Article

Modeling ‘‘Effectiveness’’in International
Relations

Journal of Conflict Resolution
00(0) 1-32
ª The Author(s) 2013
Reprints and permission:
sagepub.com/journalsPermissions.nav
DOI: 10.1177/0022002713499715
jcr.sagepub.com

Jonathan Renshon1 and Arthur Spirling2

Abstract
Are democracies better at winning wars and militarized disputes? Is there anadvantage associated with initiating a war or dispute? Noting that pairwise contest
data are the norm in applied research, we motivate a straightforward Bradley–Terrystatistical model for these problems from first principles, which will allow for acloser integration of theoretical and statistical practice for scholars of international
relations. The essence of this approach is that we learn about the latent abilities ofstates from observing conflict outcomes between them. We demonstrate thenovelty and appeal of this setup with reference to previous attempts to capture
estimands of interest and show that for many questions of concern—especiallyregarding ‘‘democratic effectiveness’’ and ‘‘initiation effects’’—our approach may be
preferred on theoretical and statistical grounds. The evidence we find only partially
supports the ideas of ‘‘democratic triumphalists’’: democracy aids effectiveness, but
only in certain contexts (while in others it actually impairs fighting ability). We also
provide estimates of possible ‘‘initiation effects,’’ and show that moving first seems
to carry little advantage in interstate wars, but a substantial one in lower-level
disputes.

1
2

Department of Political Science, University of Wisconsin–Madison, Madison, WI, USA
Department of Government, Harvard University, Cambridge, MA, USA

Corresponding Author:
Jonathan Renshon, Department of Political Science, University of Wisconsin–Madison, 110 North Hall,
Madison, WI 53706, USA.
Email: renshon@wisc.edu
Arthur Spirling, Department of Government, Harvard University, 1730 Cambridge Street, Cambridge,
MA 02138, USA.
Email: aspirling@gov.harvard.edu

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

2

Journal of Conflict Resolution 00(0)Keywords
conflict, contest data, Bradley-Terry, democratic effectiveness, power, initiation

Scholars of international relations (IR) have devoted considerable effort to translating
theoretical understandings of behavior into statistical models of outcomes (Signorino
1999; Smith 1999; Lewis and Schultz 2003; Whang 2010; Carter 2010). Though theparticular procedures used can be quite complicated, the motivation is very simple: theempirical approach must return estimates that correspond in some meaningful way tothe parameters of our theoretical understanding of interstate conflict. If we fail to do
this, we run the danger of being unable to interpret our results in terms of our original
conjectures; put otherwise, we cannot test our theories (see, especially, Signorino
2003; cf. Carrubba, Yuen, and Zorn 2007). The flip side of this idea is that we needto understand the theoretical commitments we make—albeit implicitly—when we
make choices among statistical models.
The current article takes this logic to the problem of estimating the ‘‘effectiveness’’of states in IR, in particular their ability to prevail in conflict. Although much interest
has focussed on ‘‘democratic effectiveness’’ (e.g., Reiter and Stam 1998b), the central question of ‘‘what makes states more likely to win conflicts?’’ is very generaland long standing (e.g., Wright 1965). Here, we begin from the ‘‘ground up,’’ by giving plausible foundations for a statistical model of state effectiveness in interstate
conflict. In contrast to all previous approaches of which we aware, we concentrateon the estimation of latent state abilities as a function of covariates, and we discuss alogit linear form for that relationship that connects the two in a way that is new conceptually, but easily understood by political scientists who work with binary dependent variable observational data (see, e.g., Berry, DeMeritt, and Esarey [2010] for an
overview). In so doing, we provide statistical foundations that might serve as a fruitful base for future theoretical and empirical efforts in this area.
The statistical model that subsequently emerges—a variant of the Bradley and
Terry (1952) approach to pairwise contest data (see also Turner and Firth 2010)—
is thus well motivated. We describe the model’s properties as they pertain to estimation, and we show how this technique may be taken to the type of data politicalscientists and IR scholars commonly use. Therein, we demonstrate the need for bothstates’ covariates to enter the linear predictor such that the effect of a given covariate
can be understood as the difference in relative capabilities, and not one state’s (absolute) level of ability. Our model also allows for a satisfactory way to deal with acommon problem endemic to quantitative IR research: that it is difficult to model(with the standard setup) outcomes of interactions between states if they are determined by heterogenous and unobserved factors specific to those countries involved(such as culture). We demonstrate how dependence across contests (in the sense ofGreen, Kim, and Yoon 2001; King 2001) may be taken into account with random
effects via a mixed model arrangement for such pairwise data. We contrast the

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

Renshon and Spirling

3

approach here to that taken by other scholars, and show that, at the most basic level,
our approach allows a more general question to be asked of data: in particular, we ask,‘‘What factors make states more or less likely to win conflicts?’’ rather than ‘‘What
factors make democracies more likely to win conflicts’’ or ‘‘What factors make initiators more likely to win conflicts?’’ These latter enquiries emerge as special cases of
our approach in the sense that we are not constrained to estimate the effectivenessof states with respect to a particular covariate: the model here is more theoreticallyagnostic. We make no attempts to pour scorn on previous efforts in the field, but rather
seek to demonstrate what we believe is a sensible model that will hopefully give scholars pause when they reach for more conventional logit (and probit) arrangements.
We apply the model we discuss to ‘‘standard’’ (Polity/COW [Correlates of War] /MID) IR data, with particular focus on the impact of relative levels of ‘‘democraticness’’ and the open puzzle of whether there is an advantage associated with initiating
conflicts in both wars and nonwars, a topic of some concern to scholars (see, e.g., Jervis 1978; Fearon 1997; Van Evera 1998). We do find (partial) support for a democratic
advantage in wars, but to the extent that increasing ‘‘democratic-ness’’ increases thelikelihood of victory, it only does so at certain (absolute) levels of democracy and thiseffect is partly dependent on an opponent’s characteristics. That is, in some cases,
increasing democraticness seems to impair fighting ability. Similarly, we find that
initiating those wars does not seem to be associated with an increased probabilityof victory. By contrast, for nonwar conflicts, there is something of an initiation‘‘effect,’’ with first movers doing better, on average. in the following, we speculate
on the likely mechanism/mechanisms behind such an observation.

Why We Care about Effectiveness in International Relations
Beginning at least with Wright (1965), Cannizzo (1980), and then Wayman, Singer,
and Goertz (1983), there is a voluminous IR literature on what factors makestates ‘‘powerful.’’1 Much attention has been paid specifically to ‘‘democratic
effectiveness’’—that is, the degree to which democracies are able to achieve more
successful conflict outcomes than nondemocracies.
The modern incarnation of this debate grew out of the democratic peace researchparadigm and was influenced by the work of Lake (1992, 31), who found that of thetwenty-six wars fought between democracies and nondemocracies from 1816 to 1990,
democracies won twenty-one (81 percent) of them. Lake’s explanation (that for a variety of reasons democracies are able to bring to bear overwhelming coalitions again
nondemocracies) would later be classified into the material capabilities school, in
opposition to works that argued that democracies were more likely to choose fightsthat they could win because they faced harsher political consequences for bluffing
or losing (this is known as the selection effects argument, see Fearon 1994; Schultz1999). A bevy of related work soon followed up on these initial findings.
Reiter and Stam (1998b) found that democratic initiators and targets have bothbeen more likely to win wars than other types of states. They also argued for a

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

4

Journal of Conflict Resolution 00(0)nonlinear relationship between regime type and effectiveness, while democratic
initiators were the most likely to win, the least democratic countries (autocracies)
were more likely to win wars than so-called mixed regimes. Gelpi and Griesdorf(2001, 641) examined international crises and found that democratic challengers(i.e., initiators) were more likely to prevail than other types of challengers, but that
democratic defenders were no more likely to prevail than autocratic defenders, evenwhen crucial values were at stake. Other work examined the temporal nature of thedemocratic advantage (Bennett and Stam 1998) or investigated how democratic
effectiveness might explain micro-level outcomes at the level of the individual
battles (Reiter and Stam 1998a; Biddle and Long 2004).
The main thrust of this research program may be summed up by Reiter and Stam(1998b), who write that there is ‘‘something about democratic regimes that makes it
easier for them to generate military power and achieve victory in the arena of war.’’Whether that ‘‘something’’ is primarily the ability to generate more wealth and mobilize more resources (a view advanced by, among others, Lake 1992; Bueno de Mesquita et al. 1999), the use of different strategies (Reiter and Meek 1999) or thetendency to select wars that are winnable (the ‘‘selection effects’’ argument, exemplified by Reiter and Stam 2002) is not yet settled. In recent work, the very existence ofthe so-called democratic advantage has been called into question. To wit, there has
been lively debate over case selection (see Desch 2002, 2003, 2008); that is, ‘‘What
conflicts should count?’’ (see also, Lake 2003; Reiter and Stam 2003). Scholars havealso suggested differentiating states as ‘‘initiators’’ versus ‘‘joiners’’ of wars (seeDownes 2009), with commensurately new data definitions.
The point here is that estimating the ‘‘effectiveness’’ of states matters. Rather
than ponderously critiquing the various approaches of previous scholars, we startfrom ‘‘first principles’’ and suggest a statistical model that gets to the core of theissue and that provides a platform for future formal models as well as empiricalresearch. The next section begins that process.

Modeling Effectiveness
What We WantFirst, it is helpful to consider in some detail the quantity we want to estimate. At its heart,the ‘‘democratic effectiveness’’ debate revolves around the following query: are democracies more likely to win disputes or confrontations than nondemocracies? Put more generally, scholars are interested in what factors make countries more likely to win wars.
Though this is easily stated, the implied statistical model is perhaps not so obvious.
To fix ideas, suppose that we observe a series of 1; : : : ; t; : : : T conflicts between
a set of countries. We assume that this data set is ‘‘connected’’ insofar as there is nosubset of states that never meets the others in disputes, an empirical requirement thatis met for the great majority of observations in real investigations.2 Any given dispute involves two of a total of N states, and we index the countries concerned as i and

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

Renshon and Spirling

5j. Since i either wins or loses the dispute against j, the response (the ‘‘dependent variable’’) to be predicted for observation t is binary; that is, yt 2 f0; 1g; where yt ¼ 0
implies state j is victorious over i, whereas yt ¼ 1 implies state i beats j. The goal is
to model the probability, Prðyt ¼ 1Þ, that is, the probability that i wins. When we
have two states in this scenario this probability is, in fact, Prði beats jÞ.
Keeping with just i and j for now, suppose that both countries have latent‘‘abilities’’3—ai and aj , respectively—and that the probability of any particular conflict outcome, for example, a win for state i, is some function of these unobserved
quantities. More specifically, we suppose thatPrði beats j ÞPrði beats j Þai¼¼ :Prðj beats i Þ 1  Prði beats j Þ aj

ð1ÞThat is, the odds that i beats j is just the ratio of their abilities. The fact that1  Prði beats j Þ is equivalent to Prðj beats i Þ in this context simply means we are(for now, and in general accordance with the literature) ruling out ‘‘draws’’ in international conflicts.

