Session 5x: Bonus material

(1)

Session 5x: Bonus material

Johan Koskinen http://www.ccsr.ac.uk/staff/jk.htm!

[email protected]

The Social Statistics Discipline Area, School of Social Sciences

Mitchell Centre for Network Analysis

Workshop: Mon-Fri, 7-11 July 2014 Advanced Meths SNA, Manchester

(2)

Session 5x: Bonus material

q  Bayesian analysis q  Missing data

q  Snowball sampled data

q  Fitting ERGM to LARGE data sets q  Spatial Embedded networks

q  Multilevel ERGM

q  Longitudinal ERGM

(3)

Bayesian analysis in MPNet

(4)

Bayesian inference (in MPNet):

Fishermen

Bayesian estimation

Go back into Select

parameters, start afresh by clearing all and then select

edge, ASA, ATA

BE PATIENT. Bayesian estimation can be slower (we are working on automation).

(5)

Quick MCMC settings for Bayesian

¡  We need a slightly large multiplication factor than for non-‐Bayesian estimation

¡  Maximum lag should be chosen to be roughly the lag where SACF is 0 (in order for ESS to be correct) – roughly 200-‐400

¡  If model is good we can use Pre-‐tuning only to get good initial values

§  The objective is to get high acceptance rate around .85

§  Run number of small MCMC sample sizes and press update

¡  When pre-‐tuning not too bad check ‘Nonconditional simulation’ and press update (the latter to start in a better place and get proposal covariance)

§  The objective is to get acceptance rate around .25 and SACF around lag 200 small and ESS large

§  If acceptance rate too small (say smaller than .15) reduce Proposal scaling (e.g.

divide by 2); if too large (say greater than .45) increase Proposal scaling (e.g.

multiply by 2)

§  Once SACF at large lags (say 100 or 200) is low (say, around .1) you can Improve the ESS by making the MCMC sample size bigger

¡  If you have a good run and want the perfect run read in ‘Covariance ﬁle’

(6)

Bayesian analysis in MPNet

¡  Set

§  multiplication factor to 80

§  Scale 0.005

§  MCMC sample size 1000

§  Max lag 200

§  Scaled identity

¡  After run

§  Note that Inverse D matrix is diagonal

EdgeA

Time

ts(output[, k + 1])

0 200 600 1000

-3.6-3.4-3.2-3.0-2.8

ASA

Time

ts(output[, k + 1])

0 200 600 1000

-0.3-0.2-0.10.0

ATA

Time

ts(output[, k + 1])

0 200 600 1000

0.00.20.40.60.8

Inverse D matrix:

0.0010 0.0000 0.0000

0.0000 0.0010 0.0000

0.0000 0.0000 0.0010

Acceptance rate: 0.42 Estimation results

Effects Lambda PostMean Stddev

EdgeA 2.0000 -3.2257 0.237 *

ASA 2.0000 -0.1862 0.094

ATA 2.0000 0.7372 0.139 *

SACF

Effect 10 30 190 ESS(200)

EdgeA 0.973 0.914 0.265 4

ASA 0.905 0.781 0.412 4

ATA 0.802 0.456 -0.053 12

This run just got us close to where we want to be

(7)

Bayesian analysis in MPNet

¡  Set

§  multiplication factor to 80

§  Scale 0.005

§  MCMC sample size 1000

§  Max lag 200

§  Scaled identity

¡  After run

§  Note that Inverse D matrix is diagonal

§  Press Update

§  MCMC sample size 5500; Parameter burnin 500

§  Proposal scaling 0.01

§  Nonconditional simulation

This run just got us close to where we want to be We want to draw values roughly here BUT more eﬃciently (by setting a better Proposal variance than the diagonal)

(8)

Bayesian analysis in MPNet

¡  Re-‐run with longer ‘moves’

§  Set Proposal scaling 1.50

§  rerun

-‐> It is moving around really well BUT it takes too small steps

(acceptance ratio: 0.93)

Inverse D matrix:

