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Supplementary Information for

"Inter-Rebel Alliances in the Shadow of Foreign Sponsors"

Contents

Main models in regression table 2

Predicted Probabilities 3

Alternative Controls 5

10-Fold Cross Validation 6

Selection Bias 8

Selection Bias 10

Robustness Checks 12

List of Tables

1 Pooled Models of Alliance-Making in Civil War, 1975–2009 . . . . . . . . . . . . . . . . 2

2 Alternative controls and rebel alliance (1975–2009) . . . . . . . . . . . . . . . . . . . . . 5

3 Two-Stage Heckman Tobit Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

List of Figures

1 Mean Predicted Probability of Alliance by Sponsor Type for each dyad with 50 percent

conﬁdenceintervals. ..................................... 4

2 Predictive Accuracy of Models 1-3 using multilevel logistic regression . . . . . . . . . . . 6

3 ROC Curves Predicting Inter-Rebel Alliance . . . . . . . . . . . . . . . . . . . . . . . . . 7

4 Model Criticism Plot for Model 2 (Bapat and Bond) . . . . . . . . . . . . . . . . . . . . . 8

5 Model Criticism Plot for Model 3 (Christia) . . . . . . . . . . . . . . . . . . . . . . . . . 9

6 Pooled Models of Inter-Rebel Alliance, 1975–2001 . . . . . . . . . . . . . . . . . . . . . 12

7 Bapat and Bond Pooled Model of Inter-Rebel Alliance, 1975–2001, using Bapat and Bond

MeasureofForeignSupport ................................. 13

8 Rebel-Level Variables and Cold War . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Main models in regression table

Table 1 – Pooled Models of Alliance-Making in Civil War, 1975–2009

Base Model Model 1 Model 2 Model 3

Single sponsor 0.68 0.34

(0.38) (0.37)

Diﬀerent sponsor 1.32 1.09

(0.83) (0.80)

Shared sponsor 2.27∗2.14∗

(0.39) (0.38)

Weak dyad −0.10

(0.82)

Sponsor 1.46∗

(0.32)

Sponsor x Weak dyad −0.87

(1.21)

Ratio 2.73∗

(0.71)

GDP p.c. (ln) 0.17 0.14 0.16∗0.19∗

(0.07)∗(0.08) (0.08) (0.08)

Expenditure (ln) 0.01 0.02 0.03 0.03

(0.07) (0.05) (0.05) (0.05)

Duration (ln) −1.15∗−1.27∗−1.24∗−1.17∗

(0.15) (0.15) (0.15) (0.15)

Non-Contiguity −0.08 0.20 0.08 −0.11

(1.16) (1.10) (1.17) (1.21)

Religious frac. 1.35 0.66 1.31 1.19

(2.35) (2.21) (2.36) (2.43)

Ethnic frac. −2.66 −2.44 −2.65 −2.60

(1.98) (1.88) (2.01) (2.08)

Durability (ln) 0.63∗0.65∗0.68∗0.82∗

(0.18) (0.19) (0.19) (0.20)

Intercept −0.77 −1.35 −1.59 −2.78

(1.4) (1.37) (1.42) (1.56)

Log Likelihood -289.69 -272.44 -278.18 -280.85

AIC 597.40 568.91 580.39 581.76

BIC 641.41 627.60 639.07 630.64

Num. obs. 985 985 985 985

Num. groups: cowcode 35 35 35 35

Note: Pooled coeﬃcients estimates from multiple imputations (n=500) for multilevel logistic regression with standard

errors in brackets clustered on conﬂicts. ∗p<0.05.

2

Predicted Probabilities

Figure 1 indicates a high probability of inter-rebel cooperation for the majority of dyads with shared

sponsors. My model gives a predicted probability of insurgent alliance of more than 60 percent for

roughly two-thirds of dyads in which both partners received external assistance. Notable cases include

the FUNCINPEC-KPLNF alliance that was sponsored by the United States, China and Thailand during

Cambodian civil war (1980–1991); the ZANU-ZAPU cooperation against Rhodesia with the support of the

Eastern bloc and frontline countries (Mozambique and Zambia); and a number of Palestinian groups that

received support from Arab countries. Additional cases with high probability of alliance formation include

UNITA and FNLA with the support from Mobutu’s Zaire; Hezbollah and Hamas who received support

from Iran and Syria; major Darfur groups, JEM and SLM, with the backing from Chad; as well as the

cooperation between the Tamil Tigers and TELO in the shadow of Indian support in the 1908s.

