Transcript No Slide Title

Local Networks
Overview
Overview
Personal Relations:
•Core Discussion Networks
•Getting Deals Done
•Questions to answer with local network data
•Mixing
•Local Context
•Social Support
•Collecting (Ego-)Network Data
•Cloning Headless Frogs
•Examples
•Effect of missing data
•Strategies for Analysis
•Content
•Structure
•Software:
•UCINET & PAJEK
Local Networks
Core Discussion Nets
Core Discussion networks
Question asked:
“From time to time, most people discuss important matters with other
people. Looking back over the last six months -- who are the people with whom you
discussed matters important to you? Just tell me their first names or initials.”
Why this question?
•Only time for one question
•Normative pressure and influence likely travels through strong ties
•Similar to ‘best friend’ or other strong tie generators
Local Networks
Core Discussion Nets
Types of measures:
Network Range: the extent to which a person’s ties connects them to a diverse set of
other actors.
Includes:
Size, density, homogeneity
Network Composition: The types of alters in ego’s networks.
Can include many things, here it is about kin.
Local Networks
Core Discussion Nets
Distribution of total network size, GSS 1985
25
Percent
20
15
10
5
0
0
1
2
3
4
5
6+
Local Networks
Core Discussion Nets
Network size by:
Age:
Drops with age at an increasing rate. Elderly have few close ties.
Education:
Increases with education. College degree ~ 1.8 times larger
Sex (Female):
No gender differences on network size.
Race:
African Americans networks are smaller (2.25) than White Networks (3.1).
Local Networks
Core Discussion Nets
Proportion Kin, GSS 1985
35
30
25
20
15
10
5
0
0
0.15
0.45
0.75
1
Local Networks
Core Discussion Nets
Proportion Kin by:
Age:
Proportion Kin
0.65
0.6
0.55
0.5
0.45
10
20
30
40
Age
50
60
70
Local Networks
Core Discussion Nets
Proportion Kin by:
Education:
Proportion decreases with education, but they nominate more of both kin
and non-kin in absolute numbers.
Sex (Female):
Females name slightly more kin than males do.
Race:
African American cite fewer kin (absolute and proportion) than do Whites.
Local Networks
Core Discussion Nets
Network Density
Recall that density is the average value of the relation among all pairs
of ties. Here, density is only calculated over the alters in the network.
2
1
R
3
1
3
4
5
1 2 3 4 5
2
4
5
D=0.5
1
2
3
4
5
1
1
1
1
1
Local Networks
Core Discussion Nets
40
35
30
25
20
15
10
5
0
<.25
.25-.49
.50-.74
Density
>.74
Local Networks
Core Discussion Nets
Network Density
Age:
Increases as we age.
Education:
Decreases among the most educated.
Race:
No differences by race.
Size of Place:
People from large cities have lower density than do those in small cities.
Local Networks
Core Discussion Nets
Network Heterogeneity
Heterogeneity is the variance in type of people in your network.
Networks tend to be more homogeneous than the population. Marsden
reports differences by Age, Education, Race and Gender. He finds that:
•Age distribution is fairly wide, almost evenly distributed,
though lower than the population at large
•Homogenous by education (30% differ by less than a year, on
average)
•Very homogeneous with respect to race (96% are single race)
•Heterogeneous with respect to gender
Local Networks
Core Discussion Nets
Network Heterogeneity
Heterogeneity differs by:
Age:
Tends to decrease as we age
Education:
Heterogeneity increases with education
Race:
No differences in age. Minorities tend to have higher race-heterogeneity
(consistent with Blau’s intergroup mixing model) and lower gender heterogeneity.
Size of place:
Large settings tend to be correlated with greater heterogeneity in the
network.
Social Network Data
Cloning Headless Frogs
How good is the name generator?
Bearman and Parigi ask about what is being captured in the GSS name generator,
which because of it’s placement in the GSS has become a standard question.