0.0015 -0.0005 0.0001

-0.0005 0.0002 -0.0001

0.0001 -0.0001 0.0001

EdgeA 2.0000 -3.6399 0.385 *

ASA 2.0000 -0.0596 0.138

ATA 2.0000 0.7484 0.081 *

SACF

Effect 10 30 190 ESS(200)

EdgeA 0.952 0.871 0.470 20

ASA 0.959 0.887 0.499 20

ATA 0.955 0.870 0.370 22

EdgeA

Time

ts(output[, k + 1])

0 2000 4000

-4.5-4.0-3.5-3.0-2.5

ASA

Time

ts(output[, k + 1])

0 2000 4000

-0.4-0.20.00.2

ATA

Time

ts(output[, k + 1])

0 2000 4000

0.60.70.80.91.0

0 200 600 1000

0.00.20.40.60.81.0

ESS: 14

ACF

SACF for EdgeA

0 200 600 1000

-0.20.00.20.40.60.81.0

ESS: 12

ACF

SACF for ASA

0 200 600 1000

-0.20.20.61.0

ESS: 14

ACF

SACF for ATA

(9)

Bayesian analysis in MPNet

-‐> It is moving around really well AND it takes Nice LONG strides (acceptance ratio:

EdgeA 2.0000 -3.5364 0.534 *

ASA 2.0000 -0.1223 0.185

ATA 2.0000 0.8167 0.122 *

SACF

Effect 10 … 190

ESS(200)

EdgeA 0.442 … -0.071 351

ASA 0.467 … -0.043 328

ATA 0.511 … 0.044 205

EdgeA

Time

ts(output[, k + 1])

0 1000 3000 5000

-5-4-3-2

ASA

Time

ts(output[, k + 1])

0 1000 3000 5000

-0.6-0.20.00.20.40.6

ATA

Time

ts(output[, k + 1])

0 1000 3000 5000

0.40.60.81.01.2

0 200 600 1000

0.00.20.40.60.81.0

ESS: 229

ACF

SACF for EdgeA

0 200 600 1000

0.00.20.40.60.81.0

ESS: 221

ACF

SACF for ASA

0 200 600 1000

0.00.20.40.60.81.0

ESS: 183

ACF

SACF for ATA

Eﬀective sample size. We want these to be larger than 500, else the Stddev:s are misleading.

Here, as acceptance rate GOOD, rerun the estimation with larger MCMC sample size Here SACF is almost zero allready at lag 30!!!

(10)

Bayesian analysis in MPNet

The output ﬁle, [session name]_posterior_bayesian.txt contains the Bayesian posteriors.

EdgeA

Frequency

-5 -4 -3 -2

0400800

ASA

Frequency

-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

0400800

ATA

Frequency

0.4 0.6 0.8 1.0 1.2

0400800

-5 -4 -3 -2

-0.6-0.20.00.20.40.6

EdgeA

ASA

-5 -4 -3 -2

0.40.60.81.01.2

EdgeA

ATA

(11)

Missing data in MPNet

(12)

Session 4: More complex models

q The datafile miss20.txt is an 85X85 randomly simulated matrix with a density of 0.20. This will be a matrix equivalent 20%

missing data at random.

q The datafile fish_miss20.txt is the fishermen data except that all the 1’s in miss20.txt are set to zero.

In other words, fish_miss20.txt can be regarded as the fishermen’s network with 20% missing data (both 1’s and 0’s)

q Note that to use the missing data estimation in MPNET, you need to have an indicator matrix with 1 entered into every

missing cell, and all missing cells in the original data have to be entered as o’s.

(13)

Session 4: More complex models

In MPNET, under the Bayesian estimation tab:

•  Enter the ﬁsh_miss20 ﬁle to be estimated

•  Enter the miss20 as the missing indicators ﬁle,

•  Select parameters and clear any previous parameter values (i.e.

start from 0)

•  Conduct Bayesian estimation for an edge, AS and AT model. Use 3000 as the MCMC sample size.

Our results

EdgeA 2.0000 -4.4253 0.552 *

ASA 2.0000 0.1405 0.196

ATA 2.0000 0.7759 0.177 *

(14)

Session 4: More complex models

¡ 

Make sure no ME

§ 

Are all zeros really zeros?