Roughly a quarter of cases without foreign support have 0.6 or higher probability of alliance. Most

of these cases include dyads with much weaker capabilities relative to the incumbent government. This

implies that foreign support may not be a necessary catalyst for cooperation where power asymmetry is

not a prior issue. The probability of alliance for dyads with single and diﬀerent sponsors is much lower.

While there are only ﬁve cases of dyads with single sponsors with probability higher than 0.5, there are no

dyads with diﬀerent sponsors that score a probability of alliance higher than 0.5. This suggests that foreign

support seems to be the strongest catalyst for rebel cooperation when there is a shared sponsor.

Figure 1 – Mean Predicted Probability of Alliance by Sponsor Type for each dyad with 50 percent conﬁdence

intervals.

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RJF & AL−MAHDI ARMY

CROATIAN IRREGULARS & CROATIAN REPUBLIC OF BOSNIA AND HERZEGOVINA

EGP & ORPA

FAR & ORPA

ANC & PAC

AZAPO & PAC

PALIPEHUTU−FNL & CNDD−FDD

FROLINA & PALIPEHUTU−FNL

CNDD & PALIPEHUTU−FNL

PFLP−GC & PLO

PFLP−GC & HEZBOLLAH

PFLP−GC & FATAH AL−INTIFADA

CNR & CSNPD

PFLP−GC & PLO (FATAH)

HAMAS & PFLP−GC

EGP & PGT

FAR & PGT

ORPA & PGT

HAMAS & PIJ

PIJ & PLO (FATAH)

