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<!DOCTYPE html>
<html >
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<title>Chasing The Trajectory of Terrorism: A Machine Learning Based Approach to Achieve Open Source Intelligence</title>
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<meta name="twitter:title" content="Chasing The Trajectory of Terrorism: A Machine Learning Based Approach to Achieve Open Source Intelligence" />
<meta name="author" content="Pranav Pandya">
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<li><a href="./"></a></li>
<li class="divider"></li>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html"><i class="fa fa-check"></i>Introduction</a><ul>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#definition-of-terrorism"><i class="fa fa-check"></i>Definition of terrorism</a></li>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#problem-statement"><i class="fa fa-check"></i>Problem statement</a></li>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#research-design-and-data"><i class="fa fa-check"></i>Research design and data</a></li>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#policy-and-practice-implications"><i class="fa fa-check"></i>Policy and practice implications</a></li>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html#deliverables"><i class="fa fa-check"></i>Deliverables</a></li>
</ul></li>
<li class="chapter" data-level="1" data-path="1-essentials-counter.html"><a href="1-essentials-counter.html"><i class="fa fa-check"></i><b>1</b> Essentials of Counterterrorism</a><ul>
<li class="chapter" data-level="1.1" data-path="1-essentials-counter.html"><a href="1-essentials-counter.html#intelligence-disciplines"><i class="fa fa-check"></i><b>1.1</b> Intelligence disciplines</a></li>
<li class="chapter" data-level="1.2" data-path="1-essentials-counter.html"><a href="1-essentials-counter.html#osint-and-data-relevance"><i class="fa fa-check"></i><b>1.2</b> OSINT and data relevance</a><ul>
<li class="chapter" data-level="1.2.1" data-path="1-essentials-counter.html"><a href="1-essentials-counter.html#open-source-databases-on-terrorism"><i class="fa fa-check"></i><b>1.2.1</b> Open-source databases on terrorism</a></li>
</ul></li>
<li class="chapter" data-level="1.3" data-path="1-essentials-counter.html"><a href="1-essentials-counter.html#whats-important-in-terrorism-research"><i class="fa fa-check"></i><b>1.3</b> What’s important in terrorism research?</a><ul>
<li class="chapter" data-level="1.3.1" data-path="1-essentials-counter.html"><a href="1-essentials-counter.html#primary-vs-secondary-sources"><i class="fa fa-check"></i><b>1.3.1</b> Primary vs secondary sources</a></li>
<li class="chapter" data-level="1.3.2" data-path="1-essentials-counter.html"><a href="1-essentials-counter.html#use-of-statistical-analysis"><i class="fa fa-check"></i><b>1.3.2</b> Use of statistical analysis</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="2" data-path="2-literature-review.html"><a href="2-literature-review.html"><i class="fa fa-check"></i><b>2</b> Literature Review</a><ul>
<li class="chapter" data-level="2.1" data-path="2-literature-review.html"><a href="2-literature-review.html#overview-of-prior-research"><i class="fa fa-check"></i><b>2.1</b> Overview of prior research</a><ul>
<li class="chapter" data-level="2.1.1" data-path="2-literature-review.html"><a href="2-literature-review.html#harsh-realities"><i class="fa fa-check"></i><b>2.1.1</b> Harsh realities</a></li>
<li class="chapter" data-level="2.1.2" data-path="2-literature-review.html"><a href="2-literature-review.html#review-of-relevant-literature"><i class="fa fa-check"></i><b>2.1.2</b> Review of relevant literature</a></li>
<li class="chapter" data-level="2.1.3" data-path="2-literature-review.html"><a href="2-literature-review.html#gtd-and-machine-learning-in-previous-research"><i class="fa fa-check"></i><b>2.1.3</b> GTD and machine learning in previous research</a></li>
</ul></li>
<li class="chapter" data-level="2.2" data-path="2-literature-review.html"><a href="2-literature-review.html#literature-gap-and-relevance"><i class="fa fa-check"></i><b>2.2</b> Literature gap and relevance</a></li>
</ul></li>
<li class="chapter" data-level="3" data-path="3-impact-analysis.html"><a href="3-impact-analysis.html"><i class="fa fa-check"></i><b>3</b> Impact Analysis</a><ul>
<li class="chapter" data-level="3.1" data-path="3-impact-analysis.html"><a href="3-impact-analysis.html#data-preparation"><i class="fa fa-check"></i><b>3.1</b> Data preparation</a></li>
