# Citizen insecurity in Ecuadorian provinces during the COVID-19 pandemic: multivariate statistical exploratory analysis using GGBiplotGUI

Juan Burbano-Gallegos, Katherine García-Pinargote, Isidro R. Amaro

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Juan Burbano-Gallegos, Katherine García-Pinargote, Isidro R. Amaro. Citizen insecurity in Ecuadorian provinces during the COVID-19 pandemic: multivariate statistical exploratory analysis using GGBiplotGUI. Bulletin of Computational Applied Mathematics, 2021, 9 (1), pp.97-113. hal-03558822

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<figure><img src="image_1.png" /></figure>
# Citizen insecurity in Ecuadorian provinces during the COVID-19 pandemic: multivariate statistical exploratory analysis using GGEBiplotGUI

Juan Burbano-Gallegos<fnref n="1" />,

Katherine García-Pinargote<fnref n="2" />,

Isidro R. Amaro<fnref n="3" /> <fnref n="4" />

CompAMa Vol.9, No.1, pp.97-113, 2021 - Received April 20, 2021 - Accepted September 26, 2021

Special Issue III CICB 2020, Eds. Carmen Judith Vanegas and Saúl Buitrago Boret

## Abstract

We carry out a multivariate exploratory analysis of the reports of criminal activity in Ecuador during the COVID-19 pandemic in the year 2020. This is presented as a comparative study between citizen insecurity before, during and after national lockdown. Since the number of cases and the population's compliance with distancing measures varied throughout the country, reports of criminal activity were studied by province. To analyze the data we used the R package GGEBiplotGUI. As a result, we noticed some significant differences between the criminal activity

<footnote n="1">¹Escuela de Ciencias Matemáticas y Computacionales. Universidad de Tecnología Experimental Yachay Tech, Ecuador. (juan.burbano@yachaytech.edu.ec). (ORCID iD: https://orcid.org/0000-0002-2410-5531).</footnote>

<footnote n="2">²Escuela de Ciencias Matemáticas y Computacionales. Universidad de Tecnología Experimental Yachay Tech, Ecuador. (katherine.garciap@yachaytech.edu.ec). (ORCID iD: https://orcid.org/0000-0002-1511-8277).</footnote>

<footnote n="3">³Escuela de Ciencias Matemáticas y Computacionales. Universidad de Tecnología Experimental Yachay Tech, Ecuador. (iamaro@yachaytech.edu.ec). (ORCID iD: https://orcid.org/0000-0003-2402-910X).</footnote>

<footnote n="4">⁴Corresponding author.</footnote>
before, during and after the emergency state was declared in the country. The numbers of all cases dropped dramatically and the trends in types of criminal activities changed differently in each province.

**Keywords:** Insecurity; COVID-19; Biplot; GGEBiplotGUI.

## Resumen

Llevamos a cabo un análisis exploratorio multivariante de los reportes de actividad criminal en Ecuador durante la pandemia de COVID-19 en el año 2020. Se presenta un estudio comparativo de la inseguridad ciudadana antes, durante y después de aislamiento social nacional. Dado que el número de casos y el acatamiento ciudadano de las medidas de restricción variaron a lo largo del país, los reportes de inseguridad fueron estudiados por provinicia. Para analizar los datos se utilizó el paquete GGEBiplotGUI de R. Como resultado, se evidenció diferencias significativas entre la actividad criminal antes, durante y después de la vigencia del estado nacional de emergencia. El número de reportes disminuyó dramáticamente y las tendencias de los tipos de reportes también cambiaron de acuerdo a la provincia.

**Palabras claves:** Inseguridad; COVID-19; Biplot; GGEBiplotGUI.

# 1 Introduction

The number of affected people by delinquency or violence in Ecuador is alarming. Citizen insecurity is a constant topic on the news and, almost every day, there are new cases. In 2019, the rate of homicides increased concerning 2018: from 5.8 to 6.3 cases per thousand inhabitants, according to the police general commander Patricio Carrillo [1]. In general, during 2019 delinquency and violence reports increased with respect to previous years. At the start of 2020, the reports on criminal activity that threatened citizen well-being seemed to follow the same tendency until the first positive cases of COVID-19 in Ecuador were identified.

Corona Virus Disease 2019 (COVID-19) is a type of coronavirus that appeared, based on [2], for the first time in Hubei, China. The first case of COVID-19 in Ecuador is confirmed on February 29th. In March 11th, Health Emergency state is declared, and on the 16th, the state of emergency due to COVID-19 crisis is announced [3]. Among the social distancing measures, a national curfew from 18:00 to 5:00 is dictated. Eventually, it changed from 14:00 to 5:00. Other major orders from the Emergency Operations Committee (COE) were the suspension of public transportation between provinces,
suspension of normal workdays, private transport restrictions, etc.[3]

This work is devoted to study the delinquency in Ecuador, before, during, and after the state of emergency due to the pandemic COVID-19 in 2020. Section 2 will describe the data under analysis, introduce some notation, and also the tools that will be used in this work. Next, we present the obtained results of this work and the explanation of them and we will finish with the discussion of the work, the conclusion, and some final recommendations are given.

## 2 Data description & methodology

The data used for this analysis was produced by the Statistical Commission of Citizen Security [4]. This institution identified major incidence crimes with the objective of classifying the types of felonies that are featured in the Integral Penal Code. This classification was done by type of crime, year, month and province. The types of crimes we will consider in our analysis are indicated in Table 3 together with their corresponding codes for the figures and graphs. In the same way, the provinces to be considered in our analysis are indicated in Table 2 with their corresponding codes for the figures and graphs. This kind of database can easily be presented in two-way tables. From this database, the Tables 4, 5 and 6 were constructed to conduct a comparative exploratory analysis of the crime incidence by province between the months of January and June of 2020. The province of Galápagos was not considered since it did not report any type of criminal activity.

### 2.1 Methodology

The first time that Biplots methods appeared was in 1971 in [5]. It is considered a statistical multivariate method, and a technique to reduce the dimension of the data, where the word “bi” stands for the fact that variables and individuals are represented simultaneously. This allows the interrelations between individuals and variables to be visually captured in a lower-dimensional space. The result is a multivariate matrix whose elements are coordinates for the graphical representation of individuals and variables of interest [6]. The process to obtain a Bplot representation has two parts: beginning with the construction where Singular Value Decomposition (SVD) is used, and the second where the original matrix is factored to obtain a low dimensional
Euclidean map through rows and column coordinates.

Any matrix $X$ of dimension $I \times J$ can be represented as the product of two matrices $A$ and $B$, such that: $A_{I \times S}$ and $B_{S \times J}$. When $m$ rows of $A$ and $n$ columns of $B$ are displayