Motivation

Since the late 1990s, a wealth of large-N quantitative studies have emerged with the primary goal of finding statistically significant relationships that hold across a large number of states. [7] and [8] offer two canonical efforts to analyzing intra-state conflict onset that utilize this framework and demonstrate the strengths and limitations of this approach. In both studies, the authors utilize time-series cross-sectional (TSCS) datasets with independent variables that primarily vary cross-sectionally between states, rather than temporally within the same state, and a binary dependent variable reflecting intra-state conflict onset. The primary strength of this type of large-N analysis is that it has revealed that certain structural variables such as rough terrain, GDP per capita, and population size have statistically significant and relatively stable effects on the likelihood of intra-state conflict onset across time and space ([8] and [7] cover 161 states from 1946–1992 and 123 states from 1965–1999, respectively). For example, all else being equal, poorer states with mountainous terrain and large populations are more likely to experience onsets of intra-state conflict.

Although these approaches have contributed greatly to our understanding of intra-state conflict, their main weakness is that they do not account for the actual, sub-annual level events that tend to lead to conflict. For example, population and rough terrain may affect the likelihood of conflict onset in the aggregate, but these factors by themselves do not cause onsets of conflict in the sense that they are present both before and after conflict occurs. Rather, it is specific events, such as protests, demonstrations, broken peace talks, etc., that actually triggers conflict.

Conversely, event data approaches tend to focus on highly specific, sub-annual (often weekly or monthly) level variation in a broad spectrum of politically relevant events, ranging from verbal threats to diplomatic meetings to violence. However, these studies tend to focus on events occurring in a single state or multiple states involved in a joint conflict. For example, [9] and [10] analyze the Arab-Israeli conflict, [11] and [12] focus on Serbia, and [13] is interested in Chechnya. In [10], data from more than one state are interpreted jointly, whereas in other studies, such as [4], multiple states are modeled individually and then empirical findings are informally compared. The primarily goal of most of these studies is to build accurate, objective, and temporally nuanced forecast of conflicts.

We build on previous efforts by using fine-grain, comprehensive event data at the sub-state level to compare sub-annual level event sequences across a diverse set of states. Our approach is an attempt to move towards merging the predominantly cross-sectional, large-N approaches with the time-variant, event data approaches.

Event Data

The event data used in this research come from the DARPA-funded Integrated Conflict Early Warning System [14, 15]. ICEWS has invested substantial resources in all areas of event data development including the development of the automated coders, actor and action dictionaries, and for access to a very large collection of news documents. Its investment into event data development put ICEWS on a scale not seen in prior event data coding efforts. As [14] notes,

…the ICEWS performers used input data from a variety of sources. Notably, they collected 6.5 million news stories about countries in the Pacific Command (PACOM) AOR [area of responsibility] for the period 1998–2006. This resulted in a dataset about two orders of magnitude greater than any other with which we are aware. These stories comprise 253 million lines of text and came from over 75 international sources (AP, UPI, and BBC Monitor) as well as regional sources (India Today, Jakarta Post, Pakistan Newswire, and Saigon Times).

The range was eventually extended through 2010, where this study concludes, and beyond. The initial phase of ICEWS used both the Tabari and the VRA automated coding technologies, with the latter used as one of the sources to generate the ICEWS ‘events of interest’ [16–20]. These ‘events of interest’ comprise the dependent variable in this study and are discussed in more detail below. In the second phase of the project, Lockheed-Martin developed a direct translation (with some bug corrections) of Tabari into Java called Jabari, and the data produced by that system are the data utilized here [21]. These data are coded according to a 15,000-item action dictionary using the CAMEO typology and an 8,000-item actor dictionary to code for a broad range of actors, including but not limited to military, police, rebel groups, and civilians [22]. As a result of the inclusion of local and regional news sources as well as the comprehensive actor dictionary, the ICEWS dataset provides sufficient sub-state actor nuance and spatial coverage for us to address our central research question.

Aggregation Techniques

Every event coded by the ICEWS project is coded in a “who did what to whom and when” format. This raw event data provides researchers with a tremendous amount of flexibility regarding aggregation techniques for making the data usable for empirical analysis and exists across three areas of aggregation: actors, actions, and time. In this section, we provide a brief overview of common aggregation approaches in the literature and then explain the choices we make regarding actors, actions, and time to build our event sequences.