¡ 

In principle valid for sampled data (admissible)

¡ 

MNAR impossible to check (but robustness can be assessed)

§ 

Are missing data “diﬀerent” than observed?

¡ 

If attributes are missing we can use a similar

technique of data-‐augmentation (not in Pnet

yet)

(15)

Unobserved data: snowball sampling

(16)

Unobserved data: snowball sampling

(17)

Unobserved data: snowball sampling

(18)

Unobserved data: snowball sampling

(19)

Unobserved data: snowball sampling

(20)

Unobserved data: snowball sampling

(21)

Unobserved data: snowball sampling

missing data observed data

(22)

Sampling in/on networks

=

0

x =

- 1

1

(23)

Sampling in/on networks

=

0

1

x = 1

-

- 0

1 1 0

1

(24)

Sampling in/on networks

=

0

0 1 0

x = 1

-

- 0

1 1 0

1 0

0 1

(25)

Sampling in/on networks

=

0

0 1 0

1

0 0 0 0

0 0

0

x =

-

- 0

1 1 0

1 0

0 1

(26)

Sampling in/on networks

=

0

0 1 0

1

0 0 0 0

0 0

0

x =

-

- 0

1

0 1 0 - 0

1 0

- 1

0 1 1 0 -

(27)

Sampling in/on networks

=

0

0 1 0

1 0 0

?

0 ? 0

? ?

? ? 0

0 0

0

x =

-

- 0

1 ?

? 0

1 0 - 0 ? ?

1 0

?

? -

1 0 ?

0 1 1 - ?

(28)

Ignoring non-sampled?

=

0

0 1 0

1 0 0

?

0 ? 0

? ?

? ? 0

0 0

0

x =

-

- 0

1 ?

? 0

1 0 - 0 ? ?

1 0

?

? -

1 0 ?

0 1 1 - ?

(29)

What about alter – alter across ego?

=

0

0 1 0

1 0 0

?

0 ? 0

? ?

? ? 0

0 0

0

x =

-

- 0

1 ?

? 0

1 0 - 0 ? ?

1 0

?

? -

? 0 ?

0 1 ? - ?

(30)

Unobserved data: snowball sampling

Making some (brave) assumptions

(Handcock & Gile 2010)

we can fit an ERGM

(Wang et al. 2013)

to snowball sampled networks

•  Importance sampling MCMCMLE (Handcock & Gile 2010)

•  Stochastic approximation and the missing data principle (Orchard & Woodbury,1972) (Koskinen & Snijders, 2013)

•  Bayesian data augmentation (Koskinen, Robins &

Pattison, 2010,2013) (

MPNet

⁾

•  Conditional MLE (Pattison, Robins, Snijders & Wang, 2013)(

SnowPNet

)

(31)

Unobserved data: snowball sampling

Bayesian data augmentation (Koskinen, Robins & Pattison, 2010,2013) (MPNet)

•  Need to know N

•  Need to simulate un-observed ties

•  Time-consuming

Conditional MLE (Pattison, Robins, Snijders

& Wang, 2013)(SnowPNet)

•  No need to know N

•  No need to simulate un-observed data

•  … properties of conditional MLE unclear

(32)

Estimating ERGM for LARGE networks

(33)

Stivala et al. (2014)

Take many small snowball samples from your LARGE N network

Estimate Conditional MLE for each (Pattison, Robins, Snijders & Wang, 2013)

Pool estimates using Meta-analysis

techniques

(34)

Stivala et al. (2014)

(35)

Stivala et al. (2014)

(36)

Stivala et al. (2014)

(37)

Spatial embedding

(38)

Spatial embedding (Book Ch. 8)

306 actors in Victoria, Australia

(39)

Spatial embedding (Book Ch. 8)

306 actors in Victoria, Australia

... all living within 14 kilometres of each other

spatially embedded

(40)

Spatial embedding (Book Ch. 8)

306 actors in Victoria, Australia

... all living within 14 kilometres of each other

spatially embedded

(41)

Spatial embedding (Book Ch. 8)

