Evaluating Conflict Dynamics

Abstract

Interest in processes has become increasingly pronounced in international conflict research in recent years, especially how these processes unfold across time “dynamics”. We focus in particular on “stage conceptions” of dynamics: processes that unfold over a series of sequential, and possibly recurrent, stages. We suggest that stage conceptions have two key properties: plurisectality and conditional covariate effects. We propose a novel econometric application to quantitatively assess claims regarding stage conceptions of dynamics: survival modeling. Specifically, we use multistate models to examine how a process evolves through its individual stages, and also whether covariate effects differ across these stages. We use Huth and Allee’s territorial dispute data to demonstrate the importance of conceptualizing conflict as a dynamic process, as well as empirically modeling it as such. We show democracy has different effects on dispute resolution, depending on the dispute’s stage, but that these different effects disappear after time passes.

Keywords

conflict dynamics militarized disputes militarized interstate disputes conflict process democratic peace territorial disputes conflict

Russia and Finland’s territorial dispute over the Karelia region in the aftermath of the Winter War (1940–1941) lasted for approximately six years. After the initial challenge, the dispute militarized for thirty-nine months before transitioning to a dormant phase for close to two years, in which neither Russia nor Finland actively attempted to settle the dispute. Russia and Finland then engaged in seven months of formal negotiations, which ultimately resolved the dispute (“No. 74 Finland-USSR Boundary,” 1967). The dispute’s overall duration of six years obscures its evolution over time, and how resolution occurred only after transitions between periods of militarization, inactivity, and negotiations.¹

The Russo-Finnish dispute is far from unique. On average, territorial disputes experience around eleven transitions between these various stages during their lifetimes. We have a substantive interest in understanding how these territorial disputes unfold (e.g., Huth and Allee 2002)—how one particular transition can parlay into others, for example, and why some transitions are more likely to occur than others. Put differently, we are interested in territorial disputes as a holistic process. Yet, despite this interest, we have few empirical tools that consider all of a dispute’s transitions within a single framework.² Instead, we normally focus on one or two specific transitions in isolation—the onset of militarization, for example—and say that this gives us some sense of how the dispute unfolds, though the picture it paints is admittedly incomplete.

Our territorial dispute example represents a particular conception of conflict dynamics: a process that unfolds across several stages. We call this a stage conception of dynamics. This conception has garnered increasing attention from scholars, albeit often implicitly, but has yet to receive explicit theoretical and econometric consideration. Conceptions of dynamics matter because they have implications for empirical testing. Econometric models appropriate for one conception may be inappropriate for other conceptions, precisely because these different conceptions imply distinct theoretical mechanisms.

A stage conception of dynamics has two key properties, at minimum, with substantive and empirical implications. What we call plurisectality is the first. We use the word to describe processes in which many stage transition sequences eventually terminate with the same outcome (e.g., resolution, for territorial disputes).³ Therefore, differences may exist in how each unit arrives at this outcome. Did the unit experience only one transition between stages, from the starting stage directly to the end stage? Did it experience two transitions, perhaps from the starting stage to an intermediate stage and then to the end stage? Twelve transitions? Between which stages did the unit transition—what is the sequence?⁴ If multiple sequences do indeed produce the same outcome, implications exist for our empirical calculations. If, for instance, we are interested in calculating the overall probability of arriving at the end stage, we would need to account for all the possible transition sequences into that end stage.

Second, a stage conception of dynamics suggests that covariate effects may be conditional. This point is often made in the context of the proportional hazards assumption for Cox duration models (Box-Steffensmeier, Reiter, and Zorn 2003; Licht 2011) and simple state dependence (Esarey and DeMeritt 2014), but our point is more expansive. Investigating the effect of a covariate on some outcome could be affected not only by a simple conception of time (i.e., proportional hazards) but by the stage a process currently occupies. A covariate may increase the probability of arriving at one stage, but decrease the probability of arriving at another. Such a situation necessitates a more holistic method of evaluating a covariate’s effect on the process as a whole, one that aggregates the covariate’s effect at each stage in the process to determine its overall effect.

We argue that territorial disputes, and in particular the role of regime type in territorial disputes, exemplify these properties. Drawing on Huth and Allee’s (2002) seminal work on territorial disputes, we offer new insights into the role of democracy in territorial dispute processes by using a stage conception of dynamics as our theoretical framework. For example, a plurisectal dispute process would suggest that democratic states seeking to revise the status quo may be disproportionately likely to pursue one particular sequence of resolution strategies, whereas autocratic challengers’ sequences may be more heterogeneous. Similarly, we argue that there are strong theoretical reasons to expect regime type’s effect to vary across the territorial dispute process, depending on which stage of the process a dispute-dyad currently occupies. Without considering the variation in this effect, any attempt to evaluate the effect of regime type on the timing of resolution attempts would average across all of these differences, and thus yield potentially misleading results.

Given plurisectality and conditional covariate effects, how can we empirically assess hypotheses about processes that unfold across several stages? We make the novel suggestion that survival models are capable of investigating these types of claims regarding dynamics. Specifically, multistate survival models are capable of investigating questions about multiple sequences producing the same outcome and how some covariate’s effect on an outcome might be conditioned on the current stage. Traditionally, practitioners investigate claims about dynamics (in the broad sense) using time series models. While some of these specific models are capable of accommodating parts of a stage conception of dynamics, many are not (for an overview, see Freeman and Jackson 2012, 144). Further, the intricacies of the applicable models are complex enough to be a challenge for researchers possessing only a basic grasp of time series methods. Survival models have the advantage of being easier to implement, for experts and nonexperts in survival modeling alike.

We are not the first to urge scholars to consider how dynamics matter. We are also not the first to point out the econometric ramifications of dynamics (for overviews, e.g., Beck 1991, 2001; Beck and Katz 2011; DeBoef and Keele 2008; Wilson and Butler 2007). Neither are we the first to assess hypotheses stemming from a stage conception of conflict dynamics using more sophisticated tools (e.g., Brandt, Freeman, and Schrodt 2011, 2014; Nieman 2016; Schrodt 2000). However, we are among the first to introduce a novel statistical technique, the multistate survival model, capable of empirically modeling the core properties of a stage conception of dynamics within a single analytic framework. We are also the first to apply this tool to the study of territorial disputes and to assess how the effect of democracy varies across the territorial dispute process.

Our discussion proceeds in four parts. We begin by taking stock of extant work about conflict dynamics. From there, we expand on the key characteristics of a stage conception of dynamics. Second, we discuss our illustrative application from Huth and Allee (2002). We also introduce the multistate survival model and its usefulness for assessing stage conceptions of dynamics. Third, we discuss the results of our multistate analysis, including our new insights regarding regime type’s effect. The fourth and final section briefly concludes.

Theoretical Motivations

What Are Conflict Dynamics?

To speak of conflict dynamics requires an understanding of both conflict and dynamics. When we say “conflict,” we refer to “a sharp disagreement or collision in interests between two or more actors” (D. M. Jones, Bremer, and Singer 1996, 168). Within international relations, intrastate conflict (e.g., civil war) involves disagreements between two actors located within a single state’s borders: the state’s central government and a nonstate actor (Sarkees and Wayman 2010). On the other hand, interstate conflict involves disagreements between two independent states.⁵

Most conflict studies in this vein, intra and interstate alike, focus on militarized conflict. Militarized conflicts are those in which at least one actor has taken military action against the other in an effort to resolve the disagreement. Scholars often use information on both actors at multiple points in time t to better understand how the conflict begins, progresses (e.g., escalates, militarizes), terminates, and/or potentially recurs.⁶ We use the term “conflict process” to collectively refer to these various outcomes. Typically, scholars focus on investigating one outcome at a time and suggest factors (x’s) that have an effect on the outcome.

