EGO NETWORK ANALYSIS��SOCIAL NETWORKS AND HEALTH�DUKE UNIVERSITY, 2019

Brea L. Perry

Professor of Sociology

Indiana University Network Science Institute

ROADMAP

1. Pros and cons of an ego network approach
2. Common measures and when to use them
3. Data management for ego networks
4. Regression with ego net variables
5. Multilevel modeling
6. Ego network dynamics

​

SOCIOCENTRIC NETWORKS

• Maps the overall structure of one global network, including all direct and indirect ties between actors
• Every member of a bounded group using a roster

​

​

EGOCENTRIC NETWORKS

• Many local networks - individuals’ connections to their own personal community networks from the perspective of embedded ego
• Many non-overlapping networks

​

​

​

MAJOR ADVANTAGES OF EGO NETWORKS

Practical advantages: Flexibility in data collection

• Sociocentric SNA is very time-consuming, expensive, prone to missing data, and targeted to a narrow set of research questions
• Potential sampling frames and data collection strategies for ego nets are virtually limitless
• Can easily be incorporated into large-scale or nationally-representative surveys

​

MAJOR ADVANTAGES OF EGO NETWORKS

Broader inference

• Sociocentric SNA has limited inference beyond the group (or other groups like it)
• Ideally, ego networks are completely independent and randomly selected; inference to other egos and their networks is appropriate, making them more generalizable

MAJOR ADVANTAGES OF EGO NETWORKS

Theoretical advantages: Unboundedness

• Ability to transcend the boundaries of a single group or domain to examine Simmel’s (1955) overlapping social circles
• Census in one domain will omit important interaction partners outside that domain
• Makes egocentric ideal for studying what happens to individuals – who operate in multiple contexts

EXAMPLE NAME GENERATOR

EGO NETS: DISADVANTAGES

• Heavy respondent burden compared to proxy measures, which increases exponentially with network size
• Inability to measure received or reciprocated (i.e., directed) ties
• Relies on ego’s perspective (sometimes an advantage)
• Inability to map the broader social structure in which personal networks are embedded
• Can’t assess the implications for ego of ties that DO NOT exist

DISADVANTAGES (MAYBE NOT)

Jeffrey Smith’s simulation approach constructs full networks that are consistent with each piece of information extracted from the ego network sample

Smith, Jeffrey A. 2015. “Global Network Inference from Ego Network Samples: Testing a Simulation Approach.” The Journal of Mathematical Sociology 39:125-162.

Smith, Jeffrey A. 2012. “Macrostructure from Microstructure: Generating Whole Systems from Ego Networks.” Sociological Methodology 42:155-205.

Smith, Jeffrey A. and Jessica Burrow. 2018. “Using Ego Network Data to Inform Agent Based Models of Diffusion.” Sociological Methods & Research. doi: 10.1177/0049124118769100

Comparison of diffusion curves from true networks and sampled-based estimates using Add Health

“Across all analyses, the diffusion curves based on the sampled data are very similar to the curves based on the true, complete network.”

COMMON MEASURES IN EGOCENTRIC NETWORK ANALYSIS

WHAT ARE WE TRYING TO OPERATIONALIZE?

1. Content = Social and cultural characteristics of network members, including material and non-material resources, whether or not they are accessible
2. Strength = The quality and intensity of bonds between network members
3. Function = Types of exchanges, services, or supports provided by network members
4. Structure = The presence and patterns of linkages between actors in a social network

​

MEASUREMENT

Ego network measures are based on:

• Ego-alter ties
• Alter attributes
• Alter-alter ties

EGO-ALTER TIES

Degree

• Number of alters to whom ego has a direct connection (i.e. network size)
• Can be interpreted as a measure of social integration, social capital, social activity, or prominence
• BUT can be good or bad - what ego is getting more of with each additional alter?

