Appendix for Inter-Rebel Alliances in the Shadow of Foreign Sponsors

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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
13

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
14