An interest in dynamics necessarily implies a substantive interest in the conflict process as a whole. That is, it implies an interest in many outcomes, not just one. We are specifically interested in the “stages” within a conflict process, in which “what happens in one stage of conflict has downstream consequences in a later stage” (Diehl 2006, 199). Dynamics, here, refers primarily to the interconnectivity across stages.⁷ Senese and Vasquez make a similar point in their study of interstate war, noting that their steps-to-war argument “implies a sequence of actions or even transitions across phases” (2008, 23).⁸ Elsewhere, some use the word “dynamics” to refer more to the interconnectivity of the actors involved in the conflict process (e.g., Kadera and Morey 2008; Williams and McGinnis 1988), while still others use dynamics to represent the interaction between different levels of analysis (e.g., Braumoeller 2012; Kadera, Crescenzi, and Shannon 2003). None of the usages are mutually exclusive. They simply speak to different points of theoretical emphasis, given the argument at hand.

Stage Conception of Conflict Dynamics

A stage conception of conflict dynamics views conflicts as ongoing processes comprising multiple, discrete phases.⁹ The precise number and nature of the phases within a conflict process may vary, depending on the theory to be tested and available data. As one example, a process could be composed of (1) bargaining between states prior to the onset of violence, (2) the escalation from peaceful bargaining to low-level violence, (3) the escalation to war, and (4) the postwar environment.

A number of studies have begun to conceptualize conflict not as pertaining to any one particular stage but rather as a broader process composed of many of these stages (Chiba, Metternich, and Ward 2015; Diehl 2006; Levy 1995; Senese and Vasquez 2008). This stance has borne theoretical fruit. As an example, Findley (2013) argues that peace talks consist of multiple stages and shows that the prospects for long-term peace after a civil war will vary substantially based on the peace talk’s stage. Factors that increase the likelihood of actors commencing negotiations may make it substantially more difficult for those same actors to actually implement any agreement they reach (cf. Fearon 1998).

Despite our interest in the entire conflict process, explicit attempts to model it tend to be fairly rare. Standard econometric models have difficulty in capturing two key features of a stage conception of dynamics: process plurisectality and conditional covariate effects. These features are theoretically important yet also present difficulties for standard empirical analyses.

Diverse paths across stages

Our standard empirical tools assume that, if a conflict has stages, it transitions through them in a nonrecursive, unisectal fashion, usually for the sake of theoretical or empirical simplicity (Diehl 2006, 200). Stage A leads to Stage B, which leads to Stage C, which leads to Stage D.

However, the process may be a good deal more complex—it may be plurisectal.¹⁰ Here, all conflicts eventually end in the same stage, as we typically assume. Importantly, however, the order in which a specific conflict experiences the different stages—or whether the conflict experiences all of the stages—may vary from one conflict to the next. In Russia and Finland’s dispute over Karelia, resolution was the product of a four-transition sequence: (1) transitioning from the initial status quo challenge to militarization (C → M), (2) transitioning from militarization back to a status quo challenge with no active settlement attempts (M → C), (3) transitioning from challenge to negotiations (C → N), and (4) transitioning from negotiations to resolved (N → R). The path to resolution in other territorial disputes, though, has varied. Argentina and Paraguay’s dispute over their shared border near the Pilcomayo River experienced eight transitions before it was resolved (C → N → C → N → C → N → C → N → R). By contrast, Gabon and Equatorial Guinea’s dispute over several islands in Corisco Bay in the 1970s experienced only two transitions before resolution: C → M → R. While all the illustrative examples end with resolution, they have different transition sequences leading up to that point.

Further complicating matters, conflicts may revisit the same stage on multiple occasions. Argentina and Paraguay’s dispute transitioned into the Negotiations stage on four different occasions. Russia and Finland reverted back to a status quo challenge, with no active settlement attempt, on two occasions. This recursiveness is further at odds with a pure unisectal conception of processes, which maintains that a conflict occupies a stage once and then never again.

Plurisectality and recursiveness are troublesome, from an empirical standpoint, because most of our standard econometric models assume neither exists. Put differently, our models usually employ a unisectal, nonrecursive conception of processes. They do not account for the various ways in which a conflict may transition into a particular stage, which is relevant if we are interested in calculating the probability of such a transition. Additionally, our models typically focus on one or two transitions only, at the expense of the rest, even if we have a substantive interest in the process as a whole. Our ability to investigate aspects of recursiveness is consequently limited.

Context-dependent covariate effects

The second implication of a stage conception of dynamics is that a covariate’s effect may vary, depending on the context in which it is observed. Specifically, covariate effects may depend upon the conflict’s stage. Depending on the particular stage in question, the “basic structural elements vary in their relation to each other … In other words, the variables in the bivariate relationship are right, but the relationship is not constant (i.e. the β’s vary)” (Goertz 1994, 15). These effects are potentially more interesting, as they imply a complex causal process for the outcome(s) of interest (Braumoeller 2003; Jervis 1997).

This type of causal complexity is often present in many studies of conflict. Walter (2004), for example, argues that the root causes of a state’s initial civil war are often unrelated to its propensity to experience a recurrence of violence in the future. In other words, the process that generates the first civil war is distinct from that generating subsequent rounds of fighting, because the context in which various factors are observed has changed; a state that has already experienced a civil war occupies a different phase of the conflict process compared to a state that has not experienced a civil war. Similarly, Kirschner (2010) contends that a history of atrocities can exacerbate the ability of combatants in a civil war to make credible commitments, thus prolonging conflicts. Underlying this theorizing is the notion that factors impacting states’ ability to make credible commitments will have different effects depending on the historical context in which they are observed. While these studies suggest that historical context plays an important role in moderating the effect of covariates of interest, this relationship is never explicitly specified empirically.

Example: Territorial Disputes and Democracy

A state’s regime type provides an excellent example of the two ramifications of our stage conception of conflict dynamics. First, regime type exhibits causal complexity in the conflict process: its effect differs depending on which aspect of interstate conflict is of interest, and which stage of the process a dyad occupies. More democratic regime types are more likely to employ negotiations within their disputed issues, particularly negotiations mediated by an international organization (Hansen, Mitchell, and Nemeth 2008), because democracies externalize their domestic predilection for legalistic dispute settlement. In the broader, non-issue-specific literature on interstate conflict, researchers argue that more democratic regime types are less likely to employ militarized force for both normative and institutional reasons (Maoz and Russett 1993; Russett and Oneal 2001). However, if militarization does occur, democracies tend to be involved in shorter fights than their nondemocratic counterparts, because democracies self-select into militarizations with a high ex ante chance of victory (Bueno de Mesquita, Koch, and Siverson 2004; Stanley and Sawyer 2009). Additionally, once militarization occurs, democracies are just as likely as nondemocracies to escalate the severity of the militarization, due to similar selection effects (Reed 2000; Senese 1997). Finally, some evidence suggests that democratic initiators do not differ from nondemocratic initiators in their ability to use wars to extract favorable settlements, again because of selection effects (Slantchev 2004). In short, the extant literature contains a series of hypotheses regarding regime type’s effect on the likelihood of specific transitions within the conflict process. Importantly, these hypotheses make different predictions about regime type’s effect, depending on the transition of interest, and these differences are indeed consistent with the empirical evidence.