PIJ & HEZBOLLAH

PIJ & PIJ

FATAH AL−INTIFADA & PLO

ELF & ELF FACTIONS

HAMAS & PLO

PIJ & PLO

LTTE & PLOTE

HEZBOLLAH & PNA

HAMAS & PNA

ERP & PRTC

FARN & PRTC

FPL & PRTC

FAL & PRTC

PUK & KDP

EPL & ELN

PUK & DPK

MCC & PWG

RAFD & FUCD

MLC & RCD

MLC & RCD−ML

RCD & RCD−ML

ARIF & RSO

RUF & KAMAJORS

RUF & AFRC

MRTA & SENDERO LUMINOSO

ELF FACTIONS & EPLF

SERBIAN IRREGULARS & SERBIAN REPUBLIC OF BOSNIA AND HERZEGOVINA

SERBIAN IRREGULARS & SERBIAN REPUBLIC OF KRAJINA

SLM−UNITY & SLM

JEM & SLM

SLM−MM & SLM

SPLM & SPLM−FACTION

SPM & SNM

SSDF & SPM

SSDF & SNM

LTTE & TELO

ELF & EPLF

PLOTE & TELO

ENGINE LOURD & TONTON MACOUTE

EPRP & TPLF

EPDM & TPLF

OLF & TPLF

TNSM & TTP

FACTION OF UPDA & UDCA

FOBA & UDCA

HSM−SEVERINO & UDCA

ADF & UDCA/LRA

EPDM & EPRP

RAFD & UFDD

FOBA & UFM

FEDEMO & UFM

NRA & UFM

UDCA & UFM

FNLA & UNITA

MPLA FACTION & UNITA

FEDEMO & UNLA

FOBA & UNLA

UNLA & UNLA

EPRDF & EPRP

HSM−SEVERINO & UNLA

UFM & UNLA

NRA & UNLA

UDCA & UNLA

KNF & UNLF

FEDEMO & UNRF

NRA & UNRF

UFM & UNRF

UNRF & UNLA

FOBA & UNRF

ERP & FAL

ADF & UNRF II

UDCA/LRA & UNRF II

UDCA & UPA

FACTION OF UPDA & UPA

UNRF & UPC

UNLA & UPC

UFM & UPC

FEDEMO & UPC

FOBA & UPC

NRA & UPC

FAN & FAP

UDCA & UPC

HSM−SEVERINO & UPC

FEDEMO & UPDA

NRA & UPDA

UFM & UPDA

UDCA & UPDA

UPC & UPDA

UPDA & UNRF

UPDA & UNLA

FOBA & UPDA

AMAL & LNM

EGP & FAR

UPDA & HSM−SEVERINO

UNLA & UPDA

FEDEMO & UPF

FOBA & UPF

UFM & UPF

UNLA & UPF

NRA & UPF

UDCA & UPF

UPC & UPF

UPDA & UPF

EPL & FARC

UNRF & UPF

HSM−SEVERINO & UPF

FEDEMO & UPM

FOBA & UPM

UPC & UPM

UFM & UPM

UNLA & UPM

HSM−SEVERINO & UPM

NRA & UPM

UPDA & UPM

ELN & FARC

UPF & UPM

UNRF & UPM

UDCA & UPM

USC & SNM

USC & SSDF

USC & SPM

SPM & USC−AIDEED

SSDF & USC−AIDEED

USC−AIDEED & SNM

USC & USC−AIDEED

ERP & FARN

UDCA/LRA & WNBF

ADF & WNBF

ZANU & ZAPU

ZVIADISTS & FACTION OF NATIONAL GUARD

ZVIADISTS & FORCES OF VAZHA ADAMIA

ZVIADISTS & MKHEDRIONI

HEZB−I−ISLAMI & TALEBAN

PJAK & JONDULLAH

FAL & FARN

HAMAS & FATAH AL−INTIFADA

FOBA & FEDEMO

NRA & FEDEMO

UDCA & FEDEMO

HSM−SEVERINO & FEDEMO

RAFD & AN

FLEC−FAC & FLEC−R

MJP & FN

MPCI & FN

MPIGO & FN

CNR & FNT

CSNPD & FNT

FACTION OF NATIONAL GUARD & FORCES OF VAZHA ADAMIA

MKHEDRIONI & FORCES OF VAZHA ADAMIA

FARN & FPL

ERP & FPL

ANSAR AL−ISLAM & AL−MAHDI ARMY

FAL & FPL

CNDD & FROLINA

TAKFIR WA−HIJRA & GIA

GIA & GSPC

HEZB−I−ISLAMI & HEZB−I−WAHDAT−I−ISLAMI

PLO (FATAH) & HEZBOLLAH

HAMAS & HEZBOLLAH

PLO & HEZBOLLAH

FATAH AL−INTIFADA & HEZBOLLAH

HEZBOLLAH & AMAL

ANSAR AL−ISLAM & RJF

FOBA & HSM−SEVERINO

AL−MAHDI ARMY & ISI

ANSAR AL−ISLAM & ISI

RJF & ISI

JAMAAT−I−ISLAMI & HEZB−I−ISLAMI

JAMAAT−I−ISLAMI & HEZB−I−WAHDAT−I−ISLAMI

SLM−UNITY & JEM

SLM−MM & JEM

HEZB−I−ISLAMI & JUMBISH−I−MILLI−YE ISLAMI

JUMBISH−I−MILLI−YE ISLAMI & HEZB−I−WAHDAT−I−ISLAMI

ANC & AZAPO

JAMAAT−I−ISLAMI & JUMBISH−I−MILLI−YE ISLAMI

AFRC & KAMAJORS

KNU & BCP

FUNCINPEC & KPNLF

KPNLF & KR

FUNCINPEC & KR

LAA & LNM

LEBANESE FORCES & LEBANESE ARMY (AOUN)

M−19 & ELN

M−19 & FARC

BLA & BALUCH ITTEHAD

M−19 & EPL

CNR & MDD

FARF & MDD

CSNPD & MDD

FNT & MDD

GIA & MIA/FIS

GIA & MIA/FIS/AIS

AQIM & GIA

ASG & MILF

MPIGO & MJP

CNDP & BDK

FACTION OF NATIONAL GUARD & MKHEDRIONI

RCD−ML & MLC

MILF & MNLF

MODEL & LURD

ERP & MONTONEROS

ISLAMIC LEGION & MOSANAT

MJP & MPCI

MPCI & MPIGO

FNLA & MPLA FACTION

ISLAMIC LEGION & MPS (MOSANAT)

