in each

matrix, we have 10 x 10 = 100 observations or cases.+ For many analyses, the

ties of actors with themselves (the main diagonal) are not meaningful, and are

be used to generate the most commonly used measures for each matrix

(select matrix in the dialog, and chose whether or not to include the