<li class="chapter" data-level="3.2" data-path="3-impact-analysis.html"><a href="3-impact-analysis.html#global-overview"><i class="fa fa-check"></i><b>3.2</b> Global overview</a></li>
<li class="chapter" data-level="3.3" data-path="3-impact-analysis.html"><a href="3-impact-analysis.html#the-top-10-most-active-and-violent-groups"><i class="fa fa-check"></i><b>3.3</b> The top 10 most active and violent groups</a></li>
<li class="chapter" data-level="3.4" data-path="3-impact-analysis.html"><a href="3-impact-analysis.html#the-major-and-minor-epicenters"><i class="fa fa-check"></i><b>3.4</b> The major and minor epicenters</a></li>
</ul></li>
<li class="chapter" data-level="4" data-path="4-hypothesis-testing.html"><a href="4-hypothesis-testing.html"><i class="fa fa-check"></i><b>4</b> Statistical Hypothesis Testing</a><ul>
<li class="chapter" data-level="4.1" data-path="4-hypothesis-testing.html"><a href="4-hypothesis-testing.html#data-preparation-1"><i class="fa fa-check"></i><b>4.1</b> Data preparation</a></li>
<li class="chapter" data-level="4.2" data-path="4-hypothesis-testing.html"><a href="4-hypothesis-testing.html#correlation-test"><i class="fa fa-check"></i><b>4.2</b> Correlation test</a></li>
<li class="chapter" data-level="4.3" data-path="4-hypothesis-testing.html"><a href="4-hypothesis-testing.html#hypothesis-test-fatalities-vs-groups"><i class="fa fa-check"></i><b>4.3</b> Hypothesis test: fatalities vs groups</a><ul>
<li class="chapter" data-level="4.3.1" data-path="4-hypothesis-testing.html"><a href="4-hypothesis-testing.html#anova-test"><i class="fa fa-check"></i><b>4.3.1</b> ANOVA test</a></li>
<li class="chapter" data-level="4.3.2" data-path="4-hypothesis-testing.html"><a href="4-hypothesis-testing.html#posthoc-test"><i class="fa fa-check"></i><b>4.3.2</b> PostHoc test</a></li>
<li class="chapter" data-level="4.3.3" data-path="4-hypothesis-testing.html"><a href="4-hypothesis-testing.html#interpretation"><i class="fa fa-check"></i><b>4.3.3</b> Interpretation</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="5" data-path="5-pattern-discovery.html"><a href="5-pattern-discovery.html"><i class="fa fa-check"></i><b>5</b> Pattern discovery</a><ul>
<li class="chapter" data-level="5.1" data-path="5-pattern-discovery.html"><a href="5-pattern-discovery.html#data-preparation-2"><i class="fa fa-check"></i><b>5.1</b> Data preparation</a></li>
<li class="chapter" data-level="5.2" data-path="5-pattern-discovery.html"><a href="5-pattern-discovery.html#explanation-of-key-terms"><i class="fa fa-check"></i><b>5.2</b> Explanation of key terms</a></li>
<li class="chapter" data-level="5.3" data-path="5-pattern-discovery.html"><a href="5-pattern-discovery.html#islamic-state-isil"><i class="fa fa-check"></i><b>5.3</b> Islamic State (ISIL)</a><ul>
<li class="chapter" data-level="5.3.1" data-path="5-pattern-discovery.html"><a href="5-pattern-discovery.html#apriori-model-summary"><i class="fa fa-check"></i><b>5.3.1</b> Apriori model summary</a></li>
<li class="chapter" data-level="5.3.2" data-path="5-pattern-discovery.html"><a href="5-pattern-discovery.html#top-5-patterns-isil"><i class="fa fa-check"></i><b>5.3.2</b> Top 5 patterns (ISIL)</a></li>
<li class="chapter" data-level="5.3.3" data-path="5-pattern-discovery.html"><a href="5-pattern-discovery.html#network-graph-isil"><i class="fa fa-check"></i><b>5.3.3</b> Network graph (ISIL)</a></li>
</ul></li>
<li class="chapter" data-level="5.4" data-path="5-pattern-discovery.html"><a href="5-pattern-discovery.html#taliban"><i class="fa fa-check"></i><b>5.4</b> Taliban</a><ul>
<li class="chapter" data-level="5.4.1" data-path="5-pattern-discovery.html"><a href="5-pattern-discovery.html#apriori-model-summary-1"><i class="fa fa-check"></i><b>5.4.1</b> Apriori model summary</a></li>
<li class="chapter" data-level="5.4.2" data-path="5-pattern-discovery.html"><a href="5-pattern-discovery.html#top-5-patterns-taliban"><i class="fa fa-check"></i><b>5.4.2</b> Top 5 patterns (Taliban)</a></li>
<li class="chapter" data-level="5.4.3" data-path="5-pattern-discovery.html"><a href="5-pattern-discovery.html#network-graph-taliban"><i class="fa fa-check"></i><b>5.4.3</b> Network graph (Taliban)</a></li>
</ul></li>
<li class="chapter" data-level="5.5" data-path="5-pattern-discovery.html"><a href="5-pattern-discovery.html#boko-haram"><i class="fa fa-check"></i><b>5.5</b> Boko Haram</a><ul>