Temporal Aggregation.

Researchers must temporally aggregate data in order to perform empirical analyses at levels appropriate for both their theoretical and empirical models. All of the previously mentioned event datasets code the exact day on which events occur. As the specific time-of-day that events occur is not reported, events must at the very minimum be aggregated to the daily level [9, 11, 12]. Weekly [32, 33], monthly [28, 34], quarterly [26], and even annual level aggregations are also found in the literature.

Often, the level of temporal aggregation is more subjective than the other areas of aggregation. Furthermore, a number of studies have shown that different temporal aggregations can affect the empirical results [35–37]. Therefore, it is important to both justify the level of aggregation used and, if possible, use multiple levels as robustness checks. We use both weekly and monthly levels of temporal aggregation. Doing so allows us to capture event fluctuations that occur across small periods of time and is more robust to noise than daily level aggregations. Furthermore, it allows for robustness checks across two levels of aggregation. [4] and others have attempted to move beyond traditional, calendar-based practices by aggregating according to empirically discernible temporal clusters within the data. While we do not attempt such an aggregation here, it presents an interesting alternative.

To generate weekly and monthly-level data, we sum the event counts for all relevant actor combinations (GOV-REB, REB-OTH) across each action (verbal cooperation, material cooperation, verbal conflict, material conflict), which results in eight sequences of event counts for each unit-of-analysis (the period preceding each conflict onset and the period preceding selected peaces). For example, Table 1 contains sequences that precede a conflict onset in Indonesia. This represents the data after sequence construction but prior to sequence analysis.

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Table 1. Event Count Structures Preceding Conflict in Indonesia.

https://doi.org/10.1371/journal.pone.0122472.t001

Our approach to sequence construction differs from those utilized in the related sequence analysis literature in two main ways. First, our approach is unique in that it measures the number of events that occur within fixed units of time (weeks and months), whereas other studies such as [3], [1], and [4] focus on the sequential ordering of events regardless of time, which means that they are unable to explicitly account for the amount of time that transpire between events. Second, our approach allows for multiple events to occur between multiple actors simultaneously, whereas the extant studies place events in a sequential order. Third, we build sequences from event counts as opposed to a single event [1, 3, 38] or a conflict-cooperation scaled value [4]. We argue that utilizing counts captures the greater variation in the intensity of actions. Overall, we believe our approach to sequence construction is a more effective way capture the complexity of event structures that precede intra-state conflict onsets.

Research Design

Our research design is a combination of a sequence analysis and regression approach. Using a sequence analysis, we construct variables that reflect a degree of similarity between pairs of sequences where both precede peace, one precedes peace and one precedes conflict, and where both precede conflict. After comparing the scores for each pair type, we test for the ability of event structures to distinguish pair types using a bivariate logistic regression.

The conflict onset variable (GTDS) is a binary measure constructed from a ground truth measure of intra-state conflict that has been developed by DARPA. Table 2 is a complete listing of all conflict onsets in our data. The objective of ground truth data in conflict studies is to provide a more immediate representation of a conflict than can be provided purely by journalistic or historical reporting. Although DARPA has chosen not to publicly release the explicit coding rules for the GTDS, it has been used as a dependent variables in a number of conflicted forecasting publications, some of which are specifically designed for policy planning (see [14, 39–41] for other uses of the GTDS). The GTDS contains four categories of intra-state conflict at the monthly level: Rebellion, Insurgency, Domestic Crisis, and Ethno-religious Violence.

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Table 2. GTDS intra-state conflict Onsets.

https://doi.org/10.1371/journal.pone.0122472.t002

For a state-month to be coded as an onset in our data, a positive observation in a single category must be preceded by at least three months of peace in that category. According to this operationalization of onset, it is possible for a state to experience two or more onsets in a given month so long as the onsets occur in different categories.