EGO-ALTER TIES

Degree

• Must be cautious because it is highly dependent on name generator strategy (esp. numeric limits)
• Can compare size within your sample, but not to other samples
• Don’t want to double count in multiple name generator strategy
• May choose not to count all types of ties (e.g. political discussants vs. support networks)

​

EGO-ALTER TIES

Multiplexity

• Overlap between the functions of ties or the ways that an alter is related to ego
• E.g. coworker 🡪 friend
• Affectively stronger, more motivation to maintain
• Multiplex ties associated with higher self-esteem, psych adjustment, satisfaction with relationships

EGO-ALTER TIES

Multiplexity

• Can examine freq or presence of specific combinations
• E.g. to compare groups…gender and “framily” members
• Can use as a measure of tie strength by counting ways connected or functions
• E.g. are ties with higher multiplexity less likely to dissolve over time

EGO-ALTER TIES

Tie strength

• Captures intensity, duration, affective qualities
• Closeness, freq of contact, length of relationship, important matters, strength
• Presence of strong ties = integration or regulation
• Presence of weak ties = bridging potential, access to novel resources

EGO-ALTER TIES

Tie strength

• Avg strength of tie
• E.g. if measuring neighborhood ties, operationalize community engagement
• Count of strong or weak ties
• Other measures of central tendency (e.g. max)
• Standard deviation

EGO-ALTER TIES

Other relationship characteristics

• Can be calculated and used similarly to tie strength
• E.g. frequency, central tendency, SD
• May be functions - stuff alter does for/to ego, or ego does for/to alter (e.g. support, regulation)
• May be presence of other shared activities (e.g. sex, drug use, political discussion)

ALTER ATTRIBUTES

Composition

• Reflects content - material and nonmaterial resources, knowledge, behaviors, and cultural characteristics (i.e. ideas, attitudes, values)
• Social influence
• E.g. Obesity, smoking, drinking, and happiness are “contagious”
• Access to social capital
• E.g. People are more likely to get a job at Google if they know someone in the tech industry
• Broader patterns of interaction in society
• E.g. People with more education have more educated networks

ALTER ATTRIBUTES

Composition (categorical)

• Proportion for strength or direction of influence
• E.g. proportion network democrat/republican
• Count for access to specific resources
• E.g. number of people who can help you move – more is always better, regardless of proportion

ALTER ATTRIBUTES

Composition (continuous)

• Central tendency for summarizing content
• E.g. average or median income for social class
• Min/max for access
• Max income for starting a business
• SD for diversity
• SD of income for exposure to lots of different ideas

ALTER ATTRIBUTES

Ego-alter similarity

• Three different mechanisms of similarity

1) Preference - people tend to socialize and form bonds with others like them (homophily)

• Ease of communication
• Racism, sexism, etc.
• Primitive survival instinct to fear outsiders

​

ALTER ATTRIBUTES

Ego-alter similarity

• Three different mechanisms of similarity

2) Availability - people tend to socialize and form bonds with people they come into contact with (shared foci of activity)

• Racial and SES segregation in housing
• Gender segregation in occupations and interests

​

ALTER ATTRIBUTES

Ego-alter similarity

• Three different mechanisms of similarity

3) Influence - people become more similar over time through repeated social interactions

• Applies only to achieved statuses (e.g. attitudes, decisions, behaviors), not ascribed ones (e.g. race, gender)

​

ALTER ATTRIBUTES

Ego-alter similarity

• Homophily insulates ego from outside influence and ideas and reinforces in-group behaviors and biases
• E.g. political polarization
• Homophily is identity-affirming, fostering a sense of comfort and belonging
• Can be used to impute ego characteristics (e.g. criminality, sexuality)
• Can measure social influence over time

​

ALTER ATTRIBUTES

Ego-alter similarity (categorical)

• Proportion same as ego
• E.g. if you are female and 3 out 4 of alters are female, proportion homophilous is .75
• Krackhardt and Stern’s E-I
• Ego’s propensity to have ties to alters with same characteristic
• -1 to 1 where -1 = completely homophilous and 1 = completely heterophilous