<li class="chapter" data-level="5.5.1" data-path="5-pattern-discovery.html"><a href="5-pattern-discovery.html#apriori-model-summary-2"><i class="fa fa-check"></i><b>5.5.1</b> Apriori model summary</a></li>
<li class="chapter" data-level="5.5.2" data-path="5-pattern-discovery.html"><a href="5-pattern-discovery.html#top-5-patterns-boko-haram"><i class="fa fa-check"></i><b>5.5.2</b> Top 5 patterns (Boko Haram)</a></li>
<li class="chapter" data-level="5.5.3" data-path="5-pattern-discovery.html"><a href="5-pattern-discovery.html#network-graph-boko-haram"><i class="fa fa-check"></i><b>5.5.3</b> Network graph (Boko Haram)</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="6" data-path="6-time-series.html"><a href="6-time-series.html"><i class="fa fa-check"></i><b>6</b> Time-series Forecasting</a><ul>
<li class="chapter" data-level="6.1" data-path="6-time-series.html"><a href="6-time-series.html#afghanistan-predict-future-attacks"><i class="fa fa-check"></i><b>6.1</b> Afghanistan (Predict future attacks)</a><ul>
<li class="chapter" data-level="6.1.1" data-path="6-time-series.html"><a href="6-time-series.html#data-preparation-3"><i class="fa fa-check"></i><b>6.1.1</b> Data preparation</a></li>
<li class="chapter" data-level="6.1.2" data-path="6-time-series.html"><a href="6-time-series.html#seasonality-analysis"><i class="fa fa-check"></i><b>6.1.2</b> Seasonality analysis</a></li>
<li class="chapter" data-level="6.1.3" data-path="6-time-series.html"><a href="6-time-series.html#correlation-test-1"><i class="fa fa-check"></i><b>6.1.3</b> Correlation test</a></li>
<li class="chapter" data-level="6.1.4" data-path="6-time-series.html"><a href="6-time-series.html#modelling"><i class="fa fa-check"></i><b>6.1.4</b> Modelling</a></li>
<li class="chapter" data-level="6.1.5" data-path="6-time-series.html"><a href="6-time-series.html#evaluating-models-performance"><i class="fa fa-check"></i><b>6.1.5</b> Evaluating models’ Performance</a></li>
<li class="chapter" data-level="6.1.6" data-path="6-time-series.html"><a href="6-time-series.html#ensemble"><i class="fa fa-check"></i><b>6.1.6</b> Ensemble</a></li>
<li class="chapter" data-level="6.1.7" data-path="6-time-series.html"><a href="6-time-series.html#forecast-future-number-of-attacks"><i class="fa fa-check"></i><b>6.1.7</b> Forecast future number of attacks</a></li>
</ul></li>
<li class="chapter" data-level="6.2" data-path="6-time-series.html"><a href="6-time-series.html#iraq-predict-future-fatalities"><i class="fa fa-check"></i><b>6.2</b> Iraq (Predict future fatalities)</a><ul>
<li class="chapter" data-level="6.2.1" data-path="6-time-series.html"><a href="6-time-series.html#data-preparation-4"><i class="fa fa-check"></i><b>6.2.1</b> Data preparation</a></li>
<li class="chapter" data-level="6.2.2" data-path="6-time-series.html"><a href="6-time-series.html#seasonality-analysis-1"><i class="fa fa-check"></i><b>6.2.2</b> Seasonality analysis</a></li>
<li class="chapter" data-level="6.2.3" data-path="6-time-series.html"><a href="6-time-series.html#correlation-test-2"><i class="fa fa-check"></i><b>6.2.3</b> Correlation test</a></li>
<li class="chapter" data-level="6.2.4" data-path="6-time-series.html"><a href="6-time-series.html#modelling-1"><i class="fa fa-check"></i><b>6.2.4</b> Modelling</a></li>
<li class="chapter" data-level="6.2.5" data-path="6-time-series.html"><a href="6-time-series.html#ensemble-1"><i class="fa fa-check"></i><b>6.2.5</b> Ensemble</a></li>
<li class="chapter" data-level="6.2.6" data-path="6-time-series.html"><a href="6-time-series.html#forecast-future-fatalities"><i class="fa fa-check"></i><b>6.2.6</b> Forecast future fatalities</a></li>
</ul></li>
<li class="chapter" data-level="6.3" data-path="6-time-series.html"><a href="6-time-series.html#sahel-region-predict-future-attacks"><i class="fa fa-check"></i><b>6.3</b> SAHEL Region (Predict future attacks)</a><ul>
<li class="chapter" data-level="6.3.1" data-path="6-time-series.html"><a href="6-time-series.html#data-preparation-5"><i class="fa fa-check"></i><b>6.3.1</b> Data preparation</a></li>
<li class="chapter" data-level="6.3.2" data-path="6-time-series.html"><a href="6-time-series.html#seasonality-analysis-2"><i class="fa fa-check"></i><b>6.3.2</b> Seasonality analysis</a></li>
<li class="chapter" data-level="6.3.3" data-path="6-time-series.html"><a href="6-time-series.html#correlation-test-3"><i class="fa fa-check"></i><b>6.3.3</b> Correlation test</a></li>