Second, democracy’s causal complexity underscores precisely why plurisectality matters. As evidenced by our earlier illustrative examples, territorial disputes exhibit a variety of transition sequences. If democracy had an identical effect on the probability of every transition within a territorial dispute, the different transition sequences would be of little concern. However, this is not the case—extant research suggests that democracy’s effect on militarization, conflict resolution, and other transitions of interest differs depending on a dispute’s current stage. If a process is composed of multiple stages, and a variable’s effect differs based on stage, modeling every stage is important. By doing so in this example, we can compute democracy’s direct and indirect effect on the probability of dispute resolution by aggregating democracy’s effect across all possible transition sequences ending in resolution. We can then make statements about the overall effect of democracy on resolution within the territorial dispute process. Such statements would be difficult to make by looking at extant research alone because, depending on the stage a dispute occupies, democracy may exhibit positive, negative, or null effects. We are left wondering whether or not democracy’s effect does indeed “net to a positive.”

In sum, conflict researchers have begun to increasingly offer sophisticated theoretical arguments about the nature of conflict dynamics. Stage conceptions of dynamics are one such example. However, these studies often fail to incorporate important theoretical notions associated with stage conceptions into their empirical models because our standard statistical techniques are limited in their ability to address these notions. We use democracy’s effect within territorial disputes as an illustrative example to showcase how a stage conception of dynamics may be fruitful. Below, we introduce a statistical approach that is capable of empirically capturing the two implications of a stage conception of conflict dynamics and apply it to a well-known conflict data set to reexamine the effect of democracy.

Research Design

Data

We reexamine Huth and Allee’s (2002; hereafter, H&A) study on territorial disputes to illustrate our theoretical points and the ability of our chosen estimation technique—multistate models (discussed in the next section)—to evaluate stage-based claims about conflict dynamics. We reanalyze this particular data set because H&A explicitly point to a stage conception of dynamics as a motivating factor for their study. Specifically, they “identify several stages or phases in an international dispute… [and contend] that any research design devised to test hypotheses about international conflict and cooperation should consider each of these possible stages” (pp. 2-23). This makes it an ideal testing ground, for our purposes.

H&A (2002, 300) broadly define territorial disputes as:

Disagreements between governments over (a) the location of existing international boundaries in particular sectors or along the length of their common border, (b) the refusal of one government to recognize another’s claim of sovereign rights over islands, claiming sovereignty for itself instead, or (c) the refusal of one government to recognize another state as a sovereign political-territorial unit, laying claim to the territory of that state.

Their data set contains 347 territorial disputes occurring anywhere in the world between 1919 and 1995 that involve independent states. The data are broken down further into directed state pairs over a dispute, where the states are ordered according to their relation to the status quo. States making explicit statements that challenge the territorial status quo (or statements challenging those made by another state) are listed first, followed by the state targeted by the challenger’s statement (H&A 2002, 34). We refer to these dispute–challenger–target combinations as “dispute-dyads.” There are 398 dispute-dyads in H&A’s data set.¹¹

Similar to the theoretical point we advance here, H&A point out that territorial disputes progress through several stages, as states try to resolve the dispute. States may use peaceful means (e.g., bilateral talks, arbitration) or militarized means to do so. The probability of using one resolution method versus another is a function of many factors, and importantly, the set of relevant factors (i.e., statistically significant) may be different for each resolution method, if not also the effects (β’s) of these factors on each resolution method.

H&A’s (2002) substantive interest is in the different mechanisms undergirding the democratic peace, and how the mechanism of interest may differ depending on the resolution method.¹² To investigate this, H&A use a multinomial logit model, in which they set “no resolution method chosen” in a given month (what they call “Challenge”) as the reference outcome. Their model choice allows them to parse out the effect of democracy on the probability of peaceful negotiations versus no resolution in that month, and the probability of militarized behavior versus no resolution in that month (chap. 7). H&A find that democratic challengers are more likely to initiate peaceful negotiations and that they are less likely to resort to militarized behavior (p. 152).

Nevertheless, this research design is not ideal for fully examining the dispute, as a process. It artificially restricts the manner in which a dispute might evolve over time. With their multinomial logit models, H&A are able to examine the initial transition from a challenge to either peaceful negotiations or militarized behavior (Figure 1a). However, this setup is incapable of capturing the recursive nature of many disputes: a dispute might first militarize, revert back to the Challenge stage, only then transition to Negotiations, as in the case of Russia and Finland. H&A’s analysis is only capable of modeling either (1) the first transition within the dispute process, thus ignoring all subsequent events that may occur; or (2) truncating the analysis to only include transitions into Negotiations or Military, without any information about whether the dispute experienced transitions out of (and then back into) the Challenge stage. Our multistate modeling strategy bypasses many of these weaknesses.

Figure 1.

The stages of a territorial dispute. Arrows denote possible transitions in each panel. The panels are motivated by Huth and Allee (2002), figure 2.1. Note: a = Multinomial Logit; b = Additional Transitions; c = Fully Dynamic Model.

Like H&A, we begin by dividing territorial disputes into four possible stages, illustrated in Figure 1c.¹³ We determine a particular dispute-dyad’s stage on a monthly basis using their data, which are also measured monthly:

Challenge: a territorial dispute exists between the two states in question, but the challenger takes no actions to resolve the dispute in that month (H&A 2002, 36, 45).

Negotiations: the challenger initiates formal diplomatic negotiations with the target, specifically regarding the territory in question (H&A 2002, 36, 47-48).

Military: the challenger initiates a militarized interstate dispute (MID) with the target, specifically over the territory in question (H&A 2009, 1). A MID is a threat, display, or use of military force by one state against another state (D. M. Jones, Bremer, and Singer 1996).

Resolved: the dispute has concluded, as disputant states reach some sort of resolution. Resolution can happen in one of three ways: (1) negotiations yield an agreed-upon settlement, (2) a MID yields a victory, in that one side receives the territory, (3) the dispute-dyad is between a colonizing power and another state, and becomes moot once the colony becomes independent.¹⁴ We define Resolved as an absorbing stage. Once a dispute-dyad transitions into the Resolved stage, it cannot transition out again.¹⁵

There are sixty-six unresolved dispute-dyads as of December 1995, the end of H&A’s data set. We treat these ongoing dispute-dyads as right censored in our analysis.¹⁶

Method

Our conception of conflict dynamics centers on the importance of understanding conflict as a process that unfolds through multiple, discrete stages. It suggests a number of transition sequences are theoretically possible. It also suggests that the specific stage a conflict occupies, at time t, may condition the independent variables’ effects on transitions into other stages.

This conception poses a few statistical challenges that most conventional statistical techniques cannot handle well. First, it requires an empirical strategy that captures a conflict as it transitions through successive stages over time, and can accommodate plurisectal, recursive processes. Second, the modeling strategy should allow for the probability of switching from one stage to another—a transition probability—to vary over time (Freeman and Jackson 2012, 143). Third, the potential effects of the individual coefficients in the model should also be permitted to vary by stage (Freeman and Jackson 2012, 143).

In order to meet the requirements of this stage conception of conflict dynamics, the remainder of this section introduces and discusses a class of duration models known as multistate survival models, synonymously referred to as multistate event history models (Therneau and Grambsch 2000). Multistate models have been used to explore causes of death among Norwegian citizens (Vollset, Tverdal, and Gjessing 2006), bone marrow recipients’ health (Putter, Fiocco, and Geskus 2007, 2417-22), and individuals’ cohabitation patterns (Mills 2004). Metzger and Jones (forthcoming) discuss multistate models in the context of political science and provide an introductory primer as to their use.

Multistate models are an extension of the familiar Cox survival model. Both models are concerned with some unit i being at risk of experiencing an event, and modeling how long until i experiences the event. The key difference between standard Cox models and multistate models is that two or more such events are possible for the latter. That is, there are multiple ways in which i’s “time at risk” (i.e., spell) can end. These multiple events are referred to as “transitions,” in the parlance of multistate models.