BRA & BLA

COCOYES & NINJAS

COBRAS & NINJAS

ATTF & NLFT

CPP & NPA

INPFL & NPFL

FOBA & NRA

COCOYES & NTSILOULOUS

NINJAS & NTSILOULOUS

EPDM & OLF

EPRP & OLF

0.0 0.2 0.4 0.6 0.8 1.0

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a

a

a

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a

No Sponsor

Single Sponsor

Different Sponsor

Shared Sponsor

4

Alternative Controls

In the following models, I include alternative, dyad-level, variables since the main model include only

state-level predictors. First, I include shared ideology, which is measured using Non-State Armed Groups

(NAG) dataset, I check whether the groups in those dyads shared one of the possible ideologies: left-wing,

nationalist, religious, right-wing. If both groups in a dyad followed the same ideology, then "Shared

ideology" was coded 1, and 0 otherwise. Next, I code whether any of the groups in a dyad has splintered

from the other in the past. To measure "Splinter" I use UCDP Actor Dataset (variable "splinter") which

identiﬁes the splintering and parent organization. "Splinter" is coded 1 if one of the parties has splintered

from the other in the past, and 0 otherwise. To account for the possibility that shared ethnic/sectarian

background drives alliance dynamics, I include "Shared ethnic pool" in the equation. This predictor comes

from "recruitment" variable from ACD2EPR dataset Version 2014. This variable indicates whether a rebel

group is recruiting from an ethnic group. Possible values are 0 ("no recruitment"), 1 ("recruitment"), 2

("ethnic group members are recruited by the rebels and the government"). I merge values of 1 and 2

into a single value indicating the presence of ethnic pool (1), or it absence (0). Then I compare if both

groups recruit from the same ethnic group. Sometimes rebel groups recruit from numerous ethnic groups.

If they recruited from at least one common ethnic group, I coded "Shared ethnic pool" as present or 1,

and 0 otherwise. Finally, I include logged duration to account for the temporal dimension of a dyadic

relationship. Model 4 features only alternative controls, while Model 5 includes alternative controls and

foreign sponsorship.

Table 2 – Alternative controls and rebel alliance (1975–2009)

Model 4 Model 5

Shared ideology 1.14∗1.15∗

(0.37) (0.36)

Splinter 0.46 0.32

(0.45) (0.47)

Shared ethnic pool −0.18 −0.24

(0.45) (0.45)

Duration (ln) −1.09∗−1.22∗

(0.15) (0.15)

Single sponsor 0.34

(0.37)

Diﬀerent sponsor 1.09

(0.80)

Shared sponsor 2.14∗

(0.38)

(Intercept) −0.53 −1.00∗

(0.48) (0.46)

Log Likelihood -298.04 -281.25

AIC 608.08 580.50

BIC 637.44 624.54

Num. obs. 985 985

Num. groups: conﬂict 35 35

Coeﬃcients estimates for multilevel logistic regression with standard errors in brackets clustered on conﬂicts. ∗p<0.05

5

10-Fold Cross Validation

K-fold cross validation (CV) is a way to analyze how the results of a model apply to an independent sample,

i.e. predictive accuracy of the model. The ﬁrst round of CV includes partitioning of original data into similar

folds of subsets (in my case into 10 folds of 98 or 99 observations), performing analysis on a single subset

("training dataset"), and validating the analysis on the other ("testing dataset"). After the data-partitioning,

I carry out 500 multiple imputations and then run multilevel logistic model on the training dataset. Next, I

loop over the 500 models to obtain predicted values for each fold.

One way of presenting CV results is to make a contingency table composed of two actual classes

("alliance" and "non-alliance") and two predicted classes ("alliance" and "non-alliance") for a set of test data

for which true values are known. The northwest (0/0) and southeast (1/1) quadrants are correct predictions,

and the other diagonal (northeast and southwest) represent incorrect predictions. The predictive accuracy

for each model is .72 (see Figure 2).