Bernoulli conditional on distance Empirical probability

306 actors in Victoria, Australia

... all living within 14 kilometres of each other

(42)

Spatial embedding (Book Ch. 8)

Spatial interaction function: Tie probability as a function of distance

E.g. Attenuated Power-Law:

Pr(X

_ij

= 1 | d

_ij

) = p

1+ α ^d

_ij^γ

(43)

Spatial embedding (Book Ch. 8)

Spatial interaction function: Tie probability as a function of distance

The Attenuated Power-Law:

Pr(X

_ij

= 1 | d

_ij

) = p 1+ α ^d

_ij^γ

Is equivalent to:

Pr(X = x | D = (d_ij)) = exp{θ₁ ^x_ij

i< j

∑

⁺^θ²

∑

_{i< j} ^x^ij ^log(d^ij⁾^}

exp{θ₁ ^u_ij

i< j

∑

⁺^θ²

∑

_{i< j}ûîj ^log(dîj⁾^}

∑

u∈X

p = 1 α = e

⁻^θ¹

γ = − θ

₂

with: AND: ^log(d

ij

)

(44)

Spatial embedding (Book Ch. 8)

Edges -4.87* (0.13)

Alt. star

Alt. triangel

Log distance Age

heterophily -0.07* (0.01)

Gender

homophily -1.13* (0.61)

(45)

Spatial embedding (Book Ch. 8)

Edges -4.87* (0.13) 1.56* (0.65)

Alt. star

Alt. triangel

Log distance -0.78* (0.08)

Age

heterophily -0.07* (0.01) -0.07* (0.01)

Gender

homophily -1.13* (0.61) -1.13 (0.69)

(46)

Spatial embedding (Book Ch. 8)

Edges -4.87* (0.13) 1.56* (0.65) -4.79* (0.66)

Alt. star -0.86* (0.18)

Alt. triangel 2.74* (0.15)

Log distance -0.78* (0.08)

Age

heterophily -0.07* (0.01) -0.07* (0.01) 0.001 (0.07)

Gender

homophily -1.13* (0.61) -1.13 (0.69) 0.09 (0.83)

(47)

Spatial embedding (Book Ch. 8)

Edges -4.87* (0.13) 1.56* (0.65) -4.79* (0.66) -0.20 (0.87)

Alt. star -0.86* (0.18) -0.86* (0.2)

Alt. triangel 2.74* (0.15) 2.69* (0.14)

Log distance -0.78* (0.08) -0.56* (0.07)

Age

heterophily -0.07* (0.01) -0.07* (0.01) 0.001 (0.07) 0.002 (0.06)

Gender

homophily -1.13* (0.61) -1.13 (0.69) 0.09 (0.83) 0.07 (0.47)

ERGM: distance and endogenous dependence

explain diﬀerent things

(48)

Bipartite and Multilevel ERGM

(49)

Multilevel

Level A Level B

A_ij

B_rs

X_ir

The A-‐network

The X-‐network The B-‐network

(50)

Multilevel

¡ 

Network statistics can be derived based on the same dependence assumptions

¡ 

Diﬀerent interpretation as we assume

dependencies between tie-‐variables of diﬀerent types.

∑

⎭⎬⎫

⎩⎨

⎧

+ +

= +

=

Q Q Q Q Q Q Q

Q Q Q

Q Q

Q

x b a z x

b z x

a z

x z b

z a

b z B x X

a

A ( , ) ( , ) ( , , )

) ( )

( )

exp ( )

( ) 1

, ,

Pr( θ θ θ

θ θ

κ

Three network

variables A, B and X Within level eﬀects Between level eﬀects

Interaction between within level

and between level networks Cross level eﬀects

(51)

Multilevel

¡ 

Bernoulli

¡ 

Markov

Aﬃliation based activity Aﬃliation based closure or homophily

¡ 

Social circuit and three-‐path

Aﬃliation assortativity Cross-‐level assortativity/entrainment

(52)

Multilevel

(53)

Multilevel: example, global fisheries

governance (Hollway & Koskinen, 2014)

(54)

Multilevel: example, global fisheries

governance (Hollway & Koskinen, 2014)