Competing risks models are a special type of multistate model, which makes the former useful for explaining the latter’s different features. In a classic competing risks setup, all observations (1) begin in the same stage, (2) are simultaneously at risk of experiencing two or more transitions, and (3) after experiencing one of the transitions, are no longer at risk of experiencing any other transition (Box-Steffensmeier and Jones 2004).¹⁷ In territorial disputes, once a state has challenged the territorial status quo, the dispute is simultaneously at risk of experiencing either negotiations or a MID (Figure 1a). If either transition occurs, the dispute “exits the risk set”—it is no longer able to experience the other transition, by definition. A dispute that enters into negotiations would no longer be at risk of experiencing a MID. However, this classic framework is limited in its ability to model more complex situations. We mentioned one such situation earlier—those in which, after a unit experiences one event, it is still at risk of experiencing other events (e.g., a dispute that experiences negotiations after militarization occurs, like Russia and Finland).

By contrast, multistate models are sufficiently flexible to model any number of possible process structures. They go beyond classic competing risks because they can capture situations in which events occur sequentially, repeatedly, or any combination thereof (Putter, Fiocco, and Geskus 2007; Therneau and Grambsch 2000). As one example, Figure 1b presents a multistate model that extends H&A’s basic framework in two ways: (1) by permitting disputes to transition from either Negotiations or Military back to an inactive Challenge stage and (2) by permitting possible transitions between Negotiations and Military. The multistate model that we estimate, displayed in Figure 1c, extends Figure 1b even further by adding a new stage to the analysis, a final resolution to a dispute (Resolved), as well as the possibility of transitions into the Resolved stage from the other stages.

On the whole, multistate models provide us with the flexibility to examine not only the initial transitions occurring within the dispute process but also all of the intervening transitions that occur within this process, as well as the ultimate resolution of a dispute. Notably, this permits us to test additional hypotheses of interest that a conventional approach to analyzing territorial disputes would be incapable of evaluating.

Two additional implications follow. First, multistate models recognize that unit i’s current stage determines which transitions i is at risk of experiencing. For instance, in Figure 1b, a unit in the Challenge stage is at risk of experiencing two possible transitions: one to Negotiations and one to Military. By contrast, a unit in the Negotiations stage is at risk of experiencing two separate transitions: one to Military and one to Challenge. Multistate models are capable of empirically modeling this and significantly more complex possible sequences of events, like Figure 1c. Thus, one of multistate survival models' primary advantages is the flexibility of their structure. This is of the utmost importance for analyzing stage conceptions of processes, as such processes may contain any number of transitions through intermediate stages prior to observing the ultimate outcome of interest.

Second, multistate models can handle plurisectality; they account for the heterogeneity in how different units may arrive at a particular stage. Consider the transition into the Resolved stage in Figure 1c. A standard event history model would examine transitions into Resolved by lumping together Challenge, Negotiations, and Military. In doing so, the model potentially omits some interesting and theoretically relevant byplay. By contrast, multistate models recognize that there are several ways that unit i may transition into the Resolved stage and accounts for all the possibilities when calculating transition probabilities.

Multistate models can be estimated as stratified Cox models, which differ from a standard Cox model in two key respects. First, the underlying baseline hazard is stratified for each of the possible transitions within the conflict process. A separate baseline hazard, $α_{q_{0}} (t)$ , is estimated for each possible transition q, where t refers to the amount of time that a unit has been at risk.¹⁸ For our model in Figure 1c, nine baseline hazards would be estimated, one for each directional arrow in the diagram. The underlying risk of transitioning from Challenge to Negotiations, and from Challenge to Military, will be distinct from one another and will also be distinct from the underlying risk of other transitions (e.g., Military to Challenge).¹⁹ By contrast, standard Cox models only estimate one baseline hazard, α₀(t).

Second, multistate models include transition-specific covariates, X_q , where q, as above, indexes every possible transition in a process. Doing so allows each variable to have a different effect, depending on the transition in question. For example, some x might decrease the risk of transitioning from Challenge to Negotiations, but might increase the risk of transitioning from Military to Negotiations. Allowing for such differences is important, as it allows for transition-conditional covariate effects—a key implication of a stage conception of dynamics. By contrast, a typical standard Cox model can only accommodate one transition, making the transition-specific designation irrelevant.

Thus, the hazard rate for a multistate model is given by:²⁰

α_{q} (t) = α_{q_{0}} (t) e^{β^{'} X_{q}},

where α _q (t) is transition q’s hazard of occurring in time t, $α_{q_{0}} (t)$ represents transition q’s baseline hazard rate in t, X_q is the transition-specific vector of covariates, β is the vector of coefficients, and ′ is the vector’s transpose.

Given the hazard rate identified above, cumulative transition hazards may be estimated as:

A_{q} (t) = \int_{0}^{t} α_{q} (u) d u,

where u denotes all times at which transition q occurs between 0 and t. $A_{q} (t)$ can be aggregated into an S × S matrix for each t, A(t), where S is the number of possible stages within the multistate model.²¹

Cumulative transition hazards are relevant, because they permit us to calculate transition probabilities. Specifically, we can estimate a transition probability matrix, P(s,t), as:

P (s, t) = \prod_{u \in (s, t]} (I + Δ A (u)),

where (s,t] denotes the researcher’s time interval of interest, I denotes an S × S identity matrix, and $Δ A (u) = A (u) - A (u - 1)$ —that is, the difference between the cumulative transition hazards’ values at time u and the values at u − 1 (Andersen et al. 1993, 89). The individual elements of the matrix P(s,t) contain the probability of transitioning from each stage to every other stage within the time interval (s,t].²² Each row of this matrix will sum to one because each subject must be in one of the S stages. For example, element P _1,2(6,12) would denote the probability of transitioning from Stage 1 (Challenge) at time period 6 to transitioning into Stage 2 (Negotiations) by time period 12. The probability reflects both direct transitions from stage 1 to 2 (e.g., C → N) and indirect transitions, whereby i could begin in Stage 1 in time period 6 and still arrive in Stage 2 by time period 12 (e.g., C → M → N).²³ Importantly, these transition probabilities will vary over time, because the hazards on which they are based vary as well. This means that, holding all else constant, the probability of a particular transition occurring may be substantially different at some generic time t than it is at time t + 5.

Multistate survival models, as with competing risks models, multinomial logit/probit models, ordered logit/probit models, and many other models designed to model multiple events, take the “correct” number of events (or stages) as a quantity imposed by the researcher on the basis of the theory being tested and available data. There are situations in which the appropriate number of stages is an open question and one that is arguably empirical in nature. For instance, within the interstate conflict literature, some have suggested three stages (H&A 2002; Reed 2000) versus five stages (Gochman 1993) versus six stages (Bloomfield and Leiss 1969; Rummel 1976, chap. 15).

There is surprisingly little in both the competing risks and multistate literatures about selecting the appropriate number of stages. Nearly all the discussion presupposes the existence of a stage structure and begins its exposition from there. The closest analog pertains to testing for the appropriate number of strata (e.g., Therneau and Grambsch 2000, 61-65, 174-75).²⁴ The regime-switching literature, which is more rooted in time series analysis, has far more to say about assessing the number of stages (e.g., Frühwirth-Schnatter 2006, chaps. 4, 5, 12). Transitions between stages signify a structural break, in the time series lexicon, because the transitions differ from each other in terms of their baseline hazard $(α_{q_{0}} (t))$ and/or their covariate effects (the β’s for each X_q ). Here, our interest is in building from H&A’s original study. We take their proposed stages as given and assume them to be correct.