<li class="chapter" data-level="6.3.4" data-path="6-time-series.html"><a href="6-time-series.html#modelling-2"><i class="fa fa-check"></i><b>6.3.4</b> Modelling</a></li>
<li class="chapter" data-level="6.3.5" data-path="6-time-series.html"><a href="6-time-series.html#ensemble-2"><i class="fa fa-check"></i><b>6.3.5</b> Ensemble</a></li>
<li class="chapter" data-level="6.3.6" data-path="6-time-series.html"><a href="6-time-series.html#forecast-future-attacks"><i class="fa fa-check"></i><b>6.3.6</b> Forecast future attacks</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="7" data-path="7-classification.html"><a href="7-classification.html"><i class="fa fa-check"></i><b>7</b> Predicting Class Probabilities</a><ul>
<li class="chapter" data-level="7.1" data-path="7-classification.html"><a href="7-classification.html#evolution-of-gradient-boosting-machines"><i class="fa fa-check"></i><b>7.1</b> Evolution of Gradient Boosting Machines</a><ul>
<li class="chapter" data-level="7.1.1" data-path="7-classification.html"><a href="7-classification.html#lightgbm"><i class="fa fa-check"></i><b>7.1.1</b> LightGBM</a></li>
<li class="chapter" data-level="7.1.2" data-path="7-classification.html"><a href="7-classification.html#the-mechanism-behind-the-improvised-accuracy"><i class="fa fa-check"></i><b>7.1.2</b> The mechanism behind the improvised accuracy</a></li>
</ul></li>
<li class="chapter" data-level="7.2" data-path="7-classification.html"><a href="7-classification.html#data-preparation-6"><i class="fa fa-check"></i><b>7.2</b> Data preparation</a></li>
<li class="chapter" data-level="7.3" data-path="7-classification.html"><a href="7-classification.html#overview-of-the-target-variable"><i class="fa fa-check"></i><b>7.3</b> Overview of the target variable</a><ul>
<li class="chapter" data-level="7.3.1" data-path="7-classification.html"><a href="7-classification.html#dealing-with-class-imbalance"><i class="fa fa-check"></i><b>7.3.1</b> Dealing with class imbalance</a></li>
</ul></li>
<li class="chapter" data-level="7.4" data-path="7-classification.html"><a href="7-classification.html#feature-engineering"><i class="fa fa-check"></i><b>7.4</b> Feature engineering</a></li>
<li class="chapter" data-level="7.5" data-path="7-classification.html"><a href="7-classification.html#validation-strategy"><i class="fa fa-check"></i><b>7.5</b> Validation strategy</a></li>
<li class="chapter" data-level="7.6" data-path="7-classification.html"><a href="7-classification.html#hyperparameter-optimization"><i class="fa fa-check"></i><b>7.6</b> Hyperparameter optimization</a></li>
<li class="chapter" data-level="7.7" data-path="7-classification.html"><a href="7-classification.html#modelling-3"><i class="fa fa-check"></i><b>7.7</b> Modelling</a><ul>
<li class="chapter" data-level="7.7.1" data-path="7-classification.html"><a href="7-classification.html#model-evaluation"><i class="fa fa-check"></i><b>7.7.1</b> Model evaluation</a></li>
<li class="chapter" data-level="7.7.2" data-path="7-classification.html"><a href="7-classification.html#confusion-matrix"><i class="fa fa-check"></i><b>7.7.2</b> Confusion Matrix</a></li>
<li class="chapter" data-level="7.7.3" data-path="7-classification.html"><a href="7-classification.html#feature-importance"><i class="fa fa-check"></i><b>7.7.3</b> Feature importance</a></li>
</ul></li>
<li class="chapter" data-level="7.8" data-path="7-classification.html"><a href="7-classification.html#model-interpretation"><i class="fa fa-check"></i><b>7.8</b> Model interpretation</a></li>
</ul></li>
<li class="chapter" data-level="8" data-path="8-conclusion.html"><a href="8-conclusion.html"><i class="fa fa-check"></i><b>8</b> Discussion and Conclusion</a><ul>
<li class="chapter" data-level="8.1" data-path="8-conclusion.html"><a href="8-conclusion.html#research-limitations-and-future-work"><i class="fa fa-check"></i><b>8.1</b> Research limitations and future work</a></li>
</ul></li>
<li class="appendix"><span><b>Appendix</b></span></li>
<li class="chapter" data-level="A" data-path="A-appendix-i.html"><a href="A-appendix-i.html"><i class="fa fa-check"></i><b>A</b> Appendix I</a><ul>
<li class="chapter" data-level="A.1" data-path="A-appendix-i.html"><a href="A-appendix-i.html#initial-data-preparation-script"><i class="fa fa-check"></i><b>A.1</b> Initial data preparation script</a></li>
<li class="chapter" data-level="A.2" data-path="A-appendix-i.html"><a href="A-appendix-i.html#list-of-variables-and-short-description"><i class="fa fa-check"></i><b>A.2</b> List of variables and short description</a></li>