​

N_external-N_internal

network size

ALTER ATTRIBUTES

Ego-alter similarity (categorical)

• BUT homophily is dependent on the availability of different alters
• Treat distribution in community at large as expected value in a null model of no homophily
• E.g. Suppose neighborhood is 75% white, what is expected number of white ties given the lower availability of minorities in the community

ALTER ATTRIBUTES

Ego-alter similarity (categorical)

• Phi (normalized chi-square)

1) Calculate expected value

• If degree is 12, and neigh is 75% white, expect 0.75*12 = 9 white alters, 3 minority

2) Calculate chi-square

• (10-9)²/9= 0.11 + (2-3)²/3= 0.33 for a sum of 0.44

3) Normalize so value (phi) ranges from 0-1

• Sqrt 0.44/12 = 0.19

ALTER ATTRIBUTES

Ego-alter similarity (continuous)

• Average Euclidean Distance
• Is mean squared differences between ego and alters
• Just like SD, but measures deviation around ego instead of deviation around the mean
• Higher = ego is more dissimilar (more “distant”) from alters

ALTER ATTRIBUTES

Ego-alter similarity (continuous)

• Average Euclidean Distance on age
• Where k indexes alters, a_k is the age of alter k, and e is age of ego

​

​

• 30-year old ego has three alters aged 25, 32, and 40

​

​

• Only compare egos to other egos since scale depends of variable

ALTER ATTRIBUTES

Heterogeneity or “range”

• Similarity of alters to each other rather than to ego
• Heterogeneous network provides access to a larger set of non-redundant social resources
• Advantageous for instrumental actions like gathering information
• May indicate participation in diverse social spheres that cross social, institutional, or organizational boundaries
• Racial/ethnic heterogeneity is important for outcomes like cultural awareness, reduced in-group bias, cultivation of multiple ethnic identities, and continued interracial contact

ALTER ATTRIBUTES

Heterogeneity (categorical)

• Blau’s Index (Herfindahl’s or Hirschman’s index)
• Reflects how many different types (e.g. political parties) there are in a network, and simultaneously how evenly the alters are distributed among those types

ALTER ATTRIBUTES

Heterogeneity (categorical)

• Blau’s Index

​

• Where p_k is the proportion of ego’s alters in category k
• As number of categories increases, potential Blau’s Index increases. Max is:

HETEROGENEITY

HETEROGENEITY

Heterogeneity (categorical)

• Is normalized version always better?
• Not if using heterogeneity to measure diversity (e.g. of ideas)
• E.g. someone with five kinds of alters probably experiences more diversity than someone with two kinds, even if alters are uniformly distributed across categories

​

HETEROGENEITY

HETEROGENEITY

Heterogeneity (continuous)

• Standard deviation across the distribution of alters
• E.g. SD of years of education for “population” of alters

ALTER-ALTER TIES

• Ties may be binary or valued (if valued, can dichotomize)
• Info about ties (or lack of ties) between alters is essential for computing all good measures of network structure
• Usually, we are interested in operationalizing outcomes or characteristics of structural holes
• Have been linked to innovation (Ahuja 2000), good ideas (Burt 2004), knowledge transfer (Abbasi et al. 2012), individual performance (Cross and Cummings 2004), and health (Cornwell 2009)

​

ALTER-ALTER TIES

Burt’s structural holes

• The absence of a tie between two alters
• Operationalizes two types of social capital:
• Information – The more everyone knows everyone else, the more likely it is that information is redundant (and can extend to other resources)
• Power – an ego who bridges two networks is able to control the flow of information and resources between them, and is less constrained by those alters
• E.g. if my network ties don’t know each other, I can lie to them, present myself differently, play them off of one another

ALTER-ALTER TIES

Burt’s structural holes

• In network 1, actor A is not in a strong bargaining position because both B and C have alternative exchange partners
• In network 2, actor A has an advantaged position as a direct result of the "structural hole" between B and C
• A has two alternative exchange partners; B and C have only one choice