How to Get It
To take this approach to contests to real data, we need to specify a way to estimate ai
and aj , presumably as a function of covariates. One approach is to take the logarithmof ‘‘both’’ sides of equation (1) such that we have Prði beats j Þ
ai
log
¼ log
1  Prð i beats j Þaj
ð2Þlogit pij ¼ li  lj ;where li ¼ logðai Þ for all i, and we substitute pij for Prði beats j Þ and thus logit pijhii beats j Þ
for log 1 PrðPrð
i beats j Þ . We can then make li a function of covariates of interest (i.e.,‘‘X’’s) in a way that accords with the usual setup of a generalized linear model(GLM), in the sense that we have a linear predictor (‘‘bX ’’) on the ‘‘right-handside.’’ Thus, we have li ¼ bxi and lj ¼ dxj where xi and xj are one variable thattakes (possibly) different values for the countries, with (possibly) different coefficients b and d. It is no problem to have a long vector of covariates in practice(say, ‘‘democracy,’’ ‘‘capability,’’ ‘‘nuclear power,’’ ‘‘gdp per capita,’’ etc.), but weassume a single x for exposition in this subsection. Moreover, though we specify
more elaborate models later, for now we suppose that the relevant covariate profile
for i and j do not change over the course of the data. That is, we assume that xi is thesame for any observation t or, more plainly, that the relevant attributes that contribute to i’s or j’s power are constant over time.

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

6

Journal of Conflict Resolution 00(0)What This Implies
From this simple but logical arrangement, four remarks immediately follow that, as
we will see, denote this model as different from others in IR. In part, these remarks
are summaries of properties that are ‘‘built-in’’ to the approach, and we present themhere to clarify matters to readers.
Remark 1: An observation consists of one conflict, which is used exactly once. Thus,Pr i beats j þ Pr j beats i ¼ 1:

dd

A particular conflict between i and j contributes one observation to the data: thatis, we do not count the conflict as a case of, for example, i attacking j and subsequently count the case again as j defending itself from i. Indeed, any notion of attacking or defending roles may be incorporated via the covariate profile (as discussed in
Remark 2). Note that we are agnostic as to what, precisely, a particular ‘‘conflict’’consists of it might be a battle, or war, or event defined some other way. The pointis that it is a ‘‘contest’’ between states.
In any case, a consequence of this arrangement is that the sum of the predictedprobabilities of i beating j and j beating i is equal to one. This follows directly fromthe equivalence Prði beats j Þ ¼ 1  Prðj beats i Þ, but it is distinctive insofar as a situation cannot obtain in which we predict a ‘‘victory’’ for both i and j; that is, thosepredicted probabilities cannot both be  12. In a model which uses each conflict as
two observations, such ‘‘non-sensible’’ predicted probabilities can occur.
Remark 2: logit pij is modeled as a function of features specific to the states and theirroles, not features of the conflict they are involved in.

Note that pij is defined in terms of the abilities of the states: li ¼ bxi . Here xi isproperly indexed with a subscript since it pertains to characteristics of i and i alone.
In a given contest, this might include a characteristic like ‘‘initiator,’’ but it cannot
include a characteristic of the conflict itself such as ‘‘fought at sea.’’ This is because
conflict characteristics cannot per se make it more less likely that state i wins overstate j. To see the distinction, suppose, for example, that state i is ‘‘better’’ at fighting
at sea and thus wins more sea conflicts. Then this ‘‘better-ness’’ must enter xi insome way (e.g., ‘‘number of fighting ships’’4), else it cannot affect the relative estimated abilities of the states: absent any information entering xi , fighting at sea
affects both parties equally.
To clarify matters here, notice that the model makes the assumption that we wish
to estimate the effectiveness of states in some ‘‘overall’’ sense as a latent trait of astate, wherein the conflicts from which we generate our estimates are fundamentallycomparable.5 If the analyst deems that the contests are not comparable—for example, if he or she wishes for some a priori theoretical reason to estimate effectivenessin sea conflicts as a quantity separate to effectiveness in land battles, and that some x

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

Renshon and Spirling

7

should have a differential effect therein—then this implies that the model ought to be
fit to the different data sets (‘‘sea conflicts,’’ ‘‘land conflicts’’).
Remark 3: The expression for logit pij contains no (nonzero) intercept term.

To see this, suppose that the intercept term is in fact nonzero. We have stated inequation (2) that logit pij ¼ li  lj . Adding an intercept, g, we have that
logit pij ¼ g þ li  lj :ð3ÞOf course, by symmetry (just flipping the i and j index over), we must also have
logit pji ¼ g þ lj  li :

ð4ÞSince i either wins or loses against j—there are no ‘‘ties’’ here—we must havepij ¼ 1  pji . This implies6 that
logit pij ¼  logit pji ;and thusg þ li  lj ¼ g  lj þ li :

ð5Þ

But then, g ¼ g, which is only true for g ¼ 0 which contradicts the premise thatg 6¼ 0.
Substantively, the foregoing remark says that there is no ‘‘bump’’ (up or down) in
effectiveness, simply because a country is listed as being i (first) or j (second) in a
conflict. These indices are arbitrary. Note that it may well be that initiation-status
affects the probability of winning, but this status is already included in l via thelinear predictor for the earlier model.
Remark 4: Only relative covariate levels matter for determining logit pij

From Remark 1 we have thatg þ bxi þ dxj ¼ g  ðbxj  dxi Þ;

ð6Þ

and that g ¼ 0. Hencebðxi þ xj Þ ¼ dðxi þ xj Þ;
implying that d ¼ b. Using these identities, the original regression equation (2) isrewritten as
logit pij ¼ bðxi  xj Þ:

ð7ÞAnd thus only the relative values of xi and xj (not their absolute values) determine
the log odds of a win for i (or j).

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

8

Journal of Conflict Resolution 00(0)Table 1. Stylized Monadic Data Example.
War

Country

Year

YVICT

XINIT

XDEM

...

Russo-Hungarian
Russo-Hungarian
Yom Kippur
Yom Kippur
Iran–Iraq
Iran–Iraq
..
.

RUS
HUN
ISR
EGY
IRQ
IRN
..
.

1956
1956
1973
1973
1980
1980
..
.

1
0
1
0
1
0
..
.

1
0
0
1
1
0
..
.

0
0
1
0
0
0
..
.

...
...
...
...
...
...
..
.

This assumption of the model reiterates the point that indices (i or j) are arbitrary:
it does not matter ‘‘who,’’ in state terms, has more or less of a particular covariate.
All that enters the model is how much one state has relative to the state they face in acontest.

How It Differs from Previous Approaches
Our four remarks are not, of themselves, remarkable: they follow directly from theway we conceptualized ‘‘effectiveness’’ as akin to an ability, and then the functional
form assumptions we chose to make. Nonetheless, they do mark our approach as distinctive with respect to the way that other scholars have thought about the modelingproblem. We make no particular claims that our model is ‘‘better,’’ but we do think it
answers the right question—in the sense that we posed it—and in a logically consistent way.
One obvious difference is that our model uses each conflict (or contest) only
once. One previous approach to the question of democratic effectiveness has been
to estimate models based on monadic data (e.g., Reiter and Stam 1998b; Downes2009). In this setup, each observation (or row) contains information on one state
in a conflict. Hence, though state i and state j might fight a particular war against
each other, they and their covariate profiles will take two separate entries. In Table 1,
we give a segment from a stylized version of such data. In the table, the six detailed
observations concern three conflicts: between Russia (RUS) and Hungary (HUN) in
1956, between Israel (ISR) and Egypt (EGY) in 1973, and then between Iraq (IRQ)
and Iran (IRN) in 1980. Each row then refers to one party to a given dispute. Thus,
Israel was the victor in 1973 (YVICT ¼ 1), but was not the initiator ðXINIT ¼ 0Þ,though it was democratic ðXDEM ¼ 1Þ. By contrast, for the same conflict, Egypt was
not a democracy ðXDEM ¼ 0Þ, initiated the conflict ðXINIT ¼ 1Þ, but ultimately lost
(YVICT ¼ 0).
From the perspective of simply estimating a regression equation, monadic data
present few issues. The models will generally be identified in the econometric sense,
and the properties of the estimators—unbiasedness, efficiency, and so on—will apply.
Given available technology at the time, these models were perfectly reasonable

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

Renshon and Spirling

9

choices. However, there are serious logical and inferential problems with this setup.
More concretely, there are at least three concerns. First, there is the potential for double counting in the sense that half the observations are not independent of the otherhalf (in fact, they are entirely dependent). For example, given that YINIT ¼ 1 for Egypt
in 1973, YINIT for Israel the same year must take the value 0. Our approach obviously
differs in that each contest is used exactly once in the data.
Several scholars have noted that IR are characterized by heavy dependency
between observations. One extreme version of this problem results in the ‘‘double
counting’’ we noted earlier; a slightly different problem emerges when the outcomesof interactions between states are determined by heterogenous and unobserved factors specific to those countries involved (see, e.g., Green, Kim, and Yoon 2001; King
2001). Thus, the second issue is that the standard setup shown previously does notallow for variability between states that have the same covariate profiles, a serious
problem if there is a chance that unobserved factors (e.g., resolve or culture) contribute to a state’s power and effectiveness. The statistical model we discuss below
allows for random effects (in essence, player-specific residuals) to alleviate suchconcerns, and is to our knowledge, the first contest-data model to do so.
Third, and most importantly in the standard setup, only one state’s characteristics
enter the regression equation for a given observation. To the extent that we believe
the model we derived earlier, this is clearly problematic. We acknowledge that there
are examples of scholars taking ‘‘hybrid approaches’’ in which some characteristics
of both sides are included, for instance, Sullivan (2007) includes a number of variables related to the characteristics of the target state, while Reiter and Stam (2002)
include covariates for the Polity score of the target state (in addition to the initiatingstate). We see these approaches as further evidence that most researchers would
grant the importance of including opponent characteristics if possible. Crucially,
if opponent characteristics are not included in the way we suggest—that is, for every
contest, it is the relative magnitude of the covariates that matters—then the ‘‘firstprinciples’’ justification for the contest model must be different to the account wegave. And, to the extent that our foundations are reasonable, as they are to the statistics literature, our model has a sensible interpretation in terms of abilities that is
missing in other approaches. Just as importantly, we believe that our framework andassumptions (particularly our focus on relative capability levels) will make intuitive
sense for IR scholars.
To see an example of this logic in action, consider a very simple model of international conflict where only one independent variable, x, is used to predict whether
or not a state wins a conflict. For clarity, suppose x is such that a one-unit change in x
has some intuitive meaning; for example, x might be gross domestic product (GDP)per capita (a one-unit increase is a one-dollar increase) or x might be major power
status (a one-unit increase means a state was not a major power and now has thatstatus). Suppose also, that a researcher decides to use a ‘‘hybrid’’ approach such thatboth states’ values on this covariate—xi and xj —are included on the ‘‘right-handside’’ of the (logistic) regression equation. To make our example especially stark,

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

10

Journal of Conflict Resolution 00(0)we will further suppose that xi ¼ xj (e.g., they have identical GDP figures, or areboth nonmajor powers, or whatever). With respect to the relevant logit, this model
would be set up as follows:
logit PrðY ¼ 1Þ ¼ b0 þ b1 xi þ b2 xj ;

ð8Þwhere the ‘‘left-hand side,’’ as usual, is the log of the probability of state i winning
divided by the probability of state i losing. Of course, when that log odds ratio
increases, the probability of i winning is increasing relative to the probability of ilosing. Suppose that we fit the model, and obtain estimates of b0 , b1 , and b2 ; we thenattempt to predict the outcome of an out-of-sample contest with its own value for the
ith state, written xm and for the jth state, written xn . To make life simple, suppose that
this out-of-sample xm is xi þ 1 and that xn is xj þ 1. What is our prediction for theoutcome? By definition, a one-unit increase to xi (giving us xm ) increases the log
odds by b1 . And a one-unit increase to xj (to give us xn ) increases the log odds byb2 (bear in mind that b1 and/or b2 could be negative). What is the overall effecton the log odds? It is not zero, unless b1 and b2 happen to sum to zero; that is, thelog odds must increase or decrease unless b1 ¼ b2 . But this is strange: previously,
the states were exactly evenly matched. Now, having increased the x by one unit
each, they are once again exactly evenly matched. And yet the probability of state
i winning relative to the probability of state i losing has changed. This seems theoretically wrongheaded and logically undesirable. What about in the Bradley–Terrycase? There, increasing xi and xj by one each makes no difference to the log odds:
the changes ‘‘cancel out’’ since the expression ðxi  xj Þ has not changed in value. So,
to the extent that we want to include covariates from both sides, the standard logit
set up is not the way to proceed; instead, we want to deal with differences rather
than sums.
The logic of our approach has consequences for the question asked of the data.
Recall that we ask, ‘‘What factors make states more or less likely to win conflicts?’’
Other approaches typically have to be a priori more specific. In terms of the ‘‘standard’’ logit specification described above, those approaches have to pick (possibly
arbitrarily) a state i for each observation to which the log odds applies. Thus, they ask
a question more akin to ‘‘What factors make democracies more likely to win conflicts?’’ or ‘‘what factors make initiators more likely to win conflicts?’’ This is nota semantic or trivial difference. In particular, other work assumes that the interest isin estimating a version of equation (3); that is, logit pij ¼ g þ bxi þ dxj ; where i andj have specific characteristics, such as being democratic or being initiators. As a result,
the relevant x with respect to which the equation is estimated (e.g., initiator status inmuch of the ‘‘democratic effectiveness research’’) cannot usually appear with its coefficient as an ‘‘effect.’’ Our model makes no such restrictions: i and j are simply stateswith whatever characteristics they happen to exhibit. An obvious consequence of thisis that any given xi or xj can pertain to initiator status, without having to rearrange the^ represent in terms of the underlying
data or our interpretation of what the estimated bs

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

Renshon and Spirling

11

quantity of interest. In a very real sense then, other approaches are special cases—both
theoretically and statistically—of our model. This also comes with significant benefits, not the least of which is that it allows us to generate (what we believe to be thefirst) estimates of the effect of initiating conflicts.

Statistical Choices
While the basic Bradley–Terry model seems a logical choice for the task at hand, inpractice the restrictive nature of the covariate vectors make it unacceptable for mostresearch in IR. The extended version we consider below does not suffer from theseshortcomings. More technically, we now discuss two types of quantities that we(as well as most IR scholars, we presume) would like to estimate: fixed effects andrandom effects. The former refer to the impact of independent variables that (may)change between contests (such as Polity level or military capabilities). The latter are
essentially player-specific residuals (i.e., abilities of the state unaccounted for by thecovariates we include in our model).

Fixed Effects
By ‘‘fixed effects,’’ we mean the modeling of parameters as a function of independent variables (Xs), where the parameters are considered nonrandom. In the current
context, the parameters of interest are the state abilities, denoted l. Of course, equation (7) does just this, but in that form, the model forces us to assume that covariates
are constant over sequential contests. This seems unrealistic in practice: Britain’s
level of democracy in 1900 is very different to that in 2000. To make equation (7)more general, we can allow the xri to vary across contests. Indexing a contest as k
we are interested inli  lj ¼

pX

br ðxikr  xjkr Þ:

ð9Þ

r¼1

where xikr is indeed varying across bouts, we have a ‘‘contest-specific’’ effect7 rep^ . The special case—such as the ‘‘region’’ of a
resented by our coefficient on xr , brcountry that is unchanging over time—is then constant for all k.

Random Effects
In the typical case of logit (or Bradley-Terry [BT] model), as can be readily seen in equation (3), there can be no variability between states that have identical covariate profiles:
a state’s ability is ‘‘all’’ fixed effect: li ¼ bxi . This is problematic if we believe there
may be unobserved heterogeneity in factors that contribute to state abilities. One solution is to model ‘‘random effects’’ for each player. Analogous to panel data, the idea here
is to include an error term composed of two parts. The first is the extent to which that
player’s ability differs from the overall one estimated for that state’s covariate profile

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

12

Journal of Conflict Resolution 00(0)and the second is simply a random deviation specific to that contest. If the variance ofthe random effect component is statistically significant, it must be that the random
deviations from the explanatory variable modeled abilities are in fact different. Thus,in this context, after controlling for covariates, the players still differ in ability.

Mixed Bradley–Terry Models
We would like to make the model in equation (9) more general, by allowing for correlation between the same players in different contests. But we still wish to makestatements about the influence of various independent variables which may varyover contests. Fitting the following general Bradley–Terry model facilitates these
aims:
logit pijk ¼

p
X

br ðxikr  xjkr Þ þ ðUi  Uj Þ :|ﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄ}|ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ} random effects

ð10Þ

r¼1

fixed effects

In this way, we have combined the player-specific (possibly contest specific) covariates of equation (9) with random effects represented as the difference between theerror terms. It is this latter term that will facilitate modeling correlation in unobserved influences over contests. In matrix notation, we have
logit pij ¼ Xb þ Ze;

ð11Þ

where e  N ð0; DÞ and D is a diagonal matrix whose diagonal elements are equal tos2 . The assumption here is that the sampled states are representative of a populationof nations and thus the variance term reflects the underlying heterogeneity of the dispute parties.
When we have the basic Bradley–Terry form of equation (7) or, in fact, equation (9),estimation can take place within a GLM framework (see Firth [2005] for an implementation). But GLMs will not do once we add the error term: we must now move to generalized linear mixed models (GLMMs; see McCulloch and Searle [2001] for detailed
discussion). Parameter estimation is usually via some variant of maximum likelihood,with computational complexities arising from the inclusion of the random effects component. The approach we take here relies on penalized quasi-likelihood (PQL; in thesense of Breslow and Clayton 1993) which approximates the full-maximum likelihood
solution. We need an approximation because the original likelihood equation involves acomplex integration for which there is no closed form. The specific suggestion of Breslow and Clayton (1993) involves a quadratic expansion of the Laplace approximationof the likelihood, but the essence of the technique is that the random effects, the Z matrix
earlier, are treated as if they are part of a linear mixed model. Fitting algorithms obtain^ and then use them to get best linear unbiased preestimates of the fixed effects, the bs,
dictions (BLUPs) of the random effects, e^ (see, e.g., Robinson [1991], for discussion).

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

Renshon and Spirling13^ and so on in an iterativeThose BLUPs are then used to improve the estimated bs
scheme. The variance of those random effects in our analysis will be of interest substantively, since it will give a sense as to whether, in fact, states’ performances in conflicts
are correlated over contests.
There are two immediate consequences of our approach here. First, PQL is relatively straightforward in computational terms, but because it does not make use ofa log likelihood, measures of fit that rely on that likelihood (like Akaike Information Criterion [AIC] and Bayesian Information Criterion [BIC]) will not be available. This will make it difficult to compare the fit of a mixed Bradley–Terry model
in some ‘‘overall’’ sense (assuming that AIC is a sensible choice for the comparison under consideration). Second, our model predictions—which in our case will
be predicted probabilities of winning or losing—are derived from ‘‘plugging in’’the estimated fixed and random effects along with the relevant X and Z matrices.
We note, in passing, that despite the fact that the assumption of normality for the
random effects is a requirement for PQL, this presents no theoretical bar to utilizing the logit form of the equation. Turner and Firth (2010) devote considerable
effort to designing software for the fitting of such models, and we use their R package for what follows.

An Application
To show the model in action, we now embark on an application using ‘‘standard’’
data and assumptions simply to highlight how (fitted) model interpretation differswith our approach. In what follows, we concentrate on the estimation and interpretation of ‘‘democratic’’ effectiveness, since that has dominated the literature in thisarea. Readers may wonder why we do not consider reestimating an example fromthe literature; the short answer is that the models previously used are sufficiently different from ours—in particular, they use location variables common to both players,which are simply not sensible in our setup (for reasons given in Remark 2)—suchthat a straight replication is not meaningful or helpful.

What We Used: Data
We used the EUGene software program (Bennett and Stam 2000, 2007) to generate a directed dispute data set of Militarized Interstate Disputes (MID; Jones,
Bremer, and Singer 1996), both wars and nonwars, from 1816 to 2001.8 The first
COW/MID data sets were not dyadic in nature, and thus any analysis of dyadic
data prior to that (which is a great deal of the published work in IR and security
studies) must rely on a conversion scheme in order to take pre-1993 data and convert it to dyad (or directed-dyad) form. There are two options for doing so. In thedefault option, the EUGene software performs the conversion (our discussion
focuses on this data set). The second option uses, for pre-1993 data, the Maoz
Dyadic MID data (Maoz 2005), which has a different (and purportedly stricter)

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

14

Journal of Conflict Resolution 00(0)set of criteria for generating pre-1993 dyads (both options use the same data forpost-1993 dyads). Though we focus the bulk of our discussion on the analysis of
the EUGene dyads, we note that the different conversion schemes do not changemuch of the substantive interpretation, and the results are nearly identical for our
findings on the relationship between democracy and effectiveness.
In the data, there is one observation per dispute,9 side A is always the initiator,and for each observation there is a categorical outcome variable coded one throughnine to denote different possible settlements.10 For regime types/Polity scores, we
use the Polity2 variable from the 2010 version of the Polity IV data set (Jaggers andGurr 1995).11 Polity2 scores were introduced in 2002 in order to standardize an
approach to dealing with the ‘‘special codes’’ (66, 77, and 88) that had previously been dealt with in an ad hoc manner.12 Military capabilities data are takenfrom Singer, Bremer, and Stuckey (1972). Diplomatic data were taken from the diplomatic exchange data set (Singer and Small 1966; Bayer 2006).
For our current application, and keeping in line with common practice, we do notuse ‘‘draws’’ as outcomes. We note in passing that several authors have discussed thenature and frequency of draws, and what leaving them out might mean for estimation(e.g., Bennett and Stam 1998; Reiter and Stam 2002; Fortna 2009; Downes 2009).
We refer readers there for further information.13
This leaves us with 929 MID dyads of all levels and 340 war dyads. COW
coding procedures distinguish between ‘‘originators’’ (those countries involvedin the war on day 1) and ‘‘joiners’’ (those states that joined the conflict after
the first day). Again, to make matters simple we treat both groups the same way:
our theoretical framework means that the distinction between joiners and originators is irrelevant. Our goal is to model the relative power or effectiveness ofdifferent states, and not to model their decisions concerning whether to go to
war. Whether the decision to join an ongoing war is different from a decision
to initiate one (we believe it probably is) does not matter so much as the factthat in each case there is a contest between two players, and that contest tells
us something about each player’s relative abilities. We refer readers to extensive
debates on this subject elsewhere rather than offer a redux in this article (see,e.g., Downes 2009).14
By including MIDs, we are not implying that interstate wars are in any way similar to the types of disputes that are picked up by the MIDs database. MIDs themselves represent a broad spectrum of conflict, from fishing and trade disputes tocrises, to violent conflict that falls just below the threshold of war. Thus, evenamong the MIDs, there is likely to be great variation in the dynamics at hand.
Which states, and which types of states, win these disputes may not tell us muchabout the ability to prevail in interstate wars (we would not make that inferential
leap), but—given our theoretical framework—each dispute should still be thoughtof as a contest between two actors which can tell us something about the relative
abilities of the two players. With that in mind, we fit models to both wars and more
limited disputes next.

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

Renshon and Spirling

15

What We Found: Fit
Before turning to the substantive findings, we first note the relative advantage of the
Bradley–Terry method in terms of model fit over ‘‘monadic’’ designs.15 A seemingly
natural method for such a comparison is via some metric that considers the value of the(log) likelihood, and penalizes by parameter number. Unfortunately, however the relevant regressions are constructed, monadic and dyadic approaches use observations(the Y) that are fundamentally different in nature and number. In any case, with random effects in place, the Bradley–Terry GLMM has no available (log) likelihood andthus model fit procedures relying on the deviance cannot be used. For both these reasons then, we cannot rely on measures such as the AIC or BIC, at least for the models
that uses random effects. Subject the caveats noted, we can report the AIC for themodel without random effects relative to the usual logit, and the Bradley–Terry
approach clearly does better: its AIC is less than half the value of the logit for the wars
and nonwars specification.
For a more complete picture of model fit, we consider the proportion of cases
correctly predicted by the relevant fitted models. The dyadic case is as describedin the previous sections in the sense that, for each country party to a conflict, we
model logit Prðvictory Þ ¼ X b; where the Xs entering the likelihood for a given
observation refer only to one country. Our specific interest is the fraction ofobservations for which the models predict that Prði winsÞ > 0:5 where i is thetrue winner in the data. Note that the independent variables are the same in every
case and correspond with those in the coefficient tables we introduce shortly. We
fit a Bradley–Terry model without random effects (77 percent correctly predicted
for the war model) as given in equation (9); a Bradley–Terry model with random
effects (88 percent) as given in equation (11); a monadic logit model (73 percent);
and finally, a monadic logit model where the predictions are subject to a straightforward ‘‘sensibleness’’ restriction (28 percent). In the latter case, we only countas a ‘‘correct’’ forecast those cases where the relevant i is predicted to have won,
and the relevant j is predicted to have lost. Without this restriction, the logit isable to predict a win (or loss) for both states involved in a particular dispute,which is impossible given the actual data. Perhaps unsurprisingly, the Bradley–
Terry approach with random effects (our choice in the following) outperforms theother models. For the nonwars, our results are similar with the percentage correctly predicted, respectively, being 76 percent, 83 percent, 75 percent, and 33
percent. The full table is given in Table 2.
To clarify our procedure here, and to recap our methodology section above, recall
that predictions for the mixed model are based on ‘‘plugging in’’ the BLUPs of the^ fixed effects along with their relevant covariate matrices.
random effects and the bThis is not the case for our figures that follow, however: here, we simply use thefixed effects, taking the random effects as zero. This means that we are plotting predictions for an ‘‘average’’ initiating player with the relevant Polity score versus an‘‘average’’ noninitiating player (and its Polity score). So, while the predicted

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

16

Journal of Conflict Resolution 00(0)Table 2. Proportion Correctly Predicted, BT Model versus Monadic Logit for Different War
and Nonwar Data Sets.

Wars
Nonwar(MID < 5)BT model, no
random effectBT, random
effect0.774
AIC¼ 275.717
0.760

0.878
0.829

AIC ¼ 551.208

Logit (logic
restriction)

Logit
0.726
AIC ¼ 649.090
0.749

0.278
0.329

AIC ¼ 1191.767

Note: AIC ¼ Akaike Information Criterion; MID ¼ Militarized Interstate Disputes.

Table 3. Results: Bradley–Terry Models.
EUGene dyads
Wars(Model 1)

Nonwars(Model 2)

Maoz dyads
Wars(Model 3)

Nonwars(Model 4)

Polity0.173 (0.119) 0.322* (0.07) 0.108 (0.138) 0.351*** (0.084)(continuous)
Polity  Initiation
0.036 (0.044) 0.055* (0.025)
0.113* (0.057)
0.051 (0.033)
0.026* (0.012) 0.023* (0.008)
0.009 (0.015) 0.027** (0.010)
Polity2Major power
1.165* (0.524) 0.035 (0.373)
0.483 (0.603)
0.117 (0.434)
Diplomacy score 2.201 (1.22)
0.825 (0.848) 2.557 (1.418)
1.728 (1.012)
Dyadic capability 0.207 (0.553)
0.895* (0.361)
0.736 (0.622)
0.229 (0.454)
ratio
Region 2
1.752 (0.964) 1.055* (0.614)
0.741 (0.766)
1.331 (0.698)
Region 3
2.423 (2.423)
0.507 (0.948)
31.37 (>100)
0.692 (1.252)
Region 4
0.529 (0.815) 1.027* (0.616)
0.279 (0.956)
1.359 (0.782)
Region 5
1.816* (0.901)
0.009 (0.486) 1.178 (1.014)
1.114 (0.652)
Initiation
0.235 (0.234)
0.725* (0.135) 1.354*** (0.289)
2.314*** (0.196)
Random effect
1.112* (0.222)
0.824* (0.151)
0.718 (0.252) 1.2256*** (0.189)
SD
n
279
538
147
605
^ ) p < :05, b^ ) p < :01, b^ ) p < :001:
Note: bprobabilities for the model fit are based on specific cases in the data, the graphics are
based on general (predicted) patterns of conflict.

What We Found: Overview
Here we focus on control variables that have been used in other recent quantitative
analyses of international conflict (see, e.g., Danilovic 2001; Reiter 2001; Hegre2008). Table 3 reports our estimates for two subsets, interstate wars16 and conflicts

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

Renshon and Spirling

17

that fall below the level of war (non wars), as well as for the two sources of data
(EUGene dyads and Maoz dyads).17 All variables represent the difference between
the relevant covariate for i and j, as implied by equation (10). Thus, Polity for i is
simply its Polity2 score as taken from the Polity Data set (where it ranges from
10 to þ10), while Polity in the results table should be interpreted as the effectof a one-unit increase in i’s score relative to j, with the caveat—explained later—that
we need to be careful both with interactions and with the sign of the resulting difference between the states.18 The quadratic term, Polity2, is the state’s absolute polity
value multiplied by its signed polity value such that the original direction is preserved: thus, a Polity of 3 corresponds to a Polity2 of 9. This variable gives us
a sense of possible increasing or decreasing ‘‘returns to scale’’ for democraticness:for example, it may be that being democratic is helpful for effectiveness and that
more democratic countries are disproportionately better off. Major Power is a binary
variable indicating whether or not a state is a major power as defined by the COW
data set. Its ‘‘effect’’ should be interpreted as the effect of increasing i’s score by one
unit (or in other words, turning it into a major power) relative to j. Diplomacy scores
are the proportion of states in the system that have sent diplomatic representatives toa given country in a given year (e.g., 1 if all countries have sent representatives, 0.5
if half have sent representatives). Here, it is the difference between i and j’s diplomacy scores. Dyadic capability ratio is the difference between i and j’s capability
ratio (where i’s share of the total dyadic capabilities is CINCi =ðCINCi þ CINCj Þ.
Region variables are dummy variables that denote where a country is located (asper COW: Europe ¼ 1, Middle East ¼ 2, Africa ¼ 3, Asia ¼ 4, North and SouthAmerica ¼ 5). Region 1 is the ‘‘base category’’ in this model (so, regions are ‘‘factors’’ from the point of view of taking a difference between covariates). Initiation
indicates whether or not i initiated the conflict or dispute.
Recall that the justification for using the difference between i’s and j’s covariate values (for Polity, Major Power, Diplomacy, etc.) is as given in How It
Differs from Previous Approaches section: that this is the only way that thelogit equation can make sense as written. That is, to the extent that states havelatent abilities and to the extent that the functional form we have given is theone implied when scholars typically think about interstate interactions—or is areasonable approximation to it—we need to use differences rather than sums
here.
Interpreting the coefficients is an operation similar in nature and complexity
to that in the conventional logit or probit case. As in those scenarios, coefficientsigns imply direction, as regard the relationship between that variable and theprobability of a state winning an interaction it is involved in (all else equal).
^ tell us how the log odds of victory for country i change
More specifically, the bs
as we increase the relevant X by one unit. This is exactly as suggested by equawins Þtion (10), where the log PrðiPrðj wins Þ is a (linear) function of the difference between
i’s and j’s covariate values.