<li class="chapter" data-level="A.3" data-path="A-appendix-i.html"><a href="A-appendix-i.html#r-session-info"><i class="fa fa-check"></i><b>A.3</b> R Session Info:</a></li>
</ul></li>
<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
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<section class="normal" id="section-">
<div id="hypothesis-testing" class="section level1">
<h1><span class="header-section-number">Chapter 4</span> Statistical Hypothesis Testing</h1>
<p>In this chapter, first, we examine the strength of the relationship between two numerical variables using Pearson correlation coefficient. This way, we can get an idea of which variables have strong/weak and positive/negative correlation with each other. In the second part, we perform a hypothesis test between each of the top ten groups and the number of fatalities to see which groups represent similarity and differences. We use the data related to the top ten most active and violent groups only.</p>
<div id="data-preparation-1" class="section level2">
<h2><span class="header-section-number">4.1</span> Data preparation</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">dfh <-<span class="st"> </span>df <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span><span class="kw">filter</span>(group_name <span class="op">%in%</span><span class="st"> </span>top10_groups) <span class="op">%>%</span><span class="st"> </span><span class="co"># filter data by top 10 groups</span>
<span class="st"> </span><span class="kw">replace_na</span>(<span class="kw">list</span>(<span class="dt">nkill =</span> <span class="dv">0</span>, <span class="dt">nwound =</span> <span class="dv">0</span>)) <span class="co"># replace NAs</span>
<span class="co"># Shorten lengthy group names</span>
dfh<span class="op">$</span>group_name[dfh<span class="op">$</span>group_name <span class="op">==</span><span class="st"> "Kurdistan Workers' Party (PKK)"</span>] <-<span class="st"> "PKK"</span>
dfh<span class="op">$</span>group_name[dfh<span class="op">$</span>group_name <span class="op">==</span><span class="st"> "Al-Qaida in the Arabian Peninsula (AQAP)"</span>] <-<span class="st"> "AQAP"</span>
dfh<span class="op">$</span>group_name[dfh<span class="op">$</span>group_name <span class="op">==</span><span class="st"> "Houthi extremists (Ansar Allah)"</span>] <-<span class="st"> "Houthi_Extrm"</span>
dfh<span class="op">$</span>group_name[dfh<span class="op">$</span>group_name <span class="op">==</span><span class="st"> "Tehrik-i-Taliban Pakistan (TTP)"</span>] <-<span class="st"> "TTP"</span>
dfh<span class="op">$</span>group_name[dfh<span class="op">$</span>group_name <span class="op">==</span><span class="st"> "Al-Nusrah Front"</span>] <-<span class="st"> "Al-Nusrah"</span>
dfh<span class="op">$</span>group_name[dfh<span class="op">$</span>group_name <span class="op">==</span><span class="st"> "Islamic State of Iraq and the Levant (ISIL)"</span>] <-<span class="st">"ISIL"</span>
dfh<span class="op">$</span>group_name[dfh<span class="op">$</span>group_name <span class="op">==</span><span class="st"> "Donetsk People's Republic"</span>] <-<span class="st"> "Donetsk_PR"</span> </code></pre></div>
</div>
<div id="correlation-test" class="section level2">
<h2><span class="header-section-number">4.2</span> Correlation test</h2>
<p>We use pairwise complete observations method to compute correlation coefficients for each pair of numerical variables.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co">#Extract numeric variables</span>
tmp <-<span class="st"> </span>dfh <span class="op">%>%</span>
<span class="st"> </span><span class="kw">select</span>(intl_ideological_attack, intl_logistical_attack,
part_of_multiple_attacks, n_peace_keepers, net_migration,
refugee_asylum, refugee_origin, gdp_per_capita, arms_import,
arms_export, conflict_index, population, extended,
nwound, nkill, suicide_attack, attack_success)
<span class="co"># get the correlation matrix</span>
m <-<span class="st"> </span><span class="kw">cor</span>(tmp, <span class="dt">use=</span><span class="st">"pairwise.complete.obs"</span>)
<span class="co"># Get rid of all non significant correlations</span>
ctest <-<span class="st"> </span><span class="kw">PairApply</span>(tmp, <span class="dt">symmetric=</span><span class="ot">TRUE</span>,
<span class="cf">function</span>(x, y) <span class="kw">cor.test</span>(x, y)<span class="op">$</span>p.value)