To establish pairs for comparison, we select all 13-week sequences in our dataset that precede conflict and a random sample of sequences that precede peace at a ratio of about 2:1 peace-preceding:conflict-preceding. For robustness, we have also constructed these sequences at the monthly level based on three-month periods. The 2:1 ratio is ad hoc and could bias the results towards increasing the number of predicted onsets relative to what would be predicted given a true random sample. However, the peace-preceding sequences must be sampled in some fashion to avoid excessive overlapping sequences, and given the small number of onsets generally analyzed in this literature we deem 2:1 an appropriate ratio. To avoid comparing sequences where there is very little to no rebel interactions (e.g., Australia), we only randomly sample from the 15 states that experience at least one onset. This results in 113 sequences that precede peace and 53 sequences that precede conflict onset. We then calculate the similarity scores for each pair of sequences, resulting in $\left(\genfrac{}{}{0ex}{}{166}{2}\right)$, or 13,695 pairs (observations), each with eight explanatory variables (the distances between the eight count variables of each sequence).

The Euclidean distance, the most intuitive of the three and the one through which the primary results of this paper are reported, is seen in Eq (1). (1)

To illustrate this process, consider the example in Table 3. For State A, we have eight actions measured over 13 weeks. For each of these eight actions, we calculate the Euclidean distance with the corresponding action in State B. The Euclidean distance is a conceptually and mathematically straightforward approach used to calculate the distance between two vectors, and has been used in the study of International Relations in other applications [42]. This robust approach is applied to vectors according to the formula in Eq (1), in which A and B are the two states in the pair, i is the week/month, and j is the action variable (e.g., verbal cooperation). As can be seen in Table 3 for a single action, the Euclidean distance would be calculated for the sequences {5,2,3,5,2,3,0,2,1,1,2,0,0} and {4,0,1,2,1,0,0,0,1,0,0,0,4}. In this example, the Euclidean distance approximately equals 7.28.

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Table 3. Vectors of Verbal Cooperation Counts for State A and State B.

https://doi.org/10.1371/journal.pone.0122472.t003

Despite its generality, the Euclidean distance may not adequately capture similarity given the underlying event sequences are occurring in different places and at different times. For example, the distance between states with high levels of journalistic reporting and states with low levels will always be large, even if the underlying event structures are comparable. Or, events in one country may unfold over a period of months while events in another country, although similar in structure, unfold over just a few weeks. Additionally, as a second order metric the Euclidean distance may not capture higher order interdependencies in the event structures. The sequence analysis literature across disciplines is rich in applications of distance and related metrics to account for higher order interdependencies [43–45]. To further explore such interdependencies and to extract the most information from our data, we also use the Levenshtein distance and mutual information to compare event sequences.

The Levenshtein distance is an edit distance, developed and used primarily in computer science [46, 47] but with applications to sequence analysis as well [48, 49]. The intuition behind the general class of edit distances is to measure the number of computer calculations necessary to transform one string, or vector, into another. The available transformations are shifts and substitutions. A shift is an insertion that effectively shifts the sequence to the left or right. So, if two sequences are identical except for the fact that one sequence began at time t and the other at t+1, the Levenshtein distance algorithm would simply shift the sequence in the appropriate direction, just a single calculation. Substitutions are also measured as a single calculation, regardless of the “distance” between the numbers (or characters) being substituted. That is, if two sequences are perfectly aligned with the exception of the n^th character, the Levenshtein distance algorithm would simply substitute the n^th character, again just a single calculation. In other words, whereas the Euclidean distance takes into account how far apart the n^th characters in each sequence are, the Levenshtein distance views this as a single calculation regardless of the physical number.

Mutual information is an entropy-based metric from Information Theory [50]. Rather than measuring a geometric or edit distance, mutual information measures the reduction in uncertainty (entropy) about Sequence A that may be ascertained from knowledge of Sequence B. This robust metric may be particularly useful in instances where both the Euclidean and Levenshtein distances are large, but high order interdependencies still exist that the metrics do not capture. In such cases, mutual information may discover a relationship that may be useful in characterizing the sequence outcomes as something different than what the Euclidean or Levenshtein may produce. Here, we apply Linfoot’s normalization of mutual information [51], as described in [43]. Specifically, mutual information is defined in Eq (2), where X and Y represent our discrete sequences of events and I_N is the normalization of the mutual information function. (2)