IRQ

HTI

ERI

CPV TGO

GUY

BEN SLE LBR

SOM GIN

KWT

GRD GHA

BEL

SDN

LBY VUT LCA

FSM

FJI

GMB BRB

AGO CIV LBN

PRK

MDG

SLB

DMA NGA

IRL

TUV

DJI

QAT

MUS DZA

MMR

PNG

URY

CMR MLT

BHS

KHM ISR

GEO SYC

KNA

WSM CYP

VCT

MHL SYR

SVNBHR

ATG BIH

BGD

MNE LKA

ARG

TUN CHNCAN OMN

MAR

BRN

SGP

IND ALBVNM IRN YEM

PAK HND

IDN

MYS

NOR

TUR

PHL ARE GNQ GRC

TTO

PER SLV PRT

BGR

DNK

MOZ

HRV SAU

CHL ESP ROK

ISL PAN

POL

JAM

THA COD

CUB UKR

FIN PLW JPNSWE

GBR ZAF

TLS

LVA

GAB

NAM

EGY

TON TZA KEN LTU RUS NZL

BLZ

CRI

SEN GTM

VEN

COL

BRA MEX

ITA FRA

NLD

KIR SUR

EST AUS USA JOR

DOM

MRT

COG ROU

NIC DEU

GNB

ECU MCO BOL

PRY

SMR LIE TCD

LSO

MNG

AND

LUX BLR

BWA CZE

CAF

ZWE MLI

KGZ BTN

ARM

NER BFA

SWZ

AFG TJK

SVK

COM UZB

NPL HUN RWA

MDA CHE

AZE YUG

AUT

TKM

STP

ETH KAZ

MKD MDV

BDI ZMB

LAO UGA

MWI TWN

NRU

EU

IRQ

HTI ERI

CPV TGO

GUY

BEN

SLE

LBR GIN

SOM KWT GHA

GRD

BEL SDN

LBY VUT

LCA

FSM

FJI

GMB BRB

AGO

CIV LBN

PRK MDG

SLB

DMA

NGA IRL

DJI TUV QAT

MUS

DZA MMR

PNG CMRURY

MLT BHS

KHM ISR

GEO

SYC KNA

WSM CYP

VCT

MHL

SYR BHR

SVN

ATG BIH

BGD

MNE

LKA

ARG

TUN

CAN CHN

OMN

MAR BRN

SGP

ALB

IND VNM

IRN PAK YEM

HND

IDN MYS

NOR TUR

PHL

ARE

GNQ

GRC

TTO

PER

PRT SLV

BGR

DNK MOZ HRV

SAU

ESP CHL ROK

ISL PAN

POL JAM

THA COD

CUB UKR

FIN

PLW SWE

JPN GBR ZAF

TLS

LVA

GAB NAM

EGY TON

TZA KEN

LTU NZL RUS

BLZ CRI

SEN

GTM VEN

COL

BRA

MEX

ITA FRA

NLD

KIR SUR

EST AUS

USA JOR

DOM

MRT

COG

NIC ROU

DEU

GNB ECU MCO

BOL

PRY SMR

LIE

TCD

LSO

MNG

AND

LUX

BLR BWA

CZE

CAF

ZWE

MLI KGZ

BTN

ARM NER

BFA

SWZ AFG

TJK SVK

COM

UZB NPL

HUN

RWA

CHE MDA

AZE

YUG AUT

TKM

STP ETH

KAZ

MKD

MDV

BDI ZMB

LAO

UGA

MWI TWN

NRU

154601

156815

153519

144077 153515

001378

001814 153423

001362

001384 000753 001400

001924

001383

001333 001880

153407

001817

001826 153419

153399 001657

153861

001237

154133 001199

001239 001217

001390

001183

001227 153638

153759 001858

001835 001889 001381

001251

001173

001911

153163

001958

001964

001232 154445 001388

001127 153563

001978

001132 001133

002009

001040 001991 001056

001043

153358 001112

153833

000976 001389

002034

001101 000997

153294

153889 000826

000871 000830

153354 000767

000732 002025

000741 000848

000134

000735

000536

000103 000101 000535

153475 000133

000480 000097

000587

000431 000479

000096

000502 000433

000426 000077

153479

000581 000425

000423 000457

000476 000076

000422 000141

000143

000144 000510

153179 153175

153191

000475 000128

000092

000560 144643

000730 153251 153896

000072

The A-‐network

The X-‐network

The B-‐network

(55)