Descriptive Information—Transitions

Tables 1 –3 provide some descriptive information about our data. Table 1 contains information about all 4,255 transitions in our data set, based on what stage the dispute-dyad is transitioning from (the current stage) and what stage it is transitioning to (the next stage). Transitions from the Challenge stage to the Negotiations stage appear most frequently in our data set, with 1,705 of all 4,255 transitions being of this type (40.1 percent). Interestingly, the next most frequent transition is Negotiations → Challenge—that is, back to the Challenge stage, from the Negotiations stage (1,514 transitions, 35.6 percent). This is illustrative of a larger pattern in our data: there are many transitions back to the Challenge stage, evident by looking at the Table 1’s “Challenge” column. It suggests that many dispute-dyads take multiple resolution attempts, both peaceful and militarized, before they are resolved.

Table 1.

Observed Transition Frequencies—Four-stage Model.

Current stage	Next stage				Total
Current stage	Challenge	Negotiations	Military	Resolved	Total
Challenge (row %)	—	1,705 (78.0%)	357 (16.3%)	74 (3.4%)	2,136 (97.7%)
Negotiations (row %)	1,514 (86.6%)	—	16 (0.9%)	206 (11.8%)	1,736 (99.3%)
Military (row %)	315 (81.6%)	13 (3.4%)	—	55 (14.2%)	383 (99.2%)
Resolved (row %)	—	—	—	—	—
Total	1,829	1,718	373	335	4,255

Note: Total column sums across the row, representing the number of transitions from the current stage to all other stages. Total column percentages do not sum to 100 percent because of right censoring; Resolved column does not sum to 401 also because of right censoring. Dashes indicate impossible transitions in our model.

Table 2.

Top Five Transition Sequences by Frequency.

	Sequence	Frequency	% of N	Cumulative %
1.	CNR	41	10.22	10.22
2.	CNCNR	29	7.23	17.46
3.	CMR	16	3.99	21.45
4.	CNCNCNCNR	16	3.99	25.44
5.	CNCNCNR	15	3.74	29.18

Note: N = 401 dispute-dyad-occurrences. Stage abbreviations: C = challenge, N = negotiations, M = military, R = resolved.

Table 3.

Stage Information: Frequency and Spell Length.

Stage	Frequency (mean)	Spell length (mean, in months)
Challenge	5.327	29.218
Negotiations	4.329	6.171
Military	0.955	6.580
All transitions	10.611	192.586^a

Note: N = 401 dispute-dyad-occurrences.

^aAverage duration of entire dispute-dyad-occurrence.

Table 2, which displays the five transition sequences occurring most frequently in our data set, also subtly reinforces this point. The first and third most frequently occurring sequences are Challenge → Negotiations → Resolved, and Challenge → Military → Resolved, respectively. Neither involves a transition back to the Challenge stage. However, only 14.2 percent of our dispute-dyad-occurrences²⁵ follow one of these two sequences.²⁶ A sizable 80.3 percent of our dispute-dyad-occurrences do transition back to the Challenge stage, at some point.

Table 3 rounds out the picture by providing information on the number of times a dispute-dyad-occurrence appears in each stage during its lifetime, as well as the average length of time spent in each stage. On average, our 401 dispute-dyad occurrences experience 10.6 transitions. They transition into the Challenge stage 5.3 times, on average, with a mean spell length of 29.2 months. For the Negotiations and Military stages, a divergence exists in the average number of times that dispute-dyads transition into each stage (4.3 times [N] vs. 0.9 [M]). Despite the difference, dispute-dyad-occurrences spend a surprisingly comparable amount of time (again, on average) in each stage, with 6.2 months spent in a typical spell in the Negotiations stage, versus 6.6 months for the Military stage.

Results

Replication of H&A

We estimate a semiparametric multistate model using the mstate package in R (Wreede, Fiocco, and Putter 2010, 2011) and include a number of H&A’s explanatory variables. We allow the effect of these variables to vary across each of the nine transitions in the data set, as equation 1 expresses. Doing so gives our model a chance to detect whether the same covariate has different effects on the likelihood of a given outcome (e.g., resolving the dispute) based upon the dispute’s current stage.

Table 4 contains our model results. Each column presents the covariates’ direct effect on a transition within the conflict process. Positively signed coefficients mean that higher values of the corresponding variable increase the probability of observing that transition. While a number of interesting results emerge from this analysis, we begin by comparing our results to H&A’s, to determine whether the use of a multistate model produces comparable results. We focus in particular on the effect of challenger regime type, measured using Polity III scores (H&A 2002, 91-92); higher values correspond with more democratic challengers.

Table 4.

Multistate Model of the Territorial Dispute Process.

Covariates	C → N	C → M	C → R	N → C	N → M	N → R	M→ C	M → N	M → R
Ratio of military capabilities	−0.150 (0.103)	1.236*** (0.218)	0.310 (0.507)	−0.295** (0.113)	0.746 (1.128)	0.702* (0.297)	−0.090 (0.290)	2.466 (1.718)	1.472* (0.734)
Strategic value	0.228*** (0.055)	0.377** (0.116)	−0.032 (0.281)	0.128* (0.062)	0.337 (0.590)	−0.010 (0.170)	−0.316* (0.159)	−0.058 (0.777)	0.468 (0.364)
Target engaged in other dispute	−0.097^† (0.057)	0.348** (0.122)	0.396 (0.264)	−0.051 (0.065)	1.417* (0.618)	0.168 (0.176)	−0.313* (0.144)	−0.516 (0.883)	−0.268 (0.364)
Challenger engaged in other dispute	−0.028 (0.063)	0.250* (0.122)	0.521* (0.266)	0.072 (0.072)	0.292 (0.689)	0.318^† (0.178)	−0.058 (0.157)	−0.395 (0.743)	0.219 (0.365)
Challenger regime type	0.018*** (0.004)	−0.046*** (0.009)	0.013 (0.017)	0.004 (0.004)	0.002 (0.038)	−0.006 (0.010)	0.011 (0.011)	0.038 (0.050)	−0.063* (0.026)
Target regime type	−0.002 (0.004)	−0.001 (0.008)	0.015 (0.017)	−0.006 (0.004)	−0.033 (0.040)	0.001 (0.010)	0.028** (0.010)	0.076 (0.053)	−0.031 (0.023)
Log likelihood (partial)	−16,197.51

Note: C = challenge; N = negotiations; M = military; R = resolved.

*p ≤ .05. **p ≤ .01. ***p ≤ .001. ^† p ≤ .10, two-tailed tests. Standard errors reported in parentheses.

By and large, our results match H&A’s, but we uncover some additional insights. To start, in line with what we would expect, territorial disputes involving more democratic challengers are more likely to transition to Negotiations (C → N) and less likely to transition to Military (C → M) following a status quo challenge. The findings are consistent with basic expectations from the monadic democratic peace, as democracies should be more likely to manage disputes through nonviolent means. Both findings also comport with H&A (2002, 152).

However, elsewhere, we find a somewhat surprising effect for challenger regime type. Counter to expectations, should a dispute involving a more democratic challenger transition into the Military stage, the dispute will be much less likely to be resolved (M → R), indicating that democratic challengers are likely to remain in the Military stage longer than their autocratic counterparts. This could be representative of a gambling for resurrection effect (Downs and Rocke 1994; Goemans 2000), whereby a challenger avoids terminating the MID it began due to the leadership’s fear of being removed from office for the perceived military “defeat.” Taken together, the model presents an interesting set of findings: democracies are less likely to transition into the Military stage, but their MIDs are less likely to conclusively resolve the dispute. H&A’s model suggests the first, too, but only our multistate model provides the second piece of nuance.