Others have done this, and found that the resulting list of names does not differ
significantly (see Straits 2000).
Bearman & Parigi argue that to understand the network, you need to understand what
it is people are really talking about.
The basic assumption of the GSS question is that people talk about important
matters to people who are important to them.
Social Network Data
Cloning Headless Frogs
Key Questions:
1)
What do people talk about?
2)
Why do so many people not report talking about anything with anybody?
3)
Given the heterogeneity of the topics discussed, is there a foundation from
which one could use the GSS data to describe anything meaningful about core
discussion networks?
4)
Is there a pattern of topics to alters and how does this affect comparative
analyses?
Social Network Data
Cloning Headless Frogs
Key Questions:
1)
What do people talk about? & Who did they talk to?
Note that the topic was heavily dependent on the questionnaire order. In this survey, it
was the first question.
Social Network Data
Cloning Headless Frogs
Key Questions:
1)
Why do so many people not report talking about anything with anybody?
Social Network Data
Cloning Headless Frogs
talks about what with who?
Connections are significant cells from table 5.
Social Network Data
Cloning Headless Frogs
Who talks about what?
Males
Connections are large values from figure 1.
Females
Social Network Data
Cloning Headless Frogs
1)
Why do so many people not report talking about anything with anybody?
•
44% report nobody to talk to
•
More likely to be without spouses, unemployed and non-white
•
56% report nothing important to talk about.
Social Network Data
Cloning Headless Frogs
Social Network Data
Cloning Headless Frogs
•End result suggest using questions that are linked directly to conversation
domains of substantive interest.
•Or, more generally, defining relationships that are of importance for your
topic of study.
Local Networks
Getting Deals Done
If networks provide resources and “social capital,” then different types of networks should
matter for business transactions.
-Builds on a long line of research about risk control, managing uncertainty and
information gathering through networks.
-The argument turns on a subtle difference: the networks that help you get
information about a deal (and thus bring a deal to the table) are not the same as the
networks that generate approval for the deal, and in fact might work in different
ways.
Local Networks
Getting Deals Done
Outline of the
argument &
findings.
Local Networks
Getting Deals Done
Claims the results suggest a paradox:
a) Uncertain deals require strong networks
b) But embeddedness in strong networks makes it less likely a deal will close.*
This leads them to the ‘multiple lens’ hypothesis. That decisions are best made when
subject to information that comes from multiple, disconnected sources.
(*note this works on two different notions of ‘strong’ in the actual models, so there’s some empirical slippage
here…)
Social Network Data
Network Data Sources: Existing data sources
Existing Sources of Social Network Data:
There are lots of network data archived. Check INSNA for a listing. The PAJEK data
page includes a number of exemplars for large-scale networks.
1-Mode Data
Local Network data:
•
Fairly common, because it is easy to collect from sample surveys.
•
GSS, NHSL, Urban Inequality Surveys, etc.
•
Pay attention to the question asked
•
Key features are (a) number of people named and (b) whether alters are
able to nominate each other.
Social Network Data
Network Data Sources: Existing data sources
Existing Sources of Social Network Data:
1-Mode Data
Partial network data:
• Much less common, because cost goes up significantly once you
start tracing to contacts.
• Snowball data: start with focal nodes and trace to contacts
• CDC style data on sexual contact tracing
• Limited snowball samples:
• Colorado Springs drug users data
• Geneology data
• Small-world network samples
• Limited Boundary data: select data within a limited bound
• Cross-national trade data
• Friendships within a classroom
• Family support ties
Social Network Data
Network Data Sources: Existing data sources
Existing Sources of Social Network Data:
1-Mode Data
Complete network data:
• Significantly less common and never perfect.