Sequence Comparison

We calculate the similarity scores among all possible pairs of peace-preceding sequences and conflict-preceding sequences, which results in three types of sequence pairs for comparison:

• Type 0—Neither of the compared 13-week sequences precede conflict onset
• Type 1—One of the compared 13-week sequences precede onset and the other did not
• Type 2—Both of the 13-week sequences precede conflict

Using the Euclidean Distance to build intuition for the approach, imagine a case where event sequences in periods preceding conflict are similar across time and space. In such cases, Type 2 distances should be comparatively small. Conversely, large distances between Type 2 pairs suggests that event sequences of periods preceding conflict onset may not follow similar trends across time and space. The same logic applies to distances generated by Type 0 pairs, which will be small if periods proceeding peace exhibit similar event structures. Lastly, distances generated by Type 1 pairs reflects the extent to which periods preceding peace and conflict onset vary, meaning that small distances (relative to Type 0 and Type 2 distances) suggest that we may be unable to discern between sequences preceding peace and conflict. Thus, if sequences preceding peace are similar and sequences preceding conflict are similar (but different from those preceding peace), an empirical model will struggle to correctly differentiate between Type 0 and Type 2 pairs in an out-of-sample context. If we assume that sequences preceding peace are similar (an assumption with strong empirical support), then the extent to which patterns exist between sequences preceding a conflict onset depends on the out-of-sample misclassification of Type 2 pairs, explained by the two conditions below.

• Condition 1: If patterns exist between sequences preceding conflict, the empirical model will struggle to differentiate between Type 2 and Type 0. When the model misclassifies sequences generated by Type 2 pairs, it will predict that these sequences were generated by Type 0 pairs.
• Condition 2 If patterns do not exist between sequences preceding conflict, the empirical model will struggle to differentiate between Type 2 and Type 1 pairs. When the model misclassifies sequences generated by Type 2 pairs, it will predict that these sequences were generated by Type 1 pairs.

The histograms in Figs 1 and 2 reflect the distribution of distances by pair type for the weekly and monthly aggregations using the Euclidean distance. Since the distributions of the eight distances are very similar, they are summed to add mass to the histograms to better illustrate the differences among pair types. The correlation of various action categories is a common feature of event data research and has been reported in a number of studies [16, 27, 52].

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Fig 1. Weekly Euclidean Distances.

https://doi.org/10.1371/journal.pone.0122472.g001

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Fig 2. Monthly Euclidean Distances.

https://doi.org/10.1371/journal.pone.0122472.g002

These histograms suggest two important findings. First, distances generated by Type 0 pairs tend to be small and are clustered around 0, supporting our assumption that sequences that precede peace are similar. Second, if strong patterns existed between sequences preceding intra-state conflict onsets, then we would expect to see a spike in distribution density of the Type 2 histogram near 0. Clearly, no such spike exists. Instead, these histograms illustrate that distances generated by Type 2 pairs appear more similar to those generated by Type 1 pairs than by Type 0 pairs. Although Figs 1 and 2 provide strong visual evidence suggesting support for Condition 2, we next present an empirical model to test for which condition is being met.

Regression and Classification Analysis

To more rigorously test for similarities between pair types, we estimate a bivariate logistic regression using our distance measures as regressors and include a control for the number of ongoing crises. The bivariate logistic regression is an appropriate choice because there are two outcome variables for each pair: conflict onset in State A and conflict onset in State B [53]. The bivariate logit allows us to not only calculate the marginal probabilities of Y_A and Y_B (i.e., the probability of onset in State A and the probability of onset in State B independent of one another), but it also estimates the joint probabilities of Y_{A, B} (i.e., the probability of (no) conflict in both states), providing us with an estimate of the relationship between the two marginal probabilities of onset. Furthermore, since the regressors reflect the distance between two sequences, each of which has its own outcome, we expect that the marginal probabilities of Y_A and Y_B are strongly correlated, making the bivariate logit a theoretically justified method given our data. (3)