To further assess the similarity of our results with H&A’s, we use our model to replicate several predicted probabilities for challenger regime type. We disaggregate our Challenge stage into two distinct stages, to approximate H&A’s specification as closely as possible: one stage indicates that a challenge to the territorial status quo has been initiated (Challenge), and the second indicates that the dispute has experienced at least one active settlement attempt, and is currently experiencing no such attempts (Inactive). This results in a territorial dispute process consisting of five stages rather than four, with a total of twelve transitions (Figure 2).²⁷ This specification highlights the modeling flexibility of multistate models. We can easily differentiate between inactive spells at the outset of a dispute and those that arise later and estimate distinct baseline hazards and covariate effects for transitions out of these stages.

Figure 2.

Five-stage model of the territorial dispute process. Arrows denote possible transitions.

Table 5 compares our transition probability estimates from the Online Appendix B’s five-stage model to H&A’s reported predicted probabilities. Transition probabilities express the likelihood of a dispute-dyad occupying a stage at different points in time (t) based on three sets of initial conditions: (1) how long the dispute has been ongoing so far (s, in equation 3), (2) the dispute’s stage at time s, and (3) a set of covariate values. In an effort to replicate H&A’s predicted probabilities, we estimate our transition probabilities by specifying that the dispute (1) has been ongoing for twenty-four months, (2) is currently located in the Inactive stage, indicating it has experienced at least one prior settlement attempt, with (3) all covariates set at their median values unless otherwise noted.²⁸

Table 5.

Predicted Probability Comparison: Challenger Regime Type.

Scenario #1 transition: I → M			Scenario #2 transition: I → N
Value	Multistate (%)	H&A (%)	Value	Multistate (%)	H&A (%)
−10	6.5	7.5	−10	10.4	26.9
−2	4.2	4.7	−2	11.8	31.3
+6	2.7	3.0	+6	13.4	35.8
+10	2.2	2.3	+10	14.3	38.0

Note: For multistate results (Online Appendix B), transition probabilities calculated at t = 25. Huth and Allee’s (2002) predicted probabilities come from table 7.6 (p. 154) for scenario #1, and table 7.7 (p. 156) for scenario #2.

Comparing these probability estimates makes clear that the basic substantive inferences remain unaltered, although the point estimates differ slightly between our multistate results and H&A’s results. Both sets of results confirm that when a challenger is more democratic, it is significantly more likely to transition from the Inactive stage to Negotiations (I → N) and less likely to transition to a MID (I → M).²⁹ Thus, the substantive inferences we draw from our multistate model are largely similar to those from H&A’s multinomial logit, despite some minor differences in the actual point estimates between the two sets of results.

Additional Implications: Regime Type’s Overall Effect

One of the central implications of a stage-based conception of dynamics is that the same covariate may generate different effects depending on the context in which it is observed. The above discussion underscores precisely this form of causal complexity. On the one hand, more democratic challengers are less likely to resolve a dispute if they are currently involved in a MID (M → R). On the other, challenger regime type has no significant effect on the likelihood of resolving a dispute that is currently experiencing negotiations (N → R). While causal complexity of this sort is certainly important, we are interested in more than just regime type’s effect on two transitions within the model. We also have an interest in regime type’s effect on the whole territorial dispute process.

We use our multistate model to compute regime type’s overall effect on the entire dispute process (as opposed to each transition individually). We estimate a series of simulated transition probabilities for challenger regime type. Figure 3 compares the probability that a dispute will occupy the Resolved stage for challengers with a Polity score of +7 (75th percentile, solid lines) and challengers with a Polity score of −8 (25th percentile, dashed). The plots begin one year after the initial challenge for two different stage scenarios: the dispute is in the Negotiations stage (left panel) versus the Military stage (right).³⁰ At the one-year mark, 377 of our 401 dispute-dyad-occurrences are still ongoing (94.0 percent), and 148 dispute-dyad-occurrences are still ongoing at Figure 3’s maximum time of 200 months (36.9 percent).

Figure 3.

The effect of challenger regime type on dispute resolution. Quantities computed using simulation. Thin lines = 95 percent confidence intervals.

Figure 3 nicely depicts three findings. First, the effect of challenger regime type differs, depending on a dispute-dyad’s stage at twelve months. The left panel shows that there is no difference in the likelihood that democratic and autocratic challengers will resolve their disputes when they are involved in negotiations one year after a challenge begins. The right panel, however, shows that democratic challengers are significantly less likely to resolve their disputes when they are in a MID at the twelve-month mark, compared to autocratic challengers. In short, the same covariate has a different effect on the probability of resolution, depending on the context in which it is observed.

Second, these different effects exist only for the first ten years or so of the dispute-dyad. This echoes our earlier point about covariate effects possibly changing across time. Democratic challengers have a lower propensity to resolve disputes when they are involved in a MID after one year than autocratic challengers, but this effect loses statistical significance after 127 months, evident by the overlapping confidence intervals. This suggests that challenger regime type no longer has a different effect on a dispute-dyad’s likelihood of resolving the dispute once enough time passes since the dispute’s initiation.

Finally, we can speak to “does democracy’s effect ‘net to a positive’?” Our answer is a qualified no. If true, democratic challengers should be more likely to resolve their disputes than autocratic challengers, all else equal. However, Figure 3 shows democratic challengers are actually less likely to resolve their disputes than autocratic challengers. This negative effect takes into account not only that democratic challengers are less likely to transition directly from Military to Resolved (M → R), for example, but also all of the possible indirect paths through which a dispute-dyad may arrive at the Resolved stage from Military (e.g., M → I → R).³¹ Therefore, we can conclude that not only are democratic challengers less likely to directly transition from M → R (Table 4), but they remain less likely to arrive at the Resolved stage than autocratic challengers long after their MID (Figure 3).

Our remarks merit some qualifications. They apply to the specific scenario we used to generate our transition probabilities: twelve months since the initial status quo challenge, all other covariates at their median values, and the current stage is either Negotiations or Military. What this underscores is the importance of context when assessing democracy’s effect—specifically, the timing within the dispute (Metzger forthcoming) and the dispute’s stage at that time. Using a stage conception of dynamics foregrounds these concerns theoretically, and using a multistate setup allows us to investigate these concerns empirically with a reasonable degree of ease.

Conclusion

What does it mean to speak of conflict dynamics? We advance a stage conception of conflict dynamics, which views conflicts as processes unfolding across multiple, discrete stages. This conception has two key characteristics: plurisectal transition sequences and causal complexity in the form of context-conditional covariate effects. Despite the substantive abundance of these notions in current work, our empirical ability to evaluate them has been limited. In order to explore these practical implications of a stage conception of dynamics, we introduce the multistate survival model, which is able to gain leverage over plurisectality and conditional covariate effects simultaneously.

Using this model in the context of territorial disputes reveals a number of interesting findings and conclusions that current approaches would overlook. First, several of the covariates frequently identified as important in the territorial dispute process display a considerable degree of causal complexity. Their effects on the dispute process are highly contingent on the dispute’s current stage. For instance, we find that democracies are less likely to militarize their territorial disputes, but democracies are also less likely to resolve the dispute via militarization. While the former is in line with extant work, the latter is new. We also move beyond a covariate’s direct effect on a transition and examine its overall effect within the process. We show that democratic challenger’s overall effect is to reduce the probability of resolution following a MID, compared to autocratic challengers. Second, we identify strong evidence that context matters for territorial disputes. The stage occupied by a dispute-dyad one year after the initial challenge has a substantial effect on the dispute-dyad’s future trajectory.