• Start by defining a theoretically relevant boundary
• Then identify all relations among nodes within that boundary
• Co-sponsorship patterns among legislators
• Friendships within strongly bounded settings (sororities,
schools)
• Examples:
• Add Health on adolescent friendships
• Hallinan data on within-school friendships
• McFarland’s data on verbal interaction
• Electronic data on citations or coauthorship (see Pajek data
page)
• See INSNA home page for many small-scale networks
Social Network Data
Network Data Sources: Collecting network data
Boundary Specification Problem
Network methods describe positions in relevant social fields, where flows
of particular goods are of interest. As such, boundaries are a
fundamentally theoretical question about what you think matters in
the setting of interest.
See Marsden (19xx) for a good review of the boundary specification
problem
In general, there are usually relevant social foci that bound the relevant
social field. We expect that social relations will be very clumpy.
Consider the example of friendship ties within and between a highschool and a Jr. high:
Social Network Data
Network Data Sources: Collecting network data
a)
Network data collection can be time consuming. It is better (I think) to
have breadth over depth. Having detailed information on <50% of the
sample will make it very difficult to draw conclusions about the general
network structure.
b) Question format:
• If you ask people to recall names (an open list format), fatigue will
result in under-reporting
• If you ask people to check off names from a full list, you can often get
over-reporting
c) It is common to limit people to a small number if nominations (~5). This
will bias network measures, but is sometimes the best choice to avoid
fatigue.
d) Concrete relational indicators are best (who did you talk to?) over attitudes
that are harder to define (who do you like?)
Social Network Data
Network Data Sources: Collecting network data
Boundary Specification Problem
While students were
given the option to name
friends in the other
school, they rarely do.
As such, the school likely
serves as a strong
substantive boundary
Social Network Data
Network Data Sources: Collecting network data
Local Network data:
• When using a survey, common to use an “ego-network module.”
• First part: “Name Generator” question to elicit a list of names
• Second part: Working through the list of names to get
information about each person named
• Third part: asking about relations among each person named.
GSS Name Generator:
“From time to time, most people discuss important matters with other people.
Looking back over the last six months -- who are the people with whom you
discussed matters important to you? Just tell me their first names or initials.”
Why this question?
•Only time for one question
•Normative pressure and influence likely travels through strong ties
•Similar to ‘best friend’ or other strong tie generators
•Note there are significant substantive problems with this name generator
Social Network Data
Network Data Sources: Collecting network data
Electronic Small World name generator:
Social Network Data
Network Data Sources: Collecting network data
Local Network data:
The second part usually asks a series of questions about each person
GSS Example:
“Is (NAME) Asian, Black, Hispanic, White or something else?”
ESWP example:
Will generate N x (number of attributes) questions to the survey
Social Network Data
Network Data Sources: Collecting network data
Local Network data:
The third part usually asks about relations among the alters. Do this
by looping over all possible combinations. If you are asking about a
symmetric relation, then you can limit your questions to the n(n-1)/2
cells of one triangle of the adjacency matrix:
1 2 3 4 5
1
2
3
4
5
GSS: Please think about the relations between the people you just mentioned. Some of them may
be total strangers in the sense that they wouldn't recognize each other if they bumped into each
other on the street. Others may be especially close, as close or closer to each other as they are to
you. First, think about NAME 1 and NAME 2. A. Are NAME 1 and NAME 2 total strangers? B.
ARe they especially close? PROBE: As close or closer to eahc other as they are to you?
Social Network Data
Network Data Sources: Collecting network data
Local Network data:
The third part usually asks about relations among the alters. Do this
by looping over all possible combinations. If you are asking about a
symmetric relation, then you can limit your questions to the n(n-1)/2
cells of one triangle of the adjacency matrix:
Social Network Data
Network Data Sources: Collecting network data
Snowball Samples:
• Snowball samples work much the same as ego-network modules,
and if time allows I recommend asking at least some of the basic
ego-network questions, even if you plan to sample (some of) the
people your respondent names.
• Start with a name generator, then any demographic or relational
questions.
• Have a sample strategy
• Random Walk designs (Klovdahl)
• Strong tie designs
• All names designs
• Get contact information from the people named
Snowball samples are very effective at providing network context
around focal nodes. Detailed treatments of snowball sampling
estimates are given in Frank ().