Figure 2 – Predictive Accuracy of Models 1-3 using multilevel logistic regression

Row: Predicted = 0

Col: Actual = 0

Row: Predicted = 1

Col: Actual = 1

702

77

89

112

Model 1

Proportion correct = 0.83

Row: Predicted = 0

Col: Actual = 0

Row: Predicted = 1

Col: Actual = 1

704

75

96

110

Model 2

Proportion correct = 0.82

Row: Predicted = 0

Col: Actual = 0

Row: Predicted = 1

Col: Actual = 1

707

72

91

115

Model 3

Proportion correct = 0.83

6

The predictions are classiﬁed by true negatives in the upper-left quadrant (correct predictions that there

is no intervention); true positives in the lower-right quadrant (correct predictions that there is intervention);

false positives in the upper-right quadrant (incorrect predictions that there is intervention); and false

negatives in the lower-left quadrant (incorrect predictions that there is no intervention). The higher the

number of predictions among true/false positives compared to false positives/negatives, the higher the

accuracy of our models. Accuracy is the sum of true/false positives divided by the total number of

predictions, and shows how often the classiﬁer is correct.

Another way to analyze the predictive accuracy is to make Precision-Recall (PR) curve plots. PR graphs

show how meaningful is a positive result ("alliance" occurring) given the baseline probabilities of alliance.

PR plots display pairs of recall and precision values where "recall" is a performance measure of the whole

positive part of my data (x-axis), whereas "precision" is a performance measure of positive predictions

(y-axis). Models with best performance scores are located closer to the the upper-right quadrant. Figure 3

shows that Model 1 has the best performance.

Figure 3 – ROC Curves Predicting Inter-Rebel Alliance

Model 1

Recall

Precision

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0

Model 2

Recall

Precision

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0

Model 3

Recall

Precision

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0

Joined

Recall

Precision

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0

7

Model Criticism Plot

Figure 4 – Model Criticism Plot for Model 2 (Bapat and Bond)

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AMAL & LNM−1986

AMAL & LNM−1985

FAR & PGT−1979

NRA & UPM−1986

JAMAAT−I−ISLAMI & JUMBISH−I−MILLI−YE ISLAMI−1996

ELN & FARC−1991

SPM & SNM−1989

EPDM & TPLF−1989

SSDF & SNM−1991

FAR & ORPA−1979

PIJ & PLO (FATAH)−2003

LTTE & TELO−1986

HEZBOLLAH & AMAL−1998

ASG & MILF−1994

PIJ & PLO (FATAH)−2002

LTTE & TELO−1987

PFLP−GC & HEZBOLLAH−1985

PFLP−GC & FATAH AL−INTIFADA−1985

PUK & KDP−1975

PFLP−GC & PLO (FATAH)−1989

0

250

500

750

1000

Observation (ordered by f)

0.00 0.25 0.50 0.75 1.00

Forecast Value

8

Figure 5 – Model Criticism Plot for Model 3 (Christia)

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RAFD & AN−2008

AMAL & LNM−1986

AMAL & LNM−1985

ELN & FARC−1991

SSDF & SNM−1991

NRA & UPM−1986

FAR & PGT−1979

MJP & MPCI−2003

JAMAAT−I−ISLAMI & JUMBISH−I−MILLI−YE ISLAMI−1996

SPM & SNM−1989

PFLP−GC & PLO (FATAH)−1989

HEZBOLLAH & PNA−1996

HAMAS & FATAH AL−INTIFADA−1988

HEZBOLLAH & AMAL−1995

PLO & HEZBOLLAH−1988

HEZBOLLAH & AMAL−1998

PFLP−GC & FATAH AL−INTIFADA−1985

FATAH AL−INTIFADA & PLO−1985

HAMAS & FATAH AL−INTIFADA−1987

PIJ & PIJ−1992

0

250

500

750

1000

Observation (ordered by f)

0.00 0.25 0.50 0.75 1.00

Forecast Value

9

Selection Bias

Selection bias occurs due to the systematic exclusion of a subset of data due to a speciﬁc attribute. The

exclusion of the subset will yield distorted empirical results of the population of interest. In my case, it

might be that rebel groups that do not expect to enter alliance may have less need for external support,

and thus may not appear in my dataset. I cannot analyze alliance-making between such groups because

they are systematically omitted from the sample. The issue in my case is that the missingness of foreign

support could be a function of rebel groups anticipating to form an alliance. This means that the selection

mechanism may be associated with the presence of alliance, yielding biased estimates or estimates that

apply only to the selected sub-sample.