Multilevel: example, global fisheries

governance (Hollway & Koskinen, 2014)

The B-‐network

(56)

global fish. (Hollway & Koskinen, 2014)

Eﬀects Parameter Stderr t-‐ra/o SACF

EdgeA -‐2.0222 9.526 -‐0.02 -‐0.005

ASA 0.3048 0.136 -‐0.015 -‐0.01 *

ATA 0.3388 0.113 0.007 0.001 *

GDP_SumA 0.1681 0.865 -‐0.021 -‐0.009

GDP_ProductA -‐0.0016 0.078 -‐0.022 -‐0.012

species_SumA 0.0084 0.002 -‐0.011 -‐0.02 *

distance_EdgeA -‐1.0614 0.095 -‐0.019 -‐0.01 *

XEdge -‐9.1181 0.896 -‐0.061 0.061 *

IsolatesA -‐6.0824 0.748 0.018 -‐0.014 *

XASA 4.3784 0.32 -‐0.063 0.055 *

XASB -‐1.4607 0.396 -‐0.061 0.062 *

XACA -‐0.4665 0.03 -‐0.067 -‐0.014 *

XACB 0 0.02 -‐0.045 0.033

logGDPStateTreat_XEdge 0.1467 0.041 -‐0.07 0.063 *

Star2AX 0.0458 0.011 -‐0.008 -‐0.024 *

Star2BX -‐0.5834 0.084 -‐0.046 0.045 *

TriangleXBX 2.8928 0.197 -‐0.03 0.014 *

L3XBX 3.1433 1.267 0.057 0.007 *

ATXBX -‐0.0135 0.001 -‐0.031 -‐0.024 *

L3AXB -‐0.0036 0.011 -‐0.011 -‐0.014

(57)

Multilevel: example, global fisheries

governance (Hollway & Koskinen, 2014)

EdgeA 159 159.513 14.504 -‐0.035

Star2A 1145 1125.96 138.15 0.138

Star3A 7525 6986.738 621.013 0.867

Star4A 48877 44694.13 2383.26 1.755

Star5A 264331 245549.822 7529.189 2.494

TriangleA 37 38.189 11.016 -‐0.108

ASA 326.9238 328.5935 42.319 -‐0.039

ASA2 326.9238 328.5935 42.319 -‐0.039

ATA 85.9063 86.5708 19.376 -‐0.034

A2PA 1062.2734 1045.7699 110.027 0.15

AETA 183.082 197.2195 62.753 -‐0.225

coast_SumA 18227.8 17848.9168 1698.574 0.223

coast_DiﬀerenceA 5174.2 6028.7824 655.418 -‐1.304

coast_ProductA 552268.66 507412.9956 57057.678 0.786

GDP_SumA 3581.3 3592.8811 325.357 -‐0.036

GDP_DiﬀerenceA 248.9 248.4494 19.151 0.024

GDP_ProductA 20108.9029 20174.487 1831.761 -‐0.036

species_SumA 11426 11468.939 1380.074 -‐0.031

species_DiﬀerenceA 5458 6207.877 761.398 -‐0.985

species_ProductA 229363 220670.215 43495.224 0.2

distance_EdgeA 1245.6313 1249.2669 112.117 -‐0.032

XEdge 1744 1744.314 25.393 -‐0.012

XStar2A 12297 11666.135 219.44 2.875

XStar2B 41955 41470.162 476.587 1.017

XStar3A 80932 74966.58 1091.676 5.464

XStar3B 1366512 1354528.805 5253.258 2.281

X3Path 941997 937576.735 23198.243 0.191

X4Cycle 75039 69696.854 1899.436 2.812

XECA 2265537 2120319.446 72782.425 1.995

XECB 10386840 10114999.01 223227.681 1.218

(58)