Three actor network with no structural holes

Three actor network with one structural hole

1

2

ALTER-ALTER TIES

Coleman’s closure

• Converse of structural holes is triadic closure, or transitivity
• Coleman (1988) associated closure (rather than structural holes) with social capital
• Closure 🡪 shared social norms that effectively guide the actions of an individual, interpersonal trust, obligation to group members, cohesion, cooperation
• Really, same mechanism (constraint) which may be beneficial or not depending on context
• Hence two kinds of social capital – bridging and bonding

​

ALTER-ALTER TIES

Density

• How many of ego’s alters are connected, controlling for network size?
• Strength of social safety net
• Strength of normative pressure to conform
• Very powerful in combo with composition (direction of push), e.g. use of contraception in Kenya (Kohler et al. 2001)
• More redundancy of info and resources (lack of structural holes)
• E.g. low density 🡪 adaptation and resilience after divorce (Wilcox 1981)

ALTER-ALTER TIES

Density

• Actual ties/potential ties
• Undirected ties

​

​

• Directed ties

Sparsely-knit, with 3 of 42 possible ties present

​

Density = (2*3)/(7*(7-1)) = 0.14

ALTER-ALTER TIES

Effective size

• If ego has ties to alters who are also tied to each other, there is lots of redundancy
• Redundancy = ties where alters can be reached through multiple direct and indirect pathways
• Effective size measures how many different “pots” of information ego can access
• Effective size conveys something about ego's total impact

ALTER-ALTER TIES

Effective size

• Ego’s number of alters minus the average number of ties that each alter has to other alters
• Effective size is a positive function of network size, and a negative function of the number of ties among alters

Effective size = 3

Effective size = actual size – redundancy = 3-2 = 1

ALTER-ALTER TIES

Network size = 7

Alters 1 and 5 are isolates

Alters 2, 4, 6, 7 are connected to one other alter

Alter 3 is connected to two alters

​

Mean ties per alter = (0+0+1+1+1+1+2)/7 is 0.9

​

Effective size = 7 – 0.9 = 6.1

ALTER-ALTER TIES

Efficiency

• Efficiency is very similar to effective size except that it is normed by actual size (degree)
• i.e. what proportion of ego's ties to alters are "non-redundant“
• Effective size/Network size
• Social capital per unit of relational energy (i.e. how much bang for your buck)
• May convey social and political skill, or extent to which ego chooses ties wisely to maximize this

MANAGING

EGOCENTRIC DATA

CONVENTIONAL DATA STRUCTURE

• 2-by-2 matrix in which rows (cases or observations) are entities or objects and columns (vectors or variables) are attributes
• How to store multilevel ego/alter data?

CONVENTIONAL STRUCTURE MODIFIED FOR NETWORKS

• Option 1: Conventional data structure modified for networks
• Ego attributes in columns
• Tie and alter attributes in columns, numbered sequentially
• Alter-alter ties conveyed through columns

CONVENTIONAL STRUCTURE MODIFIED FOR NETWORKS

• age = ego’s age
• female = ego’s gender
• aage1 = age of first alter named
• atie1 = how ego and alter 1 are connected (e.g. kin, friend)
• aclose1 = closeness of ego to alter 1
• aage2 = age of second alter named

​

CONVENTIONAL STRUCTURE MODIFIED FOR NETWORKS

• SAME data file
• Alter-alter ties can be valued (e.g. on likert scale) or 0/1
• afrnd1-2 = friendship between alters 1 and 2?
• afrnd1-3 = friendship between alters 1 and 3?
• afrnd1-4 = friendship between alters 1 and 4?
• afrnd2-3 = friendship between alters 2 and3?