Social Network Data
Network Data Sources: Collecting network data
Snowball Samples:
Social Network Data
Network Data Sources: Collecting network data
Complete Network data
• Data collection is concerned with all relations within a specified
boundary.
• Requires sampling every actor in the population of interest (all
kids in the class, all nations in the alliance system, etc.)
• The network survey itself can be much shorter, because you are
getting information from each person (so ego does not report on
alters).
• Two general formats:
• Recall surveys (“Name all of your best friends”)
• Check-list formats: Give people a list of names, have them
check off those with whom they have relations.
Social Network Data
Network Data Sources:
Collecting network data
Complete network surveys require
a process that lets you link answers
to respondents.
•You cannot have anonymous
surveys.
•Recall:
•Need Id numbers & a
roster to link, or handcode names to find
matches
•Checklists
•Need a roster for people
to check through
Social Network Data
Network Data Sources: Missing Data
Whatever method is used, data will always be incomplete. What are the
implications for analysis?
Example 1. Ego is a matchable person in the School
Out
Un
Ego
M
M
True Network
Out
Un
Ego
M
M
Out
Un
M
M
M
M
Observed Network
Social Network Data
Network Data Sources: Missing Data
Example 2. Ego is not on the school roster
M
M
Un
Un
M
M
M
M
M
M
M
Un
Un
Un
True Network
M
Observed Network
Social Network Data
Network Data Sources: Missing Data
Example 3:
Node population: 2-step neighborhood of Actor X
Relational population: Any connection among all nodes
1-step
2-step
3-step
F
1.1
1.2
1.3
1.4
1.5
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
3.1
3.2
3.3
F 1 2 3 4 5 1 2 3 4 5 6 7 8 1 2 3
Full (0)
Full
Full (0)
F
Full
Full
Full (0)
F
(0)
Full
Full
UK
F
(0)
Full (0)
Unknown
UK
Social Network Data
Network Data Sources: Missing Data
Example 4
Node population: 2-step neighborhood of Actor X
Relational population: Trace, plus All connections among 1-step contacts
1-step
2-step
3-step
F
1.1
1.2
1.3
1.4
1.5
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
3.1
3.2
3.3
F 1 2 3 4 5 1 2 3 4 5 6 7 8 1 2 3
Full (0)
Full
Full (0)
Full
Full (0)
F
Full
F
(0)
Full
Unknown
UK
F
(0)
Full (0)
Unknown
UK
Social Network Data
Network Data Sources: Missing Data
Example 5.
Node population: 2-step neighborhood of Actor X
Relational population: Only tracing contacts
1-step
2-step
3-step
F
1.1
1.2
1.3
1.4
1.5
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
3.1
3.2
3.3
F 1 2 3 4 5 1 2 3 4 5 6 7 8 1 2 3
Full (0)
Full
Full (0)
Full
Full (0)
F
Unknown
F
(0)
Full
Unknown
UK
F
(0)
Full (0)
Unknown
UK
Social Network Data
Network Data Sources: Missing Data
Example 6
Node population: 2-step neighborhood from 3 focal actors
Relational population: All relations among actors
Focal
1-Step
2-Step
3-Step
Focal
Full
Full
Full (0)
Full (0)
1-Step
Full
Full
Full
Full (0)
2-Step
Full
(0)
Full
Full
UK
3-Step
Full
(0)
Full (0)
Unknown
UK
Social Network Data
Network Data Sources: Missing Data
Example 7.
Node population: 1-step neighborhood from 3 focal actors
Relational population: Only relations from focal nodes
Focal
1-Step
2-Step
3-Step
Focal
Full
Full
Full (0)
Full (0)
1-Step
Full
Unknown
Unknown
Full (0)
2-Step
Full
(0)
Unknown
Unknown
UK
3-Step
Full
(0)
Full (0)
Unknown
UK
Local Network Analysis
Introduction
Local network analysis uses data from a simple ego-network survey. These might include
information on relations among ego’s contacts, but often not. Questions include:
Population Mixing
The extent to which one type of person is tied to another type of
person (race by race, etc.)