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

18

Journal of Conflict Resolution 00(0)Democratic ‘‘Effectiveness’’?
In line with the democratic effectiveness literature we cited earlier, we first turn ourattention to the potential link between a country’s Polity score and its overall military effectiveness. For our sample of wars, the estimate for Polity is negative(0.173), but not statistically significant. Moreover, using the Maoz data, with its
stricter criteria for dyads, generated almost identical results (0.108), suggestingthat this is not simply a matter of ‘‘what observations count.’’ In the following paragraphs, we explain how this estimate should be interpreted.
Holding all other variables constant, a one-unit increase in Polity corresponds to a
one-unit increase in the difference between two states. This follows from our earlier
equations, in the sense that the interest is in bðxi  xj Þ. Given this difference formula,an increase of one unit can occur via an decrease in xj (fixing xi ) or an increase in xi(fixing xj ) or some combination thereof. An extra subtlety is added by the fact thatthe original values of xi and xj affect our interpretation of the effect on the log odds.
Suppose, for example, that xi > 0 (i is at least slightly democratic), and that xj > 0
too, but that xi < xj . In this case, a positive coefficient will be multiplied by apositive difference and the effect of a one-unit increase is to raise the log odds ofa victory for i. This is not necessarily true, however, if xj > xi . Now a one-unit
increase in the difference may still be a part of a negative difference, in which casea positive coefficient will act on that negative covariate and we will decrease the log
odds of a victory for i. This could happen, for example, in the case where i’s Polity
score is 5, but xj ¼ 6. Now the difference is 5  6 ¼ 11, meaning that a oneunit increase still leaves a negative difference with commensurate effects on the log
odds of victory.
Furthermore, an increase in Polity will affect the log odds of a victory via several
coefficients: Polity itself, of course, but also the (absolute) quadratic version of thesame term, plus the interaction with initiation, and initiation status per se. To makematters stark, consider a country which initiates and for which xi > xj after the oneunit increase; for a one-unit change in Polity, the effect on the log odds is
bPolity þ bPolityInitiate þ bPolity2 þ bInitiate ¼ 0:173 þ 0:036 þ 0:026  0:235 ¼ 0:346.
In words, the negative sign implies the state is more likely to lose as it become moredemocratic. If the state is a noninitiator, the effect of a one-unit increase in its Polity
score is 0.147: still negative, and implying that more democratic states are notbetter off (i.e., the effect is not simply driven by initiation status).
What of nonwars? Here, our conclusions are somewhat different. For nonwars,
we find strong evidence for a democratic advantage: Polity has a positive and statistically significant effect on effectiveness using both the EUGene (0.322*) and Maoz
(0.351***) data. Suppose, again, that we increase the Polity difference by one for
initiators, and consider the effect on the log odds of a victory for a situation wherexi > xj . We have bPolity þ bPolityInitiate þ bPolity2 þ bInitiate ¼ 0:322 þ 0:055þ
0:026 þ 0:725 ¼ 0:966: a positive result, suggesting more democratic countries

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

Renshon and Spirling

19

–10

–5

0

10

5

0.8

0.6

0.4

0.2

state 1

0

5

10

–5
state 2

–10

Figure 1. Wars.
Note: Effect of Polity score on the probability that state i wins the conflict. Unfilled (red) surface has i astarget (and j as initiator), filled (blue) surface has i as initiator. Note that the surfaces are not monotonic inincreasing democraticness for either i or j. Vertical axis is the relevant probability of victory for i, the axis
emerging from the page refers to i’s Polity score. Horizontal axis moving from 10 to 10 left to right is j’s
Polity score.

are generally more likely to win. Note that when we remove the initiator status, thislog odds effect shrinks back to 0.296, though it is still positive.
As suggested, these results are not ‘‘cut-and-dried,’’ because they depend on
differences. In Figures 1 and 2, we display the consequences of this point for wars
and nonwars, respectively, in graphical form. There, the (red) unfilled surfaces
refer to the probability of winning contingent on not initiating, while the (blue)
filled surface correspond to the probability when initiating. Importantly, the nonvertical axes refer to Polity scores, and it can clearly be seen that the relationshipbetween democraticness and effectiveness is nonmonotonic. For some ranges,
more democratic states are more likely to win, but for others they are less likely.
For example, in the wars case, Figure 1 shows that if we fix state 2 (i.e., state j) at a
Polity of around 5, and move state 1 (i.e., state i) from 5 to zero on the Polity
scale, state i’s probability of winning is actually slightly decreasing: implying adecreasing return to democraticness. Elsewhere, for example, fixing j in the sameplace, but increasing i’s score from 5 to 10, we see a steep increase in the

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

20

Journal of Conflict Resolution 00(0)

–10

–5

0

5

10

0.7
0.6
0.5
0.4
0.3
0.2
0.1
10
5
0
–5
–10

state 1state 2

Figure 2. Nonwars.
Note: Effect of Polity score on the probability that state i wins the conflict. Unfilled (red) surface has i astarget (and j as initiator) and filled (blue) surface has i as initiator. Note that the surfaces are not monotonic
in increasing democraticness for either i or j. Vertical axis is the relevant probability of victory for i, the axis
emerging from the page refers to i’s Polity score. Horizontal axis moving from 10 to 10 left to right is j’s
Polity score.

probability that i wins. The story from Figure 2 is similarly subtle, though not quite
as complicated. Here, for a wide central swath of democraticness for i, increasing
j’s Polity score makes i less likely to win. But this is not true everywhere: for very
undemocratic and very democratic j values, increasing j’s democraticness actually
makes it less likely to win against i.
As detailed in earlier sections, our model and our data are set up in a manner different enough from previous work (on democratic effectiveness) that a direct comparison would be more misleading than illuminating. However, it is reasonable tospeculate for a moment on how our findings fit with the conventional wisdom that

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

Renshon and Spirling

21

link democracy and military effectiveness. We noted above that research on thisquestion had been divided into two broad schools: democratic triumphalists (whobelieve that, either through skillful selection or material capabilities, democracy
boosts military effectiveness) and skeptics (who are unconvinced by the evidence
for a democratic advantage). Our results are mixed: for some ranges, for some conflict types, democraticness is associated with advantages, but for some it is not. This(partially) corroborates the ‘‘swoosh’’ pattern found by Reiter and Stam (1998b,
387) in their related analysis of the Pr(initiator wins) at different levels of Polity.
We see this as providing further evidence of the nonlinear relationship between
Polity and effectiveness in war (and counter to the claim of Downes in Reiter, Stam,and Downes 2009). Similarly, the curvilinear relationship between democraticness
and victory underscore the heterogeneity among autocratic regimes (see Weeks 2008).
With this in mind, we cannot unequivocally support the arguments of democratic
triumphalists: it is not the case that increasing democraticness is always associatedwith higher probabilities of winning wars. However, we do find more consistent(though by no means completely consistent) evidence for a democratic advantage
in nonwars, which corroborates the one other effort (of which we are aware) toinvestigate democratic effectiveness in a context other than major interstate wars
(Gelpi and Griesdorf 2001).
Thus, on the one large question that drives much of this research—are democracies better at fighting?—our answer is yes, in some cases. On the many other methodological issues that separate triumphalists and skeptics (such whether a particularcountry really initiated a conflict), we remain agnostic. The passage of time is likely
to give us more, and more accurate data to work with, but that will not change ourargument that the method detailed in this article is the correct way to estimate effectiveness based on contest data.
We return to the specific issue of initiation next. The rest of our variables were
essentially controls, and we can deal with them relatively quickly here: major powers are (significantly) more effective in wars, and less so (not significantly) in nonwars. States with greater diplomatic status do worse in both scenarios, though notsignificantly. States with a greater share of the capability ratio do significantly betterin nonwars, but this seems not to help in wars. Finally, countries in region 5, Northand South America (relative to those from Europe) are significantly better off inwars, while countries from Asia and the Middle East (relative to those from Europe)
are worse off. To round out this section, we note that unsurprisingly, both sets of random effects were significant. This implies that there are, indeed, correlations in performance across contests involving the same states.