​

​

LONG-FORM (“TIDY”) DATA

• OPTION 2: Data file structured in long form
• Each row is a tie or alter
• Ego attributes are embedded in columns
• Consistent with multilevel (hierarchical) data structure

LONG-FORM (“TIDY”) DATA

• Ego 1 has three ties; ego 2 has two ties; ego 3 has three ties
• Variables age, female, and race are attributes of ego (same for all alters, or rows, linked to that ego)
• Variables aage, atie, aclose, and asmoker are attributes of the tie or alter (differ in each row)

LONG-FORM (“TIDY”) DATA

• Adjacency matrix is a characteristic of ego
• Values in adjacency matrix are the same for all alters, or rows, linked to a given ego
• Relations that do not exist are missing (NA in R)

TRANSFORMING DATA

• Can transform ego network data into different structural forms easily
• Use R’s reshape command to transform data from option 2 (multilevel) to option 1 (conventional) and back

​

MEASUREMENT AND AGGREGATION

EGOCENTRIC NETWORK ANALYSIS

Egocentric network analysis poses problems:

• Have data at two different levels, which is not suitable for traditional analysis techniques
• However, most SNA tools (designed for whole network data) are ill-suited for ego analysis
• Require joining many ego networks into one very sparse network
• OR, repeat analyses for all ego networks in the sample

EGOCENTRIC NETWORK ANALYSIS

Two strategies for dealing with these complications:

• 1) Aggregate everything to the ego level and analyze in conventional ways
• Analytically straightforward
• Limited compared to what you can do with MLM
• 2) Use multilevel model, alters nested in egos
• Analytically complex (relative to previous)
• Only for DV that varies within ego (i.e., across alters)
• Super cool

AGGREGATION TO EGO LEVEL

• Use conventional statistical software programs to aggregate alter- and tie-level data to the ego level
• Then, use standard regression tools
• Some measures are too complicated to reasonably be calculated “by hand”

EGO NETWORKS IN MULTIVARIATE REGRESSION

NETWORKS AS INDEPENDENT VARIABLES

Social integration

• Lisa Berkman

​

COMMON MODEL VIOLATIONS IN NETWORK RESEARCH

• Multicollinearity
• Non-linear relationships
• Skew
• Heteroskedasticity

PARALLEL PLAY

Regression with ego nets in R

​

Suppose we are interested in knowing

how personal network density is

associated with happiness…

​

DESCRIBING DENSITY

> describe(data$shdensity)

data$shdensity

n missing distinct Info Mean Gmd .05

1167 367 40 0.981 1.09 0.3413 0.500

.10 .25 .50 .75 .90 .95

0.700 0.917 1.050 1.333 1.500 1.500

​

lowest : 0.000 0.100 0.167 0.200 0.250, highest: 1.350 1.400 1.417 1.450 1.500

LOGISTIC REGRESSION

glm(formula = vhappy ~ shdensity + female + educyrs + married,

family = binomial(link = "logit"), data = data)

​

Deviance Residuals:

Min 1Q Median 3Q Max

-1.0629 -0.8829 -0.7396 1.4137 1.9189

​

Coefficients:

Estimate Std. Error z value Pr(>|z|)

(Intercept) -2.16586 0.43834 -4.941 7.77e-07 ***

shdensity 0.45417 0.22304 2.036 0.041723 *

female -0.03881 0.13171 -0.295 0.768280

educyrs 0.03972 0.02237 1.775 0.075845 .

married 0.49404 0.13519 3.654 0.000258 ***

​

> exp(coef(model4))

(Intercept) shdensity female educyrs married

0.1146515 1.5748642 0.9619374 1.0405213 1.6389277

Win for Burt or Coleman?

PARALLEL PLAY

Interactions with ego nets in R

​

Suppose we are interested in knowing

whether the effect of personal network density on happiness is moderated by marital status…

​

INTERACTIONS

glm(formula = vhappy ~ shdensity * married + female + educyrs,

family = binomial(link = "logit"), data = data)

​

Estimate Std. Error z value Pr(>|z|)

(Intercept) -2.85703 0.54524 -5.240 1.61e-07 ***

shdensity 1.07553 0.35851 3.000 0.00270 **

married 1.61387 0.51641 3.125 0.00178 **

female -0.02274 0.13226 -0.172 0.86348

educyrs 0.04007 0.02244 1.786 0.07411 .