Local Network Composition
Peer behavior
Cultural milieu
Opportunities or Resources in the network
Social Support
Local Network Structural
Network Size
Density
Holes & Constraint
Concurrency
Dyadic behavior
Frequency of contact
Interaction content
Specific exchange behaviors
Local Network Analysis
Introduction
Advantages
•Cost: data are easy to collect and can be sampled
•Methods are relatively simple extensions of common variable-based methods
social scientists are already familiar with
•Provides information on the local network context, which is often the primary
substantive interest.
•Can be used to describe general features of the global network context
•Population mixing, concurrency, activity distribution (limited)
Disadvantages
•Treats each local network as independent, which is false.
The poor performance of ‘number of partners’ for predicting STD spread is
a clear example.
•Impossible to account for how position in a larger context affects local network
characteristics. “popular with who”
•If “structure matters”, ego-networks are strongly constrained to limit the
information you can get on overall structure
Local Network Analysis
Network Composition
Perhaps the simplest network question is “what types of alters does ego interact with”?
Network composition refers to the distribution of types of people in your network.
Networks tend to be more homogeneous than the population. Using the
GSS, Marsden reports heterogeneity in Age, Education, Race and Gender.
He finds that:
•Age distribution is fairly wide, almost evenly distributed,
though lower than the population at large
•Homogenous by education (30% differ by less than a year, on
average)
•Very homogeneous with respect to race (96% are single race)
•Heterogeneous with respect to gender
Local Network Analysis
General Questions
Questions that you can ask / answer
Mixing
The extent to which one type of person is tied to
another type of person (race by race, etc.)
Aspects of the local context:
Peer delinquency
Cultural milieu
Opportunities
Social Support:
Extent of resources (and risks) present in a type of
network environment.
Structural context (next class)
Local Network Analysis
Mechanics
Calculating local network information.
1) From data, such as the GSS, which has ego-reported information on alter
2) From global network data, such as Add Health, where you have self-reports on
alters behaviors.
Local Network Analysis
Mechanics
Calculating local network information 1: GSS style data.
This is the easiest situation. Here you have a separate variable for each alter
characteristic, and you can construct density items by summing over the relevant
variables.
You would, for example, have variables on age of each alter such as:
Age_alt1 age_alt2 age_alt3 age_alt4 age_alt5
15
35
20
12
.
You get the mean age, then, with a statement such as:
meanage=mean(Age_alt1, age_alt2, age_alt3, age_alt4, age_alt5);
Be sure you know how the program you use (SAS, SPSS) deals with missing data.
Local Network Analysis
Mechanics
Calculating local network information 2: From a global network.
There are multiple options when you have complete network information.
Type of tie:
Sent, Received, or both?
Once you decide on a type of tie, you need to get the information of interest in a
form similar to that in the example above.
Local Network Analysis
Mechanics
Calculating local network
information from a global network.
An example network:
All senior males from a
small (n~350) public HS.
Local Network Analysis
Mechanics
Suppose you want to identify ego’s friends, calculate what proportion of ego’s female friends
are older than ego, and how many male friends they have (this example came up in a model of
fertility behavior).
You need to:
•Construct a dataset with
(a) ego's id. This allows you to link each person in the network.
(b) age of each person,
(c) the friendship nominations variables.
•Then you need to:
a) Identify ego's friends
b) Identify their age
c) compare it to ego's age
d) count it if it is greater than ego's.
There is a SAS program described in the exercise that shows you how to do this kind of
work, using the graduate student network data.
Local Network Analysis
Mechanics
1) Go over how to translate network data from one program to another
UCINET
PAJEK
2) Go over the use of ego-net macros in SAS