We use the bivariate logit to classify pair types according to the following three steps. First, we estimate our model on training data consisting of a random sample of half our observations. The regressors are the eight distance measures and a control variable to account for the number of ongoing conflicts during each state-month. The specification can be seen in Eq (3), and all estimates are computed using the VGAM package in R version 2.14.2. Second, using the estimates from the training data, predicted probabilities are calculated for each pair type using the remaining data. However, the bivariate logit provides four predicted probabilities because we have two dichotomous dependent variables—Y_A ∈ {0,1} and Y_B ∈ {0,1}—and therefore four potential outcomes: Y_{A, B} ∈ {(0,0);(0,1);(1,0);(1,1)}. The predicted probabilities for the Type 0 and Type 2 pairs are the predicted probabilities Y_{A, B} = (0,0) and Y_{A, B} = (2,2), respectively. For Type 1 pairs, the predicted probability is equal to the sum of the predicted probabilities of Y_{A, B} = (1,0) and Y_AB = (0,1) because the distance from State A to State B is the same as the distance from State B to State A (non-directional). Finally, our decision rule is to classify each pair by the highest predicted probability. For example, if the predicted probabilities of a Type 0, Type 1, and Type 2 pair are 0.7, 0.2, and 0.1 respectively, the rule classifies Type 0 to be positive while Type 1 and Type 2 are negative. The decision rule is formalized in Eq (4). (4)

The estimates from the regression model are not particularly relevant for our purposes because we are concerned with the model’s ability to distinguish among the three pair types and are not interested in the effect or explanatory power of any variable or set of variables. Additionally, high collinearity exists between the underlying count variables, which further complicates the interpretation of the coefficients. Therefore, we focus on our model’s out-of-sample classification accuracy rather than the specific covariates and their empirical significance.

The predicted and true classes for the out-of-sample observations are shown in a confusion matrix in Table 4 for the Euclidean distance. From these statistics, performance measures detailing the model’s ability to classify out-of-sample observations are calculated and reported in Table 5. Taken together, the confusion matrix and the performance measures enable the analysis of which pair types are distinguishable based on event sequences, which allows us to determine whether Condition 1 or Condition 2 receives empirical support. The performance measures of sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) are used to assess our out-of-sample classification accuracy:

• Sensitivity—the percent of all positive observations correctly classified
• Specificity—the percent of all negative observations correctly classified
• Positive Predictive Value—the percent of positive predictions that are accurate
• Negative Predictive Value—the percent of negative predictions that are accurate

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Table 4. Confusion Matrix of Bivariate Logistic Classification.

https://doi.org/10.1371/journal.pone.0122472.t004

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Table 5. Performance of Bivariate Logistic Classification.

https://doi.org/10.1371/journal.pone.0122472.t005

For our purposes, we care about the model’s ability to distinguish among types. Therefore, we would like to see that our model actually classifies observations into all three pair types. As can be seen in Table 4, at the weekly level 4,427 are predicted to be Type 0, 1,827 to be Type 1, and 674 to be Type 2, which places enough predictions in each class to move forward.

Classification Results for Levenshtein and Mutual Information.

Tables 6 and 7 detail the classification of the bivariate logit model when sequence similarity is scored using the Levenshtein distance and mutual information, both at the weekly level of aggregation. In general, the results are quite robust to the metric used and the primary finding, that Type 2 pairs continue to be classified as Type 1, remains strong in both experiments. In fact, these metrics strengthen the finding. When using the Levenshtein distance, there are 3.76 times more Type 2 pairs classified as Type 1 than there are Type 2 pairs classified as Type 0. When using the mutual information metric, there are 7.35 times more Type 2 pairs predicted to be Type 1 than there are Type 2 pairs predicted to be Type 0. In the Euclidean model, this number is 3.26. Thus, both metrics, and especially mutual information, provides more support for Condition 2 (that Type 2 pairs appear more like Type 1 than Type 0) than the Euclidean metric.