Multilevel: example, global fisheries

governance (Hollway & Koskinen, 2014)

IsolatesA 6 6.008 1.966 -‐0.004

IsolatesB 0 0.193 0.44 -‐0.438

XASA 2785.5996 2786.1502 48.835 -‐0.011

XASB 3047.4525 3048.0564 50.356 -‐0.012

XACA 4344.3993 4345.9997 60.884 -‐0.026

XACB 22625.6352 22624.8278 104.667 0.008

XAECA 293489.2989 276096.6764 7695.013 2.26

XAECB 298680.7706 278382.2566 7602.204 2.67

logGDPStateTreat_XE

dge 18782.09 18786.8598 267.542 -‐0.018

Star2AX 5261 5272.267 529.509 -‐0.021

StarAA1X 6539.459 6834.3932 922.611 -‐0.32

StarAX1A 9277.9278 9303.4066 956.331 -‐0.027

StarAXAA 3410.2835 3409.8379 78.967 0.006

TriangleXAX 1071 888.225 107.855 1.695

L3XAX 271.8552 253.8131 25.128 0.718

ATXAX 47884 45349.46 5516.119 0.459

EXTA 2273 2638.183 853.083 -‐0.428

Star2BX 2030 2030.261 26.211 -‐0.01

StarAB1X 1815.375 1824.7945 12.168 -‐0.774

StarAX1B 3833.0301 3833.2944 52.183 -‐0.005

StarAXAB 3160.9437 3161.8251 50.42 -‐0.017

TriangleXBX 396 396.673 16.435 -‐0.041

L3XBX 54.3754 54.38 0.832 -‐0.006

ATXBX 37668 37803.366 1808.02 -‐0.075

EXTB 552 566.508 5.745 -‐2.525

L3AXB 5383 5398.32 538.218 -‐0.028

C4AXB 1073 875.858 108.474 1.817

ASAXASB 8354.834 8659.1877 923.271 -‐0.33

(59)

Longitudinal ERGM

(60)

LERGM FDI electricity market (Koskinen

and Lomi, 2013)

(61)

LERGM FDI electricity market (Koskinen

and Lomi, 2013)

(62)

LERGM FDI electricity market (Koskinen

and Lomi, 2013)

(63)

Session 5x: Bonus material

Session 5x: Bonus material

Session 5x: Bonus material

q Bayesian analysis q Missing data

q Snowball sampled data

q Fitting ERGM to LARGE data sets q Spatial Embedded networks

q Multilevel ERGM

q Longitudinal ERGM

Bayesian analysis in MPNet

Bayesian inference (in MPNet):

Fishermen

Quick MCMC settings for Bayesian

Bayesian analysis in MPNet

Bayesian analysis in MPNet

Bayesian analysis in MPNet

Bayesian analysis in MPNet

Bayesian analysis in MPNet

Missing data in MPNet

Session 4: More complex models

Session 4: More complex models

Session 4: More complex models

Make sure no ME

Are all zeros really zeros?

In principle valid for sampled data (admissible)

MNAR impossible to check (but robustness can be assessed)

Are missing data “diﬀerent” than observed?

If attributes are missing we can use a similar

technique of data-­‐augmentation (not in Pnet

yet)

Unobserved data: snowball sampling

Unobserved data: snowball sampling

Unobserved data: snowball sampling

Unobserved data: snowball sampling

Unobserved data: snowball sampling

Unobserved data: snowball sampling

Unobserved data: snowball sampling

Sampling in/on networks

=

0

x =

- 1

1

Sampling in/on networks

=

0

0

1

x = 1

-

- 0

1

1 0

1

1

Sampling in/on networks

=

0

0

0

1 0

x = 1

-

- 0

1

1 0

1 0

0 1

Sampling in/on networks

=

0

0

0

1 0

1

0

0 0 0

0 0

0

0

x =

q  Bayesian analysis q  Missing data

q  Snowball sampled data

q  Fitting ERGM to LARGE data sets q  Spatial Embedded networks

q  Multilevel ERGM

q  Longitudinal ERGM

technique of data-‐augmentation (not in Pnet