shdensity:married -1.01564 0.44908 -2.262 0.02372 *

​

> exp(coef(model5))

shdensity married female educyrs shdensity:married

2.93154622 5.02223440 0.97751515 1.04088731 0.36217219

​

> # Effect of density for married individuals

2.93154622*0.36217219

[1] 1.061725

MULTILEVEL MODELS

TWO MAJOR PARTS OF ANY MODEL

Part I: Model for the means

• AKA fixed effects part of the model (i.e., fixed parameters)
• What you are used to caring about for testing hypotheses
• How the expected outcome for a given observation varies on average as a function of values of predictor variables

TWO MAJOR PARTS OF ANY MODEL

Part II: Model for the variances

• AKA random effects and residuals (i.e., stochastic or varying parameters)
• What you are used to making assumptions about
• How residuals are distributed and related across observations (persons, groups, time, etc.) are the primary way that multilevel models differ from general linear models (e.g., regression)

WHEN AND WHY TO USE AN MLM FOR EGO NETWORK RESEARCH

MLM FOR SOCIAL NETWORKS

When to use MLM for ego SNA: Formal requirements

1. DV is an alter or tie-level variable (level-1)
• If you are interested in predicting a characteristic of ego (e.g. health, employment outcomes, movement participation), MLM is not appropriate
• IVs can be alter, tie, network, or ego-level variables (level-1 or 2)
2. Personal networks of egos do not overlap (or overlap is negligible)
3. Ego observations are independent of one another

​

​

MLM FOR SOCIAL NETWORKS

Why to use MLM for ego SNA

• Vs. aggregation to ego level
• Aggregation = loss of information
• Vs. standard error adjustments
• You can explicitly model the effects of characteristics at the level of ego, alters, dyads, and networks, and their interactions (vs. e.g. cluster robust SEs)

​

MLM RESEARCH QUESTIONS

• What affects formation of ties to alters with particular attributes?
• What affects alter behavior or contributions?
• What affects characteristics of dyads, or ties between egos and alters?
• Does network context moderate the effect of ego or alter-level characteristics?

​

DEPENDENCY

Alter obs nested in same ego are not independent

DEPENDENCY

• Ignoring multi-level structure depresses standard errors, makes it easier to find significance when there really is none
• Multilevel model accounts for clustering (non-independence) and allows you to explicitly model it rather than just control for it

RANDOM INTERCEPT MODEL

We are just making piles of variance, not reducing overall variance

OLS

Random intercept MLM

RANDOM INTERCEPT MODEL

​

• Explicitly model the error dependence by splitting up the error term into level-1 (dyad) and level-2 (ego) components
• Have a random intercept for level-2 ego j that is constant across all level-1 alters
• Have an error term for each dyad or alter i clustered within ego j

zeta

epsilon

INTRACLASS CORRELATION

• Rho is a measure of between-cluster heterogeneity OR within-cluster homogeneity (two sides of the same coin)
• Typically call it the intraclass correlation, which is a measure of within-cluster correlation

​

rho

INTRACLASS CORRELATION

INTRACLASS CORRELATION

• ICC is a standardized way of expressing how much we need to worry about dependency due to cluster mean differences
• Bigger ICC 🡪 more messed up standard errors

RANDOM INTERCEPT MODEL

• Now see ij subscript, which denotes alter i of ego j

WHAT RELATIONSHIP FACTORS AFFECT LIBIDO?

• Ego Jane has three sex partners – Bob, Ann, and Don Juan
• The intercept is 6 sexual contacts per month
• What can we say about ego Jane and her sex partners?

WHAT RELATIONSHIP FACTORS AFFECT LIBIDO?

• Two egos Jane and Joe and five sex partners (dyads)
• What can we say about within and between variation?