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Table 6. Confusion Matrix Using Levenshtein and Mutual Information.

https://doi.org/10.1371/journal.pone.0122472.t006

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Table 7. Performance Using Levenshtein and Mutual Information.

https://doi.org/10.1371/journal.pone.0122472.t007

Scoring the sequences using mutual information provides an additional interesting finding that should be explored in future research. Specifically, relative to the Euclidean and Levenshtein models, the mutual information model is considerably more likely to predict Type 1 pairs. Of the 6,928 out-of-sample observations, 2,499 are predicted to be Type 1 whereas just 1,827 are predicted to be Type 1 using the Euclidean metric. While the number of correctly identified Type 1 pairs is greatest for mutual information, its PPV is just 76%, compared with 79% for Levenshtein and 83% for Euclidean. Furthermore, 230 predicted Type 1 pairs are in truth Type 0, where the Levenshtein model mispredicts 103 such cases, and the Euclidean model mispredicts 0 of them. This suggests that the mutual information metric captures a relationship not represented, or represented less, by the other metrics. In future work, perhaps combinations of these classes of metrics—geometric distances, edit distances, and entropy-based—could be exploited in an ensemble method that leverages the strengths of each.

‘Masked’ Conflict.

Although each model predicts the majority of misclassified Type 2 pairs to be Type 1, they still predict 93 (Euclidean), 92 (Levenshtein), and 49 (mutual information) to be of Type 0. In the Euclidean model, of the 3,033 Type 1 pairs, 1,151 are misclassified to be Type 0. However, at the weekly level Type 0 pairs are never misclassified as Type 1 or Type 2. The intuition is that these misclassified conflict-preceding sequences are quantitatively similar to peace-preceding sequences. In other words, they are characterized predominantly by the absence of events involving rebels. These “masked” conflicts present a challenge for event data forecasting models.

We suggest two factors that may be responsible for masked conflicts. First, it is possible that some conflict onsets are not preceded by politically relevant events and occur spontaneously. For example, we believe the Tunisian Revolution that began in December, 2010 would fall into this class of conflict. However, despite the lack of observable “events”, it is possibly that changes in popular sentiments occurred prior to the onset of conflict. Moving forward, it may be possibly to capture variation in sentiments that may occur in the absence of actual events through content analysis of social media outlets like Facebook and Twitter.

Second, rebel activity may be occurring but not reported in the news. This is possible in places where rebel activity is so common that it becomes no longer newsworthy, as may be the case in the Philippines in the early 2000s. Additionally, non-reporting of actual events may occur in regions with minimal or non-existent formal journalistic reporting. ICEWS’ use of 75 international news sources is an attempt to ameliorate this concern; regardless, there will always be reporting bias in published sources. For instance, it is highly unlikely for a Hezbollah attack in Tel Aviv to go unreported, but much easier for violence on the Solomon Islands to go unreported. When modeling events, zero-inflated models [54] or occupancy models [55] could be used to correct for the disproportionate share of zeros. However, we are referring to the more general concern of sparse data introducing a form of measurement error into the event data. Although it is difficult to account for a lack of reporting, the mutual information metric would account for lower levels of reporting in such places, and this may be one reason why that model predicts just 49 Type 2 pairs to be Type 0 while the Euclidean and Levenshtein predict 93 and 92, respectively.

To illustrate where masked conflicts occur, Fig 3 is a side-by-side-by-side bar plot by state using the Euclidean model. The black bar corresponds to the state’s proportion of the 53 conflict onsets. The dark gray bar, or the middle bar, reflects to the state’s proportion of onset sequences in Type 1 pairs that have been misclassified as Type 0. The light gray bar indicates the state’s proportion of onset sequences in Type 2 pairs that have been misclassified as Type 0. As expected, the dark gray and light gray bars are almost identical.

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Fig 3. Proportion of Onsets and Masked Conflicts by State.

https://doi.org/10.1371/journal.pone.0122472.g003

If the masked conflicts were dispersed randomly by state, the black and gray bars would be roughly the same for all states. However, we see that several states have a disproportionately high share of masked conflicts while others have a disproportionately low share. The states that appear most associated with masked conflicts are Fiji [FIJ], Madagascar [MDG], and the Solomon Islands [SLB]. This is seen by the disproportionately high gray bars in comparison to the black bar for each state. As suggested above, these states are associated with masked conflicts primarily because of the absence of reporting, and thus present a challenge for event data studies. On the other hand, masked conflicts do not occur in Indonesia [IDN], India [IND], Sri Lanka [LKA] or the Philippines [PHL], which the absence of both dark and light gray bars for these states demonstrates. The absence of masked conflicts in these states, which likely receive more comprehensive reporting, suggests potential media bias.