Innovation in networks week 7

1
Innovation in networks week 7

• Theory guided research, network measures,
• and data analysis
• Structural holes Multiple regression
• Chris Snijders
• c.c.p.snijders_at_tm.tue.nl

2
Innovation in Networks

• course structure
• Part I introduction and theory some classic
  and contemporary examples
• Part II techniques of (social network) data
  analysis
• 1 structural holes
• 2 practice putting it all together
• Part III three empirical applications of social
  network analyses in innovation science
• 1 alliances between firms (GR)
• 2 cooperation between university and businesses
  (UM)
• 3 diffusion of innovation (CS)

3
Once again why do we do this?General setup of a
quantitative scientific paper

• Problem formulation Theory Observation
• EXAMPLE inspired by our questionnaire
• Problem Which students tend to study relatively
  fast?
• Theory This has to do with at least three
  factors
• Gender females will do better (selection
  argument)
• Family background the better, the better
• Network The way in which you are connected to
  other students in your class. You need access to
  information, and the ones with the better
  network, will therefore study faster (all else
  being equal). Question remains of course what
  better means
• Observation Test your hypotheses

4
Our data

• Female Status Network Behind in study
• father charact. schedule
  (higheryes)
• Person 1 0 34 ? 4
• Person 2 1 50 ? 2
• Person 3 0 20 ? 3
• Person 23 0 88 ? 1
• For instance we want to predict whether someone
  is behind in study schedule from the other
  columns (female, status father, network
  characteristics) in the data.
• ? which network characteristic?
• ? how do I calculate this network
  characteristic?

5
Network characteristics

• (In/Out)degree, Size, Density
• Betweenness, Centrality, Closeness
• (N-)Cliques, (N-)Clans, (N-)Clubs
• Structural equivalence (density tables etc)
• Structural holes
• Calculating network data, merging to SPSS, and
  drawing conclusions

6
Ron BurtStructural holes versus network closure
as social capital
This was covered in the 2nd lecture

• Burts conclusion
• structural holes beat network closure
• when it comes to predicting which actor
• performs best
• Coleman says closure is good
• Because information goes around fast
• and it facilitates trust
• fear of a damaged reputation
• precludes opportunistic behavior
• He subsequently compares people with
• dense networks with those with
• networks rich in structural holes

University of Chicago graduate school of business
7
Social organization
This was covered in part-2.ppt
Structural holes create value
A
B
1
7
3
2
James
Robert
4
5
6

• Robert will do better than James, because of
• informational benefits
• tertius gaudens (entrepreneur)

C
8
Burts measurement of structural holes

• Burt, R.S. (1995) Structural holes the social
  structure of competition. Harvard Harvard
  University Press.
• NOTE structural holes can be defined on
  ego-networks!
• Burt split his structural holes measure in four
  separate ones
• 1 effective size
• 2 efficiency ( effective size / total size)
• 3 constraint
• (degree to which ego invests in alters who
  themselves
• invest in other alters of ego)
• 4 hierarchy
• (adjustment of constraint, dealing with the
  degree to
• which constraint on ego is concentrated in a
  single
• actor)

9
Effective size efficiency
We calculate effective size and efficiency for
actor G (note because this is an ego-network,
all would be different if we would have chosen,
for instance, actor A)
Or, the same but a bit easier Effective size
size - average degree of egos alters in egos
network (excluding ties to ego). Here 6 - 3
(A) 2(B) 0(C) 1(D) 1(E) 1(F)/6 6 -
1.33 4.67
10
Defining constraint actors must divide their
attention
What is strange about this?

• The assumption is that actors can only invest a
  certain amount of time and energy in their
  contacts, and must divide the available time and
  energy across contacts.
• If not explicitly measured, we assume all
  contacts are invested in equally.

11
Constraint

• Actor i is constrained in his relation with j to
  the extent that
• a you invest in another contact q who
• b invests in your contact j
• Total investment of i in j
• Pij ?q (piq pqj)
• Since this also equals is lack of
• structural holes, constraint
• of i in j is taken to equal
• ( Pij ?q (piq pqj) )2