Variation within

Variation between

COMMUNICATION AND LIBIDO

Both Jane and Joe get their own random intercept

Jane’s regression line

Joe’s regression line

y = # sexual contacts

x = quality of communication

3

2

1

0

COMMUNICATION AND LIBIDO

Ego’s get their own random intercept based on their alter/tie observations

Every ego gets their own regression line

• Intercept is “random” (varies)
• Slope is constant

y = # sexual contacts

PARALLEL PLAY

Random intercept

model in R

RUNNING MLM IN R

Suppose we want to look at the effects of ego and alter gender on the number of support functions provided by an alter to an ego

EMPTY RI MODEL

EMPTY RI MODEL

We usually prefer to report the variance rather than the SD of random components, and we need the variance to calculate ICC

EMPTY RI MODEL

RI MODEL WITH PREDICTORS

CLUSTER CONFOUNDING AND CONTEXTUAL EFFECTS

CLUSTER CONFOUNDING: A MAJOR THREAT TO RE MODELS

• The RE model assumes that Level-1 (alter) covariates are uncorrelated with the random intercept
• Problematic because every Level-1 variable varies both within and between clusters (ego networks)
• Put another way, all Level-1 alter variables contain information about alters and networks
• Can’t assume a variable has the same effect at both levels

CONTEXTUAL EFFECTS

• Add a contextual effect of alter/tie-level variables by including the aggregated network version of the variable
• E.g., alter closeness and cluster-mean of closeness (avg closeness across network)
• Called “contextual effect” because it tests whether cluster (i.e., network) effects have any significant influence over and above the alter/tie-level effect

​

PARALLEL PLAY

Contextual effects

in R

CONTEXTUAL EFFECTS IN R

• Maybe being in a network full of women affects how much support each alter provides to ego, above and beyond alter’s own gender.
• First, create contextual (aggregated) network variables using ave command

CONTEXTUAL EFFECTS IN R

THE RANDOM

COEFFICIENT MODEL

RANDOM COEFFICIENT MODEL

• The random intercept model is based on the premise that each Level 2 ego needs its own random intercept to account for dependency of Level 1 alters within networks
• The effects of any independent variable x (the slope) across Level 2 clusters are assumed to be equal (constant)

COMMUNICATION AND LIBIDO

Jane’s regression line

Joe’s regression line

y = # sexual contacts

x = quality of communication

3

2

1

0

RANDOM COEFFICIENT MODEL

The random coefficient linear regression model:

COMMUNICATION AND LIBIDO

Jane’s regression line

Joe’s regression line

y = # sexual contacts

x = quality of communication

2

1

0

COMMUNICATION AND LIBIDO

Egos get their own random intercept and slope based on their alters

Every ego gets their own regression line

• Intercept is “random” (varies)
• Slope is “random” (varies)

y = # sexual contacts

RANDOM COEFFICIENT MODEL

We are still just making piles of variance, not reducing overall variance

OLS

Random intercept MLM

Random coefficient MLM

PARALLEL PLAY

Random coefficient

Model in R

RC MODEL IN R

• Suppose I wanted to know if the effect of alter gender on support provision varies across egos…
• Why might this be true?

RC MODEL WITH PREDICTORS

I perform a nested Likelihood Ratio test using stored estimates to determine whether the random slopes are significantly different from zero…

​

​

​

​

​

​

​

​

If p-value is less than .05, I reject the null hypothesis that the random coefficients are equal to zero and use random coefficient model

RC MODEL

SD of the random slopes

RC MODEL

Correlation between random slopes and random intercepts

Correlation of .13 between random slopes and intercepts suggests that in ego networks that provide more support functions, on average (intercept), the effect of alter gender (slope) is larger compared to networks that support less.

RC MODEL

Intraclass correlation

CROSS-LEVEL

INTERACTIONS

CROSS-LEVEL INTERACTIONS ARE COOL!

• Level-1 (alter/tie) variables and Level-2 (network/ego) variables interact to produce an effect on some outcome
• Usually, how does the effect of some alter-level variable vary as a function of network context or some ego characteristic
• Not that different from regular interactions, except that you want to make sure you’re using a random coefficient model. Why?