Initiation: Findings
Notice that this setup allows us to properly estimate the effect of initiating a war.
This is, we believe, the first ‘‘clean’’ estimate of the value of moving first in war andhelps to shed light on a question of substantial interest to IR scholars (see, e.g., Jervis

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

22

Journal of Conflict Resolution 00(0)1978; Fearon 1997; Van Evera 1998): has offense been dominant in modern political
history? Previous works have debated the answer to this question for different periods, but substantial difficulties remain since it is often difficult to come to an agreement on whether a specific technological advance favors offense or defense.
Figure 1 illustrates more clearly the pattern we observe in the regression results inTable 3, namely that there is no evidence of an ‘‘initiation’’ effect in wars. That is,moving first in wars provides no advantage to initiators in our model. If anything, thepattern depicted in Figure 1—specifically that the unfilled (red) lattice surface is above
the filled (blue) surface for almost every value of Polity for both i and j—is suggestiveof the reverse: that initiating wars carries with it a disadvantage. However, we caution
against overinterpretation here, as the same model applied to the Maoz dyadic data
yielded conflicting findings. In that model, initiation was positively associated withvictory in wars. When divergent findings such as this emerge, one positive benefit
is in spurring future research designed to further sharpen our understanding.
With that in mind, we note (speculatively) that the findings in model 1 related toinitiation do fit well with extant theories of initiation dynamics. For example, Nevin(1996) finds that war outcomes influence future decisions to initiate such that winning makes states more likely to initiate in the future, while losing makes them lesslikely to do so. This seems likely to lead to overconfidence, such that an easy victoryin the past may embolden leaders to make more risk-seeking decisions. This finding
also dovetails with that of Geller (2000), who found that initiators were equally
likely to be superior or inferior in capabilities relative to their opponents.
Intriguingly, the results for nonwars are substantially different from those forwars. These, shown for models 2 and 4 in Table 3 and then depicted in Figure 2 show
clear evidence of an ‘‘initiation effect.’’ In contrast to the results for war, in nonwars
it is obvious that the filled (blue) surface is substantially higher on the y-axis than is
the unfilled (red) surface. The gap between these two lattice surfaces represents thedifference between initiating and not initiating. The higher y values for initiatingsuggest that doing so is associated with a higher probability of victory. Critically,
the same result emerges using the Maoz data as well, suggesting once again that thisresult is not sensitive to different specification of dyads.
Why does initiation increase the likelihood of victories for disputes short of war, but
provide no discernible advantage for initiators in wars? One possible explanation lies withthe different dynamics and incentives that states face in the two contexts. For example, aquick glance at the data reveals that many disputes that fall short of war occur between
allies (the United States and Canada, e.g., have ‘‘fought’’ in six disputes since 1974). The
lack of any true threat between the disputants in such cases lends itself to a higher likelihood of conciliatory bargaining since better relations between the states both makes
issue linkage easier (‘‘if you give in on issue x, we will give you what you want on issuey’’) and allows the states to trust that their concessions will be reciprocated over time.
Similarly, the stakes involved in disputes that fall short of war are almost certain to belower than those that are involved in wars, so states might find it easier to concede a dispute than they would be to concede the issue that is the cause of an interstate war.

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

Renshon and Spirling

23

Table 4. Table Comparing Some Selected Predicted Probabilities for ‘‘Vanilla’’ Logit andBT Model.
Year

Conflict

State
1

State
2

1843
1853
1876
1896
1912
1939
1940
1940
1940
1944
1944
1944
1964
1964
1964
1974
1977
1977
1990
1990

Mexican American War
USA
Crimean War
TURFirst Central American War
GUA
Greco-Turkish War
TURFirst Balkan War
BULWorld War II
GMY
World War II
GRCWorld War II
GRCWorld War II
FRNWorld War II
FRNWorld War II
FRNWorld War II
BRA
Vietnam War
DRV
Vietnam War
CHN
Vietnam War
RUS
Cyprus War
TUR
Ethiopian–Somalian Ogaden War CUB
Ethiopian–Somalian Ogaden War ETH
Persian Gulf War
SAU
Persian Gulf War
SAU

MEX
RUS
SAL
GRC
TUR
FRN
FRN
ITA
ITA
GMY
JPN
FIN
USA
USA
USA
CYP
SOM
SOM
IRQ
JOR

Logit probability BT probability(state 1)(state 1)
0.236
0.160
0.178
0.184
0.138
0.184
0.129
0.132
0.183
0.145
0.151
0.240
0.070
0.082
0.086
0.212
0.232
0.234
0.137
0.167

0.515
0.157
0.315
0.030
0.517
0.113
0.244
0.210
0.243
0.148
0.100
0.530
0.018
0.062
0.056
0.150
0.466
0.575
0.636
0.322

Note: In every case, state 1 ‘‘won’’ the conflict in practice, and we present the predicted probability of thisoutcome from the two models. Boldface values indicate the more accurate prediction.

Comparing Models
Given these distinctive findings, we wanted more information on what—that is,which conflicts—drive it relative to the ‘‘vanilla’’ logit approach. To that end, we
looked at the twenty ‘‘worst-case’’ scenarios for the usual logit: in particular, tencases where the logit predicted a loss, but the state actually won, and ten cases where
the model predicted a win, but the state actually lost. We then compared the Bradley–Terry predictions (without random effects, to keep the models relatively similar)
to those from the usual procedure. Table 4 contains the results of that analysis, andwe present everything in ‘‘probability that actual winner won’’ form to make things
easily comparable (recall, these are two-sided contests, but the logit treats them as‘‘one sided’’). One interesting pattern emerges from this. The BT model does bettermore often (twelve times of the twenty) than does the ‘‘vanilla’’ logit model, but
simply counting correct predictions understates the higher accuracy of the BTmodel. For the twelve predicted better by the BT model, they were better by an average of 0.21, while for the eight cases for which the logit model made better predictions, its predictions were better by only .06 on average. In other words, for cases

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

Journal of Conflict Resolution 00(0)

0.2

0.4

0.6

0.8

logit better (27%)

BT better (73%)

0.0

abs deviation from Y [BT]

1.0

24

0.2

0.4

0.6

0.8

abs deviation from Y [logit]

Figure 3. Relative performance of the logit and Bradley–Terry models across full (wars) data set.
Note: Points below the lines are where the Bradley–Terry model does better in terms of its predictedprobability relative to y. Points above the line are areas where the logit does better.

where the logit model was ‘‘better,’’ it was not better by much, whereas when the BTmodel out performs the logit model, its predictions are much better.
So, where does the BT model do better than logit? One obvious pattern isthe overrepresentation of large, multilateral wars in this table: Crimean War, First
Balkan War, World War II, Vietnam War, and Persian Gulf dyads account for fourteenof the twenty worst predictions of the logit model. This bears out the warnings of Poast(2010) and Valeriano and Vasquez (2010) that more flexible methods may be better suited to analyzing this very specific subset of wars (though we note that even under thesevery difficult conditions, the BT model generally performs significantly better than acomparable logit model). The BT model also does significantly better in the Persian Gulf
War, which involves several nondemocracies. Here, it is likely that the ability of the BTmodel to take differences in democraticness into account aids in its predictive power.
Although we may be able to draw substantive insight on model performance forparticular conflicts from Table 4, it is helpful to see the larger picture of relative estimation accuracy. In Figure 3, we present a plot that does just this. There, every point
represents one side of a conflict. The x-axis represents the predictive accuracy ofthe logit model, in terms of the deviation from the ‘‘truth’’ of the predicted probability produced by that model for that side of the conflict. The ‘‘truth’’ is whatevervalue the dependent variable took in practice. Thus, if a state won a conflict, andthe logit predicts they won it with probability .63, the deviation is calculated as
1  :63 ¼ :37. The y-axis is the same deviation, but from the point of view of the
Bradley–Terry model. So, any (blue, circle) points falling below the 45 line arecases where the Bradley–Terry model is doing better than the logit; any (red triangle) points falling above the 45 line are cases where the logit model does better.

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

Renshon and Spirling25

As can be readily seen, there are many more points below the line: indeed, some 73
percent of the observations are better predicted by the Bradley–Terry approach;moreover, where it predicts well, the Bradley–Terry model does much better thanthe logit—this can be seen by the ‘‘piling up’’ of the points at the bottom left of theplot, implying very little prediction error for that model.

Discussion
The foregoing article set out a statistical model of ‘‘effectiveness’’ in IR, and did so fromfirst principles of states with latent abilities that are revealed from the contests they win
or lose. We allowed for random effects (thus avoiding the error of overattributing effects
to variables of interest) and showed how researchers might naturally account for the relevant characteristics of both players in a dispute. We also showed that, in model fit
terms, the BT model outperforms more traditional options in predicting war outcomes.
The key innovation, though, is that this model asks the ‘‘right’’ question of conflict data—in particular, ‘‘what factors make states more likely to win wars’’—anddoes so in a way that has a sensible interpretation in terms of underlying (but unobserved) ‘‘abilities.’’ We make no claims that we have radically overturned previous
findings in this area: democracy still matters, though perhaps in more subtle ways
than previously thought. But what is new is that our estimates can be related backto a sensible model of the data generating process and interpreted in that light. Whatis also new is the flexibility and generality of the model, and we hope that researchers will find its introduction here helpful.
Substantive findings are of course intertwined with empirical strategies, andbecause our approach freed us from conditioning the results on initiation status,
we were able to provide a ‘‘clean’’ estimate of an initiation effect. We found strong
evidence that moving first was associated with a significantly higher likelihood of
victory in nonwars. However, we found that initiation effects for wars were highly
sensitive to how one constructed the data set, whether using EUGene or Maoz codings. This has relevance both for traditional IR debates on whether or not offense or
defense is ‘‘dominant,’’ but for contemporary foreign policy debates as well. However, as is often the case, answering one question (Does ‘‘moving first’’ provide anadvantage in lower-level disputes?) generates numerous additional research topics.
In this case, we provided evidence that initiation matters for nonwars, but how it
affects war outcomes remains an open question. Additionally, we did not fully
explore why this is the case. Some previous work (e.g., Betts 1982) has suggested
that the surprise itself is what contributes to a high probability of victory. After all,an unexpected first strike that devastates the opposition should logically contributeto a higher likelihood of winning. However, it might also be the case that smart leaders simply select lower-level conflicts that they are likely to win (with or without theadvantage of surprise). Notice that these theories are not mutually exclusive, andmore evidence is needed (on everything from leaders’ beliefs about relative capabilities to more granular data on surprise attacks ) in order to assess the relative merit ofDownloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

26

Journal of Conflict Resolution 00(0)the two explanations as well as the empirical observation that we do not find evidence for a strong ‘‘initiation effect’’ in interstate wars.
What is next for this approach? Earlier, we had little to say about a possible ‘‘selection stage’’ in conflicts. That is, it may well be the case that certain characteristics ofstates see them (strategically) initiate wars with one another, while a (possibly different) set of covariates determines the outcomes of those conflicts. It has been the latterstage that this note has sought to model. Future work might consider the ramificationsof selection effects—especially with respect to bias in the sense of Heckman (1979)—
and how scholars might deal with such concerns. In the Appendix we give some speculative comments specifically on these issues. All in all, there is much still to do, but
we think we have a provided a fruitful new avenue for this line of research.