q
piq
pqj
i
j
pij
What is strange about this?
What is strange about that?
12
Calculating constraint using matrices (1)
c1 c2 c3 c4 c5 c6 c7 r1
0 .25 0 0 .25 .25 .25 r2 .333
0 0 .333 0 0 .333 r3 0 0
0 0 0 0 1 r4 0 .5
0 0 0 0 .5 r5 .5 0 0
0 0 0 .5 r6 .5 0 0 0
0 0 .5 r7 .17 .17 .17 .17 .17
.17 0
Adjacency matrix P (see two slides ago) all
investment from i in j in 1 step
c1 c2 c3 c4 c5
c6 c7 r1 .37575 .0425 .0425 .12575
.0425 .0425 .33325 r2 .05661 .30636 .05661
.05661 .13986 .13986 .24975 r3 .17 .17
.17 .17 .17 .17 0 r4
.2515 .085 .085 .2515 .085 .085
.1665 r5 .085 .21 .085 .085 .21
.21 .125 r6 .085 .21 .085 .085
.21 .21 .125 r7 .22661 .1275
0 .05661 .0425 .0425 .52411
Matrix product P2 PP all investments from
i in j in 2 steps
13
Calculating constraint using matrices (2)
c1 c2 c3 c4 c5 c6 c7 r1 .37
.29 .04 .12 .29 .29 .58 r2 .38 .30
.05 .38 .13 .13 .58 r3 .17 .17 .17
.17 .17 .17 1 R4 .25 .58 .08 .25
.08 .08 .66 r5 .58 .21 .08 .08 .21
.21 .62 r6 .58 .21 .08 .08 .21 .21
.62 r7 .39 .29 .17 .22 .21 .21 .52
P P2 All investments from i to j in 1 or 2
steps Pij ?q (piq pqj)
(0.666)2 0.444 Etc
c1 c2 c3 c4 c5 c6 c7 r1
.141 .085 .002 .015 .085 .085 .340 r2 .151
.093 .003 .151 .019 .019 .339 r3 .028
.028 .028 .028 .028 .028 1 r4 .063 .342
.007 .063 .007 .007 .444 r5 .342 .044 .007
.007 .044 .044 .390 r6 .342 .044 .007
.007 .044 .044 .390 r7 .157 .088 .028 .051
.045 .045 .274
Hadamard matrix product (PP2)2h PP2 squared
element wise Constraint(i,j) can be read from
this matrix
14
Calculating constraint using matrices (3)
Total constraint for actor i sum of all
constraints Cij with j?i
c1 c2 c3 c4 c5 c6 c7 r1
.141 .085 .002 .015 .085 .085 .340 r2 .151
.093 .003 .151 .019 .019 .339 r3 .028
.028 .028 .028 .028 .028 1 r4 .063 .342
.007 .063 .007 .007 .444 r5 .342 .044 .007
.007 .044 .044 .390 r6 .342 .044 .007
.007 .044 .044 .390 r7 .157 .088 .028 .051
.045 .045 .274
0.755 lt- Constraint(1) 0.779 lt-
Constraint(2) 1.173 lt- Constraint(3) 0.934 lt-
Constraint(4) 0.879 lt- Constraint(5) 0.879 lt-
Constraint(6) 0.691 lt- Constraint(7)
15
Hierarchy

• degree to which constraint is concentrated in a
  single actor
• Cij constraint from j on i (as on previous
  pages)
• N number of contacts in is network
• C sum of constraints across all N relationships
• Hierarchy (i)
• Minimum 0 (all is constraints are the same)
• Maximum 1 (all is constraint is concentrated
  in a single contact)

16
Practice exam use structural holes (1)

• Come up with a prediction that connects
  structural holes to variables in the class data,
  and test that prediction with these data.
• In the IIN-data, try to predict whether someone
  tends to lthear rumours firstgt.

17
Practice exam use structural holes (2)

• Calculate the measures of structural holes on
  the reach2006.dl data. Symmetrize these data
  first.
• Merge these data to the SPSS base data.
• Note - be careful when dealing with missing
  values
• (if there are any)
• - use SPSS syntax files (.sps)!
• Run the relevant analysis (regression / t-test /
  something else), and draw your conclusions
• - again use SPSS syntax files (.sps)

18
Is 20 cases enough?

• Suppose you want to test whether males more than
  females expect to have a financially prosperous
  future (and let us suppose we have a group
  consisting of roughly 50 men, 50 women).
• The sample size depends on
• How certain you want to be about finding a
  difference if it is there (Power)
• How high you allow the probability to be that you
  do wrongly conclude that there is a difference
  although there is none (Alpha)
• Size of the difference (effect size)
• Suppose Power 0.90
• Alpha 5
• Effect size 0.3 vs 0.5
• You would then need a sample of about 265
  individuals (half men, half women).

19
Sample size as dependent on effect size
0.3 vs 0.35 ? 3800
NB in principle, sample size does NOT depend on
population size!
0.3 vs 0.4 ? 1000
0.3 vs 0.9 ? 60
CONCLUSION basically, with n20, we can only
expect to find statistical differences if the
differences between groups are quite large