Although we confine the present study to interstate territorial disputes, we expect the implications of a stage conception of conflict dynamics to be broadly applicable in studies of conflict. Moreover, we expect many of the implications to be generalizable to broader questions of democratic reversals (Metzger and Jones forthcoming), the development of political identities, politicians’ career trajectories, and more. In much the same way, we expect multistate models to be of considerable value to researchers in these research areas, given multistate models’ relation to the widely used Cox model, and their inherent flexibility in modeling any number of individual transitions, as well as larger processes as a whole.

Supplemental Material

Supplemental Material - Evaluating Conflict Dynamics: A Novel Empirical Approach to Stage Conceptions

Supplemental Material for Evaluating Conflict Dynamics: A Novel Empirical Approach to Stage Conceptions by Benjamin T. Jones and Shawna K. Metzger in Journal of Conflict Resolution

Footnotes

Authors’ Note

The authors’ names appear in alphabetical order. This article was presented at the 2014 meeting of Peace Science Society (International) and the 2015 meeting of the International Studies Association. We bear sole responsibility for any remaining errors and shortcomings. All analyses are performed using R 3.3.1 unless noted otherwise. Our replication files are available on JCR’s website and both authors’ websites (www.benjamintjones.com, ).

Acknowledgments

We thank Patrick Brandt, Bear Braumoeller, Jude Hays, Kelly Kadera, Eleonora Mattiacci, Cliff Morgan, Paul Poast, and the participants of the University of Mississippi’s International Relations Workshop for feedback on earlier drafts.

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 of this article.

Supplemental Material

Supplementary material for this article is available online.

Notes

References

Andersen

Per Kragh

Borgan

Ornulf

Gill

Richard D.

Keiding

Niels

. 1993. Statistical Models Based on Counting Processes. New York: Springer.

Beck

Nathaniel

. 1991. “Comparing Dynamic Specifications: The Case of Presidential Approval.” Political Analysis 3 (1): 51–87.

Beck

Nathaniel

. 2001. “Time-series-cross-section Data: What Have We Learned in the Past Few Years?” Annual Review of Political Science 4 (1): 271–93.

Beck

Nathaniel

Katz

Jonathan

. 2011. “Dynamics in Time Series Cross Section Data.” Annual Review of Political Science 14 (1): 331–52.

Bloomfield

Lincoln P.

Leiss

Amelia C.

. 1969. Controlling Small Wars: A Strategy for the 1970’s. New York: Alfred A. Knopf.

Box-Steffensmeier

Janet M.

Jones

Bradford S.

. 2004. Event History Modeling: A Guide for Social Scientists. Cambridge, UK: Cambridge University Press.

Box-Steffensmeier

Janet M.

Reiter

Dan

Zorn

Christopher J. W.

. 2003. “Nonproportional Hazards and Event History Analysis in International Relations.” Journal of Conflict Resolution 47 (1): 33–53.

Brandt

Patrick T.

Freeman

John R.

Schrodt

Philip A.

. 2011. “Real Time, Time Series Forecasting of Inter- and Intra-state Political Conflict.” Conflict Management and Peace Science 28 (1): 41–64.

Brandt

Patrick T.

Freeman

John R.

Schrodt

Philip A.

. 2014. “Evaluating Forecasts of Political Conflict Dynamics.” International Journal of Forecasting 30 (4): 944–62.

10.

Braumoeller

Bear F.

2003. “Causal Complexity and the Study of Politics.” Political Analysis 11 (3): 209–33.

11.

Braumoeller

Bear F.

2012. The Great Powers and the International System: Systemic Theory in Empirical Perspective. Cambridge, UK: Cambridge University Press.

12.

Bueno de Mesquita

Bruce

Koch

Michael T.

Siverson

Randolph M.

. 2004. “Testing Competing Institutional Explanations of the Democratic Peace: The Case of Dispute Duration.” Conflict Management and Peace Science 21 (4): 255–67.

13.

Casper

Gretchen

Wilson

Matthew

. 2015. “Using Sequences to Model Crises.” Political Science Research and Methods 3 (2): 381–97.

14.

Chiba

Daina

Metternich

Nils W.

Ward

Michael D.

. 2015. “Every Story Has a Beginning, Middle, and an End (but Not Always in That Order): Predicting Duration Dynamics in a Unified Framework.” Political Science Research and Methods 3 (3): 515–41.

15.

DeBoef

Suzanna

Keele

Luke

. 2008. “Taking Time Seriously.” American Journal of Political Science 52 (1): 184–200.

16.

Diehl

Paul F.

2006. “Just a Phase?: Integrating Conflict Dynamics over Time.” Conflict Management and Peace Science 23 (3): 199–210.

17.

Diehl

Paul F.

Goertz

Gary

. 2000. War and Peace in International Rivalry. Ann Arbor: University of Michigan Press.

18.

Downs

George W.

Rocke

David M.

. 1994. “Conflict, Agency, and Gambling for Resurrection: The Principal-Agent Problem Goes to War.” American Journal of Political Science 38 (2): 362–80.

19.

Esarey

Justin

DeMeritt

Jacqueline H. R.

. 2014. “Defining and Modeling State-dependent Dynamic Systems.” Political Analysis 22 (1): 61–85.

20.

Fearon

James D.

1998. “Bargaining, Enforcement, and International Cooperation.” International Organization 52 (2): 269–305.

21.

Filson

Darren

Werner

Suzanne

. 2002. “A Bargaining Model of War and Peace: Anticipating the Onset, Duration, and Outcome of War.” American Journal of Political Science 46 (4): 819–37.

22.

Findley

Michael G.

2013. “Bargaining and the Interdependent Stages of Civil War Resolution.” Journal of Conflict Resolution 57 (5): 905–32.

23.

Freeman

John R.

Jackson

John E.

. 2012. “Symposium on Models of Path Dependence.” Political Analysis 20 (2): 137–45.

24.

Frühwirth-Schnatter

Sylvia

. 2006. Finite Mixture and Markov Switching Models. New York: Springer.

25.

Geskus

Ronald B.

2015. Data Analysis with Competing Risks and Intermediate States. Boca Raton, FL: Chapman and Hall/CRC.

26.

Gochman

Charles S.

1993. “The Evolution of Militarized Disputes.” International Interactions 19 (1-2): 49–76.

27.

Goemans

H. E.

2000. War and Punishment: The Causes of War Termination and the First World War. Princeton, NJ: Princeton University Press.

28.

Goertz

Gary

. 1994. Contexts of International Politics. Cambridge, UK: Cambridge University Press.

29.

Hansen

Holley E.

Mitchell

Sara McLaughlin

Nemeth

Stephen C.

. 2008. “IO Mediation of Interstate Conflicts: Moving Beyond the Global versus Regional Dichotomy.” Journal of Conflict Resolution 52 (2): 295–325.

30.

Hensel

Paul R.

1999. “An Evolutionary Approach to the Study of Interstate Rivalry.” Conflict Management and Peace Science 17 (2): 175–206.

31.

Hensel

Paul R.

2001. “Contentious Issues and World Politics: The Management of Territorial Claims in the Americas, 1816-1992.” International Studies Quarterly 45 (1): 81–109.

32.

Hensel

Paul R.

Mitchell

Sara McLaughlin

Sowers

Thomas E.

Thyne

Clayton L.

. 2008. “Bones of Contention: Comparing Territorial, Maritime, and River Issues.” Journal of Conflict Resolution 52 (1): 117–43.

33.

Huth

Paul K.

Allee

Todd L.

. 2002. The Democratic Peace and Territorial Conflict in the Twentieth Century. Cambridge, UK: Cambridge University Press.

34.

Huth

Paul K.

Allee

Todd L.

. 2009. “Codebook for Huth and Allee Status Quo Data.” Accessed April 9, 2011. http://hdl.handle.net/1902.1/10636.

35.

Jervis

Robert

. 1997. System Effects: Complexity in Political and Social Life. Princeton, NJ: Princeton University Press.