m[ctest <span class="op">></span><span class="st"> </span><span class="fl">0.05</span>] <-<span class="st"> </span><span class="ot">NA</span> <span class="co"># Replace p value > 0.05 with NAs</span>
<span class="kw">PlotWeb</span>(m, <span class="dt">lwd =</span> <span class="kw">abs</span>(m[<span class="kw">lower.tri</span>(m)] <span class="op">*</span><span class="st"> </span><span class="dv">10</span>),
<span class="dt">main=</span><span class="st">"Correlation Web Plot"</span>,
<span class="dt">cex.lab =</span> <span class="fl">0.85</span>, <span class="dt">pt.bg =</span> <span class="st">"#f2f2f2"</span>,
<span class="dt">args.legend =</span> <span class="kw">list</span>(<span class="dt">x =</span> <span class="st">"bottomright"</span>, <span class="dt">cex =</span> <span class="fl">0.75</span>, <span class="dt">bty =</span> <span class="st">"0"</span>,
<span class="dt">title =</span> <span class="st">"Correlation"</span>))</code></pre></div>
<div class="figure" style="text-align: center"><span id="fig:unnamed-chunk-28"></span>
<img src="thesis_files/figure-html/unnamed-chunk-28-1.png" alt="Correlation web plot" width="100%" />
<p class="caption">
Figure 4.1: Correlation web plot
</p>
</div>
<p>In the plot above, line width between the nodes is used in proportion to the correlation of two variables. To focus only on significant correlations, I have replaced observations with p-value more than 0.05 with NA. Legend on the bottom right represents correlation coefficient by line width and color depending on positive or negative linear relationship. The variables on the left-hand side of the plot are extracted from World Bank data (development indicators) and variables on the right-hand side are from GTD.</p>
<p>Specifically, we are more interested in the relationship to the variables on the right-hand side which will be used in time-series forecasting and classification modeling as the target variable. For example, a number of people wounded (nwound) variable has a positive linear relationship with a suicide attack. The conflict index variable shows a strong positive relationship with international ideological attacks and minor positive relationship with a part of multiple attacks. Overall, we can see that the majority of numerical variables shows a relationship with each other.</p>
</div>
<div id="hypothesis-test-fatalities-vs-groups" class="section level2">
<h2><span class="header-section-number">4.3</span> Hypothesis test: fatalities vs groups</h2>
<p>The objective behind this hypothesis test is to determine whether or not means of the top 10 groups with respect to average fatalities are same. If at least one sample mean is different to others then we determine which pair of groups are different.</p>
<p><span class="math display">\[
\large
\begin{aligned}
{H_0 : } & \text{ The means of the different groups are the same} \\
&{(ISIL)} = {(Taliban)} = {(AQAP)} = {(PKK)} = \\
&{(Al-Shabaab)} = {(TTP)} = {(Boko Haram)} = \\
&{(Al-Nusrah)} = {(Donetsk_PR)} = {(Houthi_Extrm)} \\ \\
H_a: & \text{ At least one sample mean is not equal to the others}
\end{aligned}
\]</span></p>
<p>First, we use a box plot to examine distribution by quartiles for each group.</p>
<div class="figure" style="text-align: center"><span id="fig:unnamed-chunk-29"></span>
<img src="thesis_files/figure-html/unnamed-chunk-29-1.png" alt="Boxplot: group vs fatalities" width="100%" />
<p class="caption">
Figure 4.2: Boxplot: group vs fatalities
</p>
</div>
<p>In statistical terms, we have some extreme outliers i.e. nkill ~ 1500 in ISIL group so X axis is log transformed for visualization purpose.</p>
<div id="anova-test" class="section level3">
<h3><span class="header-section-number">4.3.1</span> ANOVA test</h3>
<p>The ANOVA model computes the residual variance and the variance between sample means in order to calculate the F-statistic. This is the first step to determine whether or not means are different in a pair of groups.</p>
<p><span class="math display">\[
\large
\begin{aligned}
F-statistic = & (S^2_{between}\ / S^2_{within})
\end{aligned}
\]</span></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co">#------------------------------------------</span>
<span class="co"># Compute the analysis of variance (ANOVA)</span>
<span class="co">#------------------------------------------</span>
r.aov <-<span class="st"> </span><span class="kw">aov</span>(nkill <span class="op">~</span><span class="st"> </span>group_name , <span class="dt">data =</span> dfh)