Appendix
Bradley–Terry Models, Selection, and Selection Bias
One way to conceive of the data generating process is that states are randomly pairedwith others (i.e., the pairings are not dependent on the various characteristics thestates possess) and that a contest takes place as soon as one of the states initiates.
In this scenario, there is no selection bias in the estimation of the abilities.
An obvious concern is that the contests are, in fact, not exogenous. Instead,
there is a selection stage in which states choose (in the sense that they attack)another state with whom to fight and then an outcome stage in which the relevant
winner or loser is determined. To keep matters simple, suppose that a given state
can choose at any time to attack any other: what, if any, bias might we expect? In
this case, we are in a situation akin to that of Heckman (1979), albeit with binary
outcomes at both stages (see Dubin and Rivers [1990], for discussion of fitting
such models: we use their notation shown below).19 For the selection equation,
we might represent matters asy1i ¼ b1 ðxi  xj Þ þ e1i :Here, the decision by i to attack (initiate) against j is partly due to (the difference
between) i’s and j’s observed covariates, and partly due to some other unmeasured
variables and residing in the error term e1i .20 As written, y1i is latent, and we would
let y1i ¼ 1 if y1i > 0 and be zero otherwise. One interpretation of this scenario isthat i attacks if he expects to win. The outcome equation may be specified in asimilar way.
y2i ¼ b2 ðxi  xj Þ þ e2i ;where, this time, the outcome of victory or defeat for i is a function of the covariate
differences between him and j and some error term. In the preceding article, it isfrom a variant of this second equation that we have sought to estimate the abilitiesof the states in our data. To make clear the potential for bias, suppose that one

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

Renshon and Spirling27

component of e1i is having a ‘‘clever leader’’—someone who is good at picking
relatively weak states to prey on—whether that leader be democratic or a dictator.
Suppose, in addition, that the interest is the effectiveness of democracies in the outcome equation and that we expect more democratic countries to be better at fighting
wars. The problem is that states with ‘‘big’’ errors (clever leaders) end up winningconflicts along with more democratic states who are also good at fighting wars. As aresult, if democracy does aid fighting effectiveness, our estimate of its contribution
to ability is biased down. Generally speaking, the larger the effect that the unmeasured variable (clever leader) has on selection and the higher the correlation between
the error terms, the worse this selection bias becomes.
Under what circumstances would this potential bias not be a problem? First, if theunmeasured variables in the selection equation—for us, ‘‘clever leader’’—are uncorrelated with the unmeasured factors influencing victory in the outcome equation. This
seems admittedly unlikely: surely a leader good at picking fights is good at winning themtoo. Second, if all factors that determine selection (here, initiation) are controlled for in theoutcome equation. Again, this seems unlikely for the simple reason that some things are
simply impossible to measure or observe, especially for international relations data sets.
Where does this logic leave the merits of the Bradley–Terry model presented in thisarticle? First, one can choose to buy in to the somewhat heroic assumptions that meanpotential bias may be ignored. These are the assumptions generally maintained in theeffectiveness literature that was our jumping off point for this article.21 Second, andmore importantly, our claim here is that the Bradley–Terry model is the right choicefor the modeling of the outcome equation: it estimates the right thing (abilities) in theright way (as a function of differenced covariate values). We accept that estimates may
be biased, but we are now at least focusing on the correct estimand.
Acknowledgments
We gratefully acknowledge comments from Iain Johnston, Gary King, Vipin Narang, Jane
Vaynman, and the audiences at both the IQSS Applied Statistics and Security Studies workshops. Two anonymous referees and the editor provided us with helpful guidance on both content and structure.

Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding
The author(s) received no financial support for the research, authorship, and/or publication ofthis article.

Notes
1. In economics as well, see the (theoretical) literature on ‘‘contest success functions’’(Hirshleifer 2000).

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

28

Journal of Conflict Resolution 00(0)2. This does not mean that every state meets every other in a conflict, simply that no twostates are in conflict of which neither party meets any other. So, if there are three states
A, B, and C, and A fights B and B fights C, we do not need A to also fight C. However, if
there were four states and A fights B only, while C fights D only, we do not have a ‘‘connected’’ design: we have no way to compare the two sets of conflicts since they do nothave a common player.
3. Note that while IR scholars typically use the term ‘‘latent capabilities’’ to refer to industrial capacity (and thus power that has not yet been brought to bear in a military conflict,but could be; see Walt 1985; Mearsheimer 2001), we use ‘‘latent abilities’’ in its morenarrow sense: as an unobserved quality inferred through the observation of data that aremeasurable (here, contest outcomes).
4. This ‘‘better-ness’’ might well be something difficult to measure, such as ‘‘more
advanced strategy’’ or ‘‘more experienced Admirals,’’ but in principle, that somethingis still a characteristic of the state (and not the conflict itself).
5. We are assuming we wish to know how effective the United States is ‘‘overall’’ (and whatthat depends on, in terms of predictors) rather than the effectiveness of the ‘‘US at sea’’ orthe ‘‘US on land.’’
6. Recall that logit pij ¼ logðpij Þ  logðpji Þ and logit pji ¼ logðpji Þ  logðpij Þ.
7. We mean ‘‘contest-specific’’ in the sense that some state covariate varies by contest, notthat the contest itself is exerting a particular effect.
8. Thus, one significant difference between our data and that of previous works (over andabove the already discussed difference in the structure of the data) is the temporal scope.
Reiter and Stam (1998b) contains 197 observations (remember, they count each countryin each conflict as one observation), beginning in 1823 with the Franco-Spanish War, andending in 1982 with the Lebanon War between Israel and Syria. Reiter, Stam, andDownes (2009) and Downes (2009) both contain 234 observations of wars, beginningin 1823 with the Franco-Spanish war, and ending with the Second Sino-Vietnamese War,which took place from 1985 to 1987.
9. Thus, multilateral wars (such as World War I and II [WWI and WWII, respectively]) aredecomposed into several dyads each. Although we agree with Valeriano and Vasquez(2010) that these ‘‘complex’’ wars are in many ways different than wars involving only
one dyad, we note only that they can still be thought of as contests in which the outcome
can provide information about relative abilities. Poast (2010) similarly notes several
potential problems that arise from using dyadic data to analyze ‘‘k-adic’’ events. A multilateral Bradley–Terry model is a possible avenue for future research.
10. After generating the data set from EUGene, we modified our data set to match it as closely
as possible to that used by Reiter and Stam (1998b), and the rest of the literature on democratic effectiveness. In practice, this simply meant correcting some obvious coding errors
in COW, such as changing Germany to the initiator in the Germany–Poland dyad in 1939
and changing the United States to the winner of the United States–Japan dyad in WWII.
11. Polity scores vary from 10 to þ10. Generally, scores above þ7 are considered democracies, below 7 are considered autocracies, and those in the middle are considered‘‘anocracies’’ or mixed regimes.

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

Renshon and Spirling29

12. More specifically, the Polity2 variable converts: 66 (foreign interruption) to ‘‘system
missing’’; 77 (interregnum or anarchy) to a neutral score of 0 and 88 (transition) codes
are prorated across the spans of the transition. For more information on this, see the Polity
IV Project Codebook.
13. Dealing with draws in the Bradley–Terry model is not impossible, though, it involves anextension of the method; Rao and Kupper (1967) and Davidson (1970) consider such an
approach, though, interestingly, Turner and Firth (2010) find that simply treating a tie as‘‘half a win’’ works well in practice.
14. However, excluding joiners from the nonwars or wars þ nonwars models does not change
the results presented below relating to Polity and initiation. Restricting joiners from thewars-only model yields too few observations to make any meaningful inferences.
15. Again, our specific discussion here applies to models 1 and 2, the EUGene-created dyadic
data, but results are similar for the Maoz data as well.
16. Following the traditional definition from the Correlates of War project: conflicts in which
there were at least 1,000 battle-related fatalities; that is, conflicts in which the cwhostd or
mzhostd variable is equal to 5.
17. In general, our analysis distinguishes between wars and nonwars. However, including MID
level 4 (use of force) observations along with MIDs at level 5 (wars) to create a sample of‘‘violent conflicts’’ does not affect estimates for our main variable of interest, Polity.
18. We acknowledge that many previous accounts focus on a binary Democracy variable.
However, much recent research uses a continuous measure and we follow that lead here(see, e.g., Oneal and Russett 1997; Elkins 2000; Bennett 2006).
19. See also Freedman and Sekhon (2010) for discussion of options for fitting specifically forthe probit case.
20. As in the material, this might be a difference in error terms, but we write it as one term
here for notational clarity.
21. We fully acknowledge the increasingly large literature that takes selection (e.g., Reed
2000) and strategy (e.g., Signorino 1999) seriously in IR, but note that this has not, to ourknowledge been applied to abilities estimation per se.

References
Bayer, R. 2006. ‘‘Diplomatic Exchange Data Set, v2006.’’ http://www.correlatesofwar.org/
COW2%20Data/Diplomatic/Diplomatic.html.
Bennett, D. 2006. ‘‘Toward a Continuous Specification of the Democracy–Autocracy
Connection.’’ International Studies Quarterly 50 (2): 313-38.
Bennett, D., and A. Stam. 1998. ‘‘The Declining Advantages of Democracy: A Combined
Model of War Outcomes and Duration.’’ Journal of Conflict Resolution 42 (3): 344-66.
Bennett, D. S., and A. C. Stam. 2000. ‘‘EUGene: A Conceptual Manual.’’ International Interactions 26:179-204. http://www.eugenesoftware.org/documentation.asp
Bennett, D. S., and A. C. Stam. 2007. ‘‘EUGene Documentation.’’Berry, W., J. DeMeritt, and J. Esaarey. 2010. ‘‘Testing for Interaction in Binary Logit and Probit
Models: Is a Product Term Essential?’’ American Journal of Political Science 54 (1): 248-66.

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

30

Journal of Conflict Resolution 00(0)Betts, R. 1982. Surprise Attack: Lessons for Defense Planning. Washington, DC: Brookings
Institution Press.
Biddle, S., and S. Long. 2004. ‘‘Democracy and Military Effectiveness: A Deeper Look.’’
Journal of Conflict Resolution 48 (4): 525-46.
Bradley, R., and M. Terry. 1952. ‘‘Rank Analysis of Incomplete Block Designs, I. The
Method of Paired Comparisons.’’ Biometrika 39:324-45.
Breslow, N., and D. Claytyon. 1993. ‘‘Approximate Inference in Generalized Linear Mixed
Models.’’ Journal of the American Statistical Association 88:9-25.
Bueno de Mesquita, B., J. Morrow, R. Siverson, and A. Smith. 1999. ‘‘An Institutional Explanation of the Democratic Peace.’’ American Political Science Review 93 (4): 791-807.
Cannizzo, C. 1980. ‘‘The Costs of Combat: Death, Duration, and Defeat.’’ In The Correlatesof War II: Testing Some RealPolitik Models, edited by J. David Singer, 233-57. New York:Free Press.
Carrubba, C., A. Yuen, and C. Zorn. 2007. ‘‘In Defense of Comparative Statics: Specifying
Empirical Tests of Models of Strategic Interaction.’’ Political Analysis 15 (4): 465-82.
Carter, D. 2010. ‘‘The Strategy of Territorial Conflict.’’ American Journal of Political Science
54 (4): 969-87.
Danilovic, V. 2001. ‘‘The Sources of Threat Credibility in Extended Deterrence.’’ Journal ofConflict Resolution 45 (3): 341-69.
Davidson, R. 1970. ‘‘On Extending the Bradley-Terry Model to Accommodate Ties in Paired
Comparison Experiments.’’ Journal of the American Statistical Association 65 (329): 317-28.
Desch, M. 2002. ‘‘Democracy and Victory: Why Regime Type Hardly Matters.’’ International Security 27 (2): 5-47.
Desch, M. 2003. ‘‘Democracy and Victory: Fair Fights or Food Fights?’’ International Security 28 (1): 180-94.
Desch, M. 2008. Power and Military Effectiveness: The Fallacy of Democratic Triumphalism.
Baltimore: Johns Hopkins University Press.
Downes, A. 2009. ‘‘How Smart and Tough are Democracies? Reassessing Theories of
Democratic Victory in War.’’ International Security 33 (4): 9-51.
Dubin, J., and D. Rivers. 1990. ‘‘Modern Methods of Data Analysis,’’ In Selection Bias inLinear Regression, Logit and Probit Models, edited by J. Fox and S. Long, 410-42.
Thousand Oaks, CA: Sage.
Elkins, Z. 2000. ‘‘Gradations of Democracy? Empirical Tests of Alternative Conceptualizations.’’ American Journal of Political Science 44 (2): 293-300.
Fearon, J. 1994. ‘‘Domestic Political Audiences and the Escalation of International Disputes.’’American Political Science Review 88 (3): 577-92.
Fearon, J. 1997. ‘‘The Offense-Defense Balance and War Since 1648.’’ http://www.stanford.
edu/~jfearon/papers/OFFDEF1.pdf.
Firth, D. 2005. ‘‘Bradley-Terry Models in R.’’ Journal of Statistical Software 12 (1): 1-12.
Fortna, P. 2009. ‘‘Where have all the Victories Gone? Peacekeeping and War Outcomes’’
http://www.columbia.edu/~vpf4/victories%20Sept%202009.pdf.
Freedman, D., and J. Sekhon. 2010. ‘‘Endogeneity in Probit Response Models.’’ Political
Analysis 18 (2): 138-50.

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

Renshon and Spirling

31

Geller, D. 2000. ‘‘Status Quo Orientation, Capabilities, and Patterns of War Initiation in
Dyadic Rivalries.’’ Conflict Management and Peace Science 18 (1): 73-96.
Gelpi, C., and M. Griesdorf. 2001. ‘‘Winners or Losers? Democracies in International Crisis,
1918-94.’’ American Political Science Review 95 (03): 633-47.
Green, D., S. Kim, and D. Yoon. 2001. ‘‘Dirty Pool.’’ International Organization 55 (2): 441-68.
Heckman, J. 1979. ‘‘Sample Selection Bias as a Specification Error.’’ Econometrica 47 (1): 153-61.
Hegre, H. 2008. ‘‘Gravitating Toward War: Preponderance May Pacify, but Power Kills.’’
Journal of Conflict Resolution 52 (4): 566-89.
Hirshleifer, J. 2000. ‘‘The Macrotechnology of Conflict.’’ Journal of Conflict Resolution
44 (6): 773-92.
Jaggers, K., and T. Gurr. 1995. ‘‘Tracking Democracy’s Third Wave with the Polity III Data.’’
Journal of Peace Research 32 (4): 469-82.
Jervis, R. 1978. ‘‘Cooperation under the Security Dilemma.’’ World Politics: A Quarterly
Journal of International Relations 30 (2): 167-214.
Jones, D. M., S. A. Bremer, and J. D. Singer. 1996. ‘‘Militarized Interstate Disputes, 18161992: Rationale, Coding Rules, and Empirical Patterns.’’ Conflict Management and Peace
Science 15 (2): 163-213.
King, G. 2001. ‘‘Proper Nouns and Methodological Propriety: Pooling Dyads in International
Relations Dyad.’’ International Organization 55 (2): 497-507.
Lake, D. 1992. ‘‘Powerful Pacifists: Democratic States and War.’’ The American Political
Science Review 86 (1): 24-37.
Lake, D. 2003. ‘‘Fair Fights? Evaluating Theories of Democracy and Victory.’’ International
Security 28 (1): 154-67.
Lewis, J., and K. Schultz. 2003. ‘‘Revealing Preferences: Empirical Estimation of a Crisis
Bargaining Game with Incomplete Information.’’ Political Analysis 11 (4): 345-67.
Maoz, Z. 2005. ‘‘Dyadic MID Dataset (version 2.0).’’ http://psfaculty.ucdavis.edu/zmaoz/
dyadmid.html
McCulloch, C., and S. Searle. 2001. Generalized, Linear and Mixed Models. New York: John
Wiley.
Mearsheimer, J. 2001. The Tragedy of Great Power Politics. New York: W. W. Norton.
Nevin, J. 1996. ‘‘War Initiation and Selection by Consequences.’’ Journal of Peace Research
33 (1): 99-108.
Oneal, J., and B. Russett. 1997. ‘‘The Classical Liberals were Right: Democracy, Interdependence, and Conflict, 1950–1985.’’ International Studies Quarterly 41 (2): 267-94.
Poast, P. 2010. ‘‘(Mis) Using Dyadic Data to Analyze Multilateral Events.’’ Political Analysis
18 (4): 403-25.
Rao, P. V., and L. L. Kupper. 1967. ‘‘Ties in Paired-comparison Experiments: A Generalization of
the Bradley-Terry Model.’’ Journal of the American Statistical Association 62 (317): 194-204.
Reed, W. 2000. ‘‘A Unified Statistical Model of Conflict Onset and Escalation.’’ American
Journal of Political Science 44 (1): 84-93.
Reiter, D. 2001. ‘‘Does Peace Nurture Democracy?’’ The Journal of Politics 63 (3): 935-48.
Reiter, D., and C. Meek. 1999. ‘‘Determinants of Military Strategy, 1903-1994: A Quantitative Empirical Test.’’ International Studies Quarterly 43 (2): 363-87.

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013

32

Journal of Conflict Resolution 00(0)Reiter, D., and A. Stam. 1998a. ‘‘Democracy and Battlefield Military Effectiveness.’’ Journalof Conflict Resolution 42 (3): 259-77.
Reiter, D., and A. Stam. 1998b. ‘‘Democracy, War Initiation, and Victory.’’ American Political Science Review 92 (2): 377-89.
Reiter, D., and A. Stam. 2002. Democracies at War. Princeton, NJ: Princeton University Press.
Reiter, D., and A. Stam. 2003. ‘‘Understanding Victory: Why Political Institutions Matter.’’International Security 28 (1): 168-79.
Reiter, D., A. Stam, and A. Downes. 2009. ‘‘Another Skirmish in the Battle over Democracies
and War.’’ International Security 34 (2): 194-204.
Robinson, G. K. 1991. ‘‘That BLUP is a Good Thing: The Estimation of Random Effects.’’
Statistical Science 6 (1): 15-32.
Schultz, K. 1999. ‘‘Do Democratic Institutions Constrain or Inform? Contrasting Two Institutional
Perspectives on Democracy and War.’’ International Organization 53 (2): 233-66.
Signorino, C. 1999. ‘‘Strategic Interaction and the Statistical Analysis of International
Conflict.’’ American Political Science Review 93 (2): 279-97.
Signorino, C. 2003. ‘‘Strategic Misspecification in Regression Models.’’ American Journal of
Political Science 47 (3): 551-66.
Singer, J., S. Bremer, and J. Stuckey. 1972. ‘‘Capability Distribution, Uncertainty, andMajor Power War, 1820-1965.’’ In Peace, War and Numbers, edited by B. Russett, 19-48.
Thousand Oaks, CA: Sage.
Singer, J., and M. Small. 1966. ‘‘The Composition and Status Ordering of the International System:
1815-1940.’’ World Politics: A Quarterly Journal of International Relations 18 (2): 236-82.
Smith, A. 1999. ‘‘Testing Theories of Strategic Choice: The Example of Crisis Escalation.’’American Journal of Political Science 43 (4): 1254-83.
Sullivan, P. 2007. ‘‘War Aims and War Outcomes: Why Powerful States Lose Limited Wars.’’
Journal of Conflict Resolution 51 (3): 496-524.
Turner, H., and D. Firth. 2012. ‘‘Bradley-Terry Models in R: The BradleyTerry2 Package.’’
Journal of Statistical Software 48 (9): 1-21.
Valeriano, B., and J. Vasquez. 2010. ‘‘Identifying and Classifying Complex Interstate Wars.’’
International Studies Quarterly 54 (2): 561-82.
Van Evera, S. 1998. ‘‘Offense, Defense, and the Causes of War.’’ International Security 22 (4): 5-43.
Walt, S. 1985. ‘‘Alliance Formation and the Balance of World Power.’’ International Security
9 (4): 3-43.
Wayman, F., J. Singer, and G. Goertz. 1983. ‘‘Capabilities, Allocations, and Success in
Militarized Disputes and Wars, 1816-1976.’’ International Studies Quarterly 27 (4): 497-515.
Weeks, J. 2008. ‘‘Autocratic Audience Costs: Regime Type and Signaling Resolve.’’ International Organization 62 (1): 35-64.
Whang, T. 2010. ‘‘Empirical Implication of Signaling Models: Estimation of Belief Updatingin International Crisis Bargaining.’’ Political Analysis 18 (3): 381-402.
Wright, Q. 1965. ‘‘The Escalation of International Conflicts.’’ Journal of Conflict Resolution
9 (4): 434-49.

Downloaded from jcr.sagepub.com at UNIV OF WISCONSIN on August 30, 2013