36.

Jones

Benjamin T.

2013. “The Past Is Ever-present: Civil War as a Dynamic Process.” PhD diss., The Ohio State University, Columbus, OH.

37.

Jones

Daniel M.

Bremer

Stuart A.

David Singer

. 1996. “Militarized Interstate Disputes, 1816-1992: Rationale, Coding Rules, and Empirical Patterns.” Conflict Management and Peace Science 15 (2): 163–213.

38.

Kadera

Kelly M.

Crescenzi

Mark J. C.

Shannon

Megan L.

. 2003. “Democratic Survival, Peace, and War in the International System.” American Journal of Political Science 47 (2): 234–47.

39.

Kadera

Kelly M.

Morey

Daniel S.

. 2008. “The Trade-offs of Fighting and Investing: A Model of the Evolution of War and Peace.” Conflict Management and Peace Science 25 (2): 152–70.

40.

Kirschner

Shanna A.

2010. “Knowing Your Enemy: Information and Commitment Problems in Civil Wars.” Journal of Conflict Resolution 54 (5): 745–70.

41.

Leventoğlu

Bahar

Slantchev

Branislav L.

. 2007. “The Armed Peace: A Punctuated Equilibrium Theory of War.” American Journal of Political Science 51 (4): 755–71.

42.

Levy

Jack S.

1995. “On the Evolution of Militarized Interstate Conflicts.” In The Process of War: Advancing the Scientific Study of Wars, edited by Bremer

Stuart A.

Cusak

Thomas R.

, 219. Amsterdam, the Netherlands: Overseas Publishers Association.

43.

Licht

Amanda A.

2011. “Change Comes with Time: Substantive Interpretation of Nonproportional Hazards in Event History Analysis.” Political Analysis 19 (2): 227–43.

44.

Maoz

Zeev

. 1982. Paths to Conflict: Interstate Dispute Initiation, 1816-1976. Boulder, CO: Westview Press.

45.

Maoz

Zeev

Russett

Bruce

. 1993. “Normative and Structural Causes of Democratic Peace, 1946-1986.” American Political Science Review 87 (3): 624–38.

46.

Metzger

Shawna K.

2013. “Conflict Dynamics in Militarized Interstate Disputes.” PhD diss., University of Pittsburgh, Pittsburgh, PA.

47.

Metzger

Shawna K.

Forthcoming. “Time Is on My Side? The Impact of Timing and Dispute Type on Militarized Conflict Duration.” Conflict Management and Peace Science.

48.

Metzger

Shawna K.

Jones

Benjamin T.

. Forthcoming. “Surviving Phases: Introducing Multi-state Survival Models.” Political Analysis.

49.

Mills

Melinda

. 2004. “Stability and Change: The Structuration of Partnership Histories in Canada, the Netherlands, and the Russian Federation.” European Journal of Population 20 (2): 141–75.

50.

Morey

Daniel S.

2011. “When War Brings Peace: A Dynamic Model of the Rivalry Process.” American Journal of Political Science 55 (2): 263–75.

51.

Nieman

Mark David

. 2016. “Moments in Time: Temporal Patterns in the Effect of Democracy and Trade on Conflict.” Conflict Management and Peace Science 33 (3): 273–93.

52.

“No. 74 Finland-USSR Boundary.” 1967. International Boundary Study. Washington, DC: Office of the Geographer.

53.

Owsiak

Andrew P.

2014. “Conflict Management Trajectories in Militarized Interstate Disputes: A Conceptual Framework and Theoretical Foundations.” International Studies Review 16 (1): 50–78.

54.

Page

Scott E.

2006. “Path Dependence.” Quarterly Journal of Political Science 1 (1): 87–115.

55.

Pierson

Paul

. 2004. Politics in Time: History, Institutions, and Social Analysis. Princeton, NJ: Princeton University Press.

56.

Powell

Robert

. 2004. “Bargaining and Learning While Fighting.” American Journal of Political Science 48 (2): 344–61.

57.

Putter

Fiocco

Geskus

R. B.

. 2007. “Tutorial in Biostatistics: Competing Risks and Multi-state Models.” Statistics in Medicine 26 (11): 2389–430.

58.

Reed

William

. 2000. “A Unified Statistical Model of Conflict Onset and Escalation.” American Journal of Political Science 44 (1): 84–93.

59.

Rummel

R. J.

1976. Understanding Conflict and War. Vol. 2. Beverly Hills, CA: Sage.

60.

Russett

Bruce

Oneal

John R.

. 2001. Triangulating Peace: Democracy, Interdependence, and International Organizations. New York: W. W. Norton.

61.

Sarkees

Meredith Reid

Wayman

Frank Whelon

. 2010. Resort to War: 1816-2007. Washington, DC: CQ Press.

62.

Schrodt

Philip A.

2000. “Pattern Recognition of International Crises Using Hidden Markov Models.” In Political Complexity: Nonlinear Models of Politics, edited by Richards

Diana

, 296–328. Ann Arbor: University of Michigan Press.

63.

Senese

Paul D.

1997. “Between Dispute and War: The Effect of Joint Democracy on Interstate Conflict Escalation.” Journal of Politics 59 (1): 1–27.

64.

Senese

Paul D.

Vasquez

John A.

. 2008. The Steps to War: An Empirical Study. Princeton, NJ: Princeton University Press.

65.

Slantchev

Branislav L.

2004. “How Initiators End Their Wars: The Duration of Warfare and the Terms of Peace.” American Journal of Political Science 48 (4): 813–29.

66.

Slantchev

Branislav L.

2011. Military Threats: The Costs of Coercion and the Price of Peace. Cambridge, UK: Cambridge University Press.

67.

Smith

Alastair

Stam

Allan C.

. 2004. “Bargaining and the Nature of War.” Journal of Conflict Resolution 48 (6): 783–813.

68.

Stanley

Elizabeth A.

Sawyer

John P.

. 2009. “The Equifinality of War Termination.” Journal of Conflict Resolution 53 (5): 651–76.

69.

Therneau

Terry M.

Grambsch

Patricia M.

. 2000. Modeling Survival Data: Extending the Cox Model. New York: Springer.

70.

Vasquez

John A.

2009. The War Puzzle Revisited. Cambridge, UK: Cambridge University Press.

71.

Vollset

Stein Emil

Tverdal

Aage

Gjessing

Håkon K.

. 2006. “Smoking and Deaths between 40 and 70 Years of Age in Women and Men.” Annals of Internal Medicine 144 (6): 381–89.

72.

Walter

Barbara F.

2004. “Does Conflict Beget Conflict? Explaining Recurring Civil War.” Journal of Peace Research 41 (3): 371–88.

73.

Williams

John T.

McGinnis

Michael D.

. 1988. “Sophisticated Reaction in the U.S.-Soviet Arms Race: Evidence of Rational Expectations.” American Journal of Political Science 32 (4): 968–95.

74.

Wilson

Sven E.

Butler

Daniel M.

. 2007. “A Lot More to Do: The Sensitivity of Time-series Cross-section Analyses to Simple Alternative Specifications.” Political Analysis 15 (2): 101–23.

75.

Wreede

Liesbeth C. de

Fiocco

Marta

Putter

Hein

. 2010. “The mstate Package for Estimation and Prediction in Non- and Semi-parametric Multi-state and Competing Risks Models.” Computer Methods and Programs in Biomedicine 99 (3): 261–74.

76.

Wreede

Liesbeth C. de

Fiocco

Marta

Putter

Hein

. 2011. “mstate: An R Package for the Analysis of Competing Risks and Multi-State Models.” Journal of Statistical Software 38 (7): 1–30.

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