Table 3 – Two-Stage Heckman Tobit Model

Model 6

SELECTION (DV: Foreign support):

GDP p.c. (ln) 0.13∗

(0.01)

Expenditure (ln) −0.01

(0.01)

Weak link 0.04

(0.37)

Religious frac. 1.71∗

(0.34)

Ethnic frac. 0.90∗

(0.40)

Intercept −1.99∗

(0.37)

OUTCOME (DV: Alliance):

Durability (ln) 0.04

(0.02)

Duration (ln) −0.19∗

(0.03)

Shared ideology −0.11

(0.07)

Shared ethnic ties 0.23∗

(0.07)

Splinter 0.10

(0.11)

Intercept 0.50∗

(0.10)

Inverse Mills Ratio −0.14

(0.09)

sigma 0.42

N A

rho −0.34

N A

R20.26

Adj. R20.23

Num. obs. 536

Censored 358

Observed 178

∗p<0.05

10

To account for this problem, I use a tobit two-step Heckman selection model (Heckman 1979). I ﬁrst

model the probability of dyads receiving foreign support: in this step, dyads are coded 1 if they received

external support from one or more foreign governments (based on UCDP External Support Dataset) and 0

otherwise. The selection model includes a number of variables from Salehyan, Gleditsch and Cunningham

(2011) such as logged GDP per capita, strength of the dyad relative to the government, military expenditure

and ethnic and religious fractionalization. I then use the information from the ﬁrst step to compute the Mills

inverse ratio and include it in the outcome step. The signiﬁcance of the coeﬃcient of the Inverse Mills ratio

will indicate if there is selection bias. The outcome step includes durability of the countryâĂŹs regime, the

logged duration of dyad, shared ideological and ethnic ties, splintered group and Inverse Mills ratio (IMR)

as covariates. Table 3 in the Appendix presents the results of the Heckman model. In short, the results

show that the IMR is small (beta -0.15) and the p-value is large (0.16), so I cannot reject the null that the

errors are uncorrelated.

11

Robustness Checks

Figure 6 – Pooled Models of Inter-Rebel Alliance, 1975–2001

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Durability (ln)

Ethnic frac.

Religious frac.

Non−Contiguity

Duration (ln)

Expenditure (ln)

GDP p.c. (ln)

Shared sponsor

Different sponsor

Single sponsor

−6 −4 −2 0 2 4

Coefficient Estimates

Model 7

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Durability (ln)

Ethnic frac.

Religious frac.

Non−Contiguity

Duration (ln)

Expenditure (ln)

GDP p.c. (ln)

Sponsor x

Weak Dyad

Sponsor

Weak Dyad

−5.0 −2.5 0.0 2.5

Coefficient Estimates

Model 8

12

Figure 7 – Bapat and Bond Pooled Model of Inter-Rebel Alliance, 1975–2001, using Bapat and Bond

Measure of Foreign Support

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Durability (ln)

Ethnic frac.

Religious frac.

Non−Contiguity

Duration (ln)

Expenditure (ln)

GDP p.c. (ln)

Sponsor x

Weak Dyad

Sponsor

Weak Dyad

−5.0 −2.5 0.0 2.5 5.0

Coefficient Estimates

Model 9

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Figure 8 – Rebel-Level Variables and Cold War

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Duration (ln)

Shared ethnic pool

Splinter

Shared ideology:Cold War

Cold War

Shared ideology

−2 −1 0 1 2

Coefficient Estimates

●Model 10: Cold War

Model 11: Interaction

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