​

PARALLEL PLAY

Cross-level interactions

Model in R

CROSS-LEVEL INTERACTIONS IN R

• Suppose I wanted to know if the effect of alter gender differs for male and female egos…
• Why might this be true?

CROSS-LEVEL INTERACTIONS IN R

CROSS-LEVEL INTERACTIONS IN R

• When ego is a man, there is no significant effect of an alter being a woman (b=-0.02) on number of support functions. However, when ego is a woman, women alters are expected to provide 0.17 more support functions than men alters.
• Interaction at Level-2 is

not significant

​

EGO NETWORK

DYNAMICS

WHAT WE KNOW ABOUT SOCIAL NETWORK DYNAMICS

• Structural properties of networks tend to remain fairly stable over time
• BUT lots of “turnover” or “churn” in the individuals that make up a network
• Toronto, Ontario residents: only 27% of ties persist over a decade (Wellman et al. 1997)
• Loss of ties does not mean networks are getting smaller – may just be replacement

WHAT WE KNOW ABOUT SOCIAL NETWORK DYNAMICS

Networks are comprised of two basic components:

• a smaller and more stable core
• Densely-knit, mostly kin, highly supportive
• a larger set of temporary or sporadic ties (the periphery)
• Most turnover occurs in periphery

WHAT WE KNOW ABOUT SOCIAL NETWORK DYNAMICS

Periphery is a problem for cross-sectional network studies

• People engage in periods of brief and sporadic periods of meaningful contact (e.g. old friend visits, weak tie provides info)
• The likelihood of these sometimes-inactive relationships being present in a snapshot of a network is essentially random
• When peripheral ties are not captured, they are assumed to be absent rather than inactive
• Instability does not mean real change

HOW TO MEASURE NETWORK CHANGE

Problem 1: Real change or methodological artifact?

• Respondents forget to name alters from previous waves 5-10% of the time
• Respondents deliberately underreport alters in subsequent waves because they know each alter = more work
• Respondents give different names or spellings in subsequent waves

HOW TO MEASURE NETWORK CHANGE

Problem 2: Determining what alter-level changes underlie network-level change

Suppose the mean freq of contact with network members decreases from W1 to W2. This can be due to…

1. ego decreasing contact with alters who were present at both W1 and W2
2. the loss of past alters with whom ego had frequent contact
3. and/or the addition of new alters with whom ego has infrequent contact

​

HOW TO MEASURE NETWORK CHANGE

Solution: Real change or methodological artifact?

• In each follow-up wave of a study…
1. have egos name their current alters
2. show them their roster from the previous wave or waves
3. have them match alters across waves
4. ask them why they didn’t name any dropped alters, and add if they report forgetting

HOW TO MEASURE NETWORK CHANGE

MEASURES OF NETWORK CHANGE

Measures that capture network turnover

• N/Prop alters dropped
• N/Prop alters added
• N/Prop stable alters

MEASURES OF NETWORK CHANGE

N dropped or added

N unique alters pooled

​

Network turnover, Perry & Pescosolido (2012)

​

HOW TO ANALYZE NETWORK CHANGE

If goal is to describe change:

​

• Simple comparison of ego network characteristics over time
• E.g., Avg degree at W1 compared to avg at W2
• Measure of difference between two waves
• E.g., W2 degree – W1 degree

​

HOW TO ANALYZE NETWORK CHANGE

If goal is to describe change:

​

• Distinguish alters dropped, maintained, or added across W1 and W2
• Can present number or percent of each
• E.g., 35% of alters dropped, 35% maintained, 30% added
• Compare characteristics of each
• E.g., 75% of maintained alters are “very close” compared to 35% of dropped alters

HOW TO ANALYZE NETWORK CHANGE

• If goal is to predict network change or use network change to predict outcomes

​

• Use longitudinal multilevel models
• Same as earlier, but now have observations over time nested in egos (or obs nested in alters nested in egos)
• Requires a special class of MLM called growth models that explicitly estimate the effects of time and time*predictors

​