<span class="co"># display result</span>
<span class="kw">summary</span>(r.aov)</code></pre></div>
<pre><code> Df Sum Sq Mean Sq F value Pr(>F)
group_name 9 111070 12341 40.7 <0.0000000000000002 ***
Residuals 21770 6597154 303
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</code></pre>
<p>The model summary provides us F value and Pr(>F) corresponding to the p-value of the test. As we can see that the p-value is < 0.05, which means there are significant differences between the groups. In other words, we reject the null hypothesis. From this test, we identified that some of the group means are different however we don’t know which pair of groups have different means.</p>
</div>
<div id="posthoc-test" class="section level3">
<h3><span class="header-section-number">4.3.2</span> PostHoc test</h3>
<p>PostHoc test is useful to determine where the differences occurred between groups. For this test, we use several different methods for the comparison purpose. This method can be classified as either conservative or liberal approach. Conservative methods are considered to be robust against committing Type I error as they use more stringent criterion for statistical significance. First, we run the PostHoc test by comparing results (p-value) from The Fisher LSD (Least Significant Different), Scheffe and Dunn’s (Bonferroni) test.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co">#------------------------------------------</span>
<span class="co"># compare p-values for 3 methods</span>
<span class="co">#------------------------------------------</span>
posthoc1 <-<span class="st"> </span><span class="kw">as.data.frame</span>(
<span class="kw">cbind</span>(
<span class="dt">lsd=</span> <span class="kw">PostHocTest</span>(
r.aov, <span class="dt">method=</span><span class="st">"lsd"</span>)<span class="op">$</span>group_name[,<span class="st">"pval"</span>], <span class="co"># The Fisher LSD</span>
<span class="dt">scheffe=</span> <span class="kw">PostHocTest</span>(
r.aov, <span class="dt">method=</span><span class="st">"scheffe"</span>)<span class="op">$</span>group_name[,<span class="st">"pval"</span>], <span class="co"># Scheffe</span>
<span class="dt">bonf=</span><span class="kw">PostHocTest</span>(
r.aov, <span class="dt">method=</span><span class="st">"bonf"</span>)<span class="op">$</span>group_name[,<span class="st">"pval"</span>]) <span class="co"># Bonferroni</span>
)
posthoc1 <-<span class="st"> </span><span class="kw">rownames_to_column</span>(posthoc1, <span class="dt">var =</span> <span class="st">"Pair of groups"</span>) <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span><span class="kw">arrange</span>(<span class="kw">desc</span>(scheffe)) </code></pre></div>
<table class="kable_wrapper table" style="font-size: 11px; width: auto !important; margin-left: auto; margin-right: auto;">
<caption style="font-size: initial !important;">
<span id="tab:unnamed-chunk-32">Table 4.1: </span>Posthoc test (lsd, scheffe, bonf)
</caption>
<tbody>
<tr>
<td>
<table>
<thead>
<tr>
<th style="text-align:left;">
Pair of groups
</th>
<th style="text-align:right;">
lsd
</th>
<th style="text-align:right;">
scheffe
</th>
<th style="text-align:right;">
bonf
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
Donetsk_PR-Al-Shabaab
</td>
<td style="text-align:right;">
0.9191
</td>
<td style="text-align:right;">
1.0000
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
Houthi_Extrm-Al-Shabaab
</td>
<td style="text-align:right;">
0.7934
</td>
<td style="text-align:right;">
1.0000
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
Houthi_Extrm-Donetsk_PR
</td>
<td style="text-align:right;">
0.7797
</td>
<td style="text-align:right;">
1.0000
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
Taliban-AQAP
</td>
<td style="text-align:right;">
0.6811
</td>
<td style="text-align:right;">
1.0000
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
PKK-Donetsk_PR
</td>
<td style="text-align:right;">
0.5800
</td>
<td style="text-align:right;">
1.0000
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
Houthi_Extrm-AQAP
</td>
<td style="text-align:right;">
0.4850
</td>
<td style="text-align:right;">
1.0000
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
Donetsk_PR-AQAP
</td>
<td style="text-align:right;">
0.3615
</td>
<td style="text-align:right;">
0.9997
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
PKK-Houthi_Extrm
</td>
<td style="text-align:right;">
0.3152
</td>
<td style="text-align:right;">
0.9994
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
PKK-Al-Shabaab
</td>
<td style="text-align:right;">
0.3021
</td>
<td style="text-align:right;">
0.9993
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
AQAP-Al-Shabaab
</td>
<td style="text-align:right;">
0.2561
</td>
<td style="text-align:right;">
0.9984
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
Taliban-Houthi_Extrm
</td>
<td style="text-align:right;">
0.1928
</td>
<td style="text-align:right;">
0.9954
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
TTP-AQAP
</td>
<td style="text-align:right;">
0.1508
</td>
<td style="text-align:right;">
0.9904
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
Taliban-Donetsk_PR
</td>
<td style="text-align:right;">
0.1476
</td>
<td style="text-align:right;">
0.9898
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
TTP-Taliban
</td>
<td style="text-align:right;">
0.1253
</td>
<td style="text-align:right;">
0.9846
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
Boko Haram-Al-Nusrah
</td>
<td style="text-align:right;">
0.0851
</td>
<td style="text-align:right;">
0.9656
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
PKK-AQAP
</td>
<td style="text-align:right;">
0.0610
</td>
<td style="text-align:right;">
0.9406
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
TTP-Houthi_Extrm
</td>
<td style="text-align:right;">
0.0324
</td>
<td style="text-align:right;">
0.8694
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
TTP-Donetsk_PR
</td>
<td style="text-align:right;">
0.0278
</td>
<td style="text-align:right;">
0.8481
</td>
<td style="text-align:right;">
1.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
Taliban-Al-Shabaab
</td>
<td style="text-align:right;">
0.0135
</td>
<td style="text-align:right;">
0.7301
</td>
<td style="text-align:right;">
0.6094
</td>
</tr>
<tr>
<td style="text-align:left;">
TTP-Al-Shabaab
</td>
<td style="text-align:right;">
0.0024
</td>
<td style="text-align:right;">
0.4187
</td>
<td style="text-align:right;">
0.1088
</td>
</tr>
<tr>
<td style="text-align:left;">
ISIL-Al-Nusrah
</td>
<td style="text-align:right;">
0.0008
</td>
<td style="text-align:right;">
0.2574
</td>
<td style="text-align:right;">
0.0354
</td>
</tr>
<tr>
<td style="text-align:left;">
Taliban-PKK
</td>
<td style="text-align:right;">
0.0005
</td>
<td style="text-align:right;">
0.2071
</td>
<td style="text-align:right;">
0.0226
</td>
</tr>
<tr>
<td style="text-align:left;">
ISIL-Boko Haram
</td>
<td style="text-align:right;">
0.0002
</td>
<td style="text-align:right;">
0.1338
</td>
<td style="text-align:right;">
0.0097
</td>
</tr>
</tbody>
</table>
</td>
<td>
<table>
<thead>
<tr>
<th style="text-align:left;">
Pair of groups
</th>
<th style="text-align:right;">
lsd
</th>
<th style="text-align:right;">
scheffe
</th>
<th style="text-align:right;">
bonf
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
TTP-PKK
</td>
<td style="text-align:right;">
0.0002
</td>
<td style="text-align:right;">
0.1172
</td>
<td style="text-align:right;">
0.0076
</td>
</tr>
<tr>
<td style="text-align:left;">
TTP-ISIL
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0072
</td>
<td style="text-align:right;">
0.0001
</td>
</tr>
<tr>
<td style="text-align:left;">
TTP-Al-Nusrah
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0006
</td>
<td style="text-align:right;">
0.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
ISIL-AQAP
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
ISIL-Donetsk_PR
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
AQAP-Al-Nusrah
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
Donetsk_PR-Al-Nusrah
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
Houthi_Extrm-Al-Nusrah
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
Taliban-Al-Nusrah
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
ISIL-Houthi_Extrm
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
TTP-Boko Haram
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
Al-Shabaab-Al-Nusrah
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
PKK-Al-Nusrah
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
Donetsk_PR-Boko Haram
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
Boko Haram-AQAP
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
Houthi_Extrm-Boko Haram
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
<td style="text-align:right;">
0.0000
</td>
</tr>
<tr>
<td style="text-align:left;">
Taliban-ISIL
</td>
<td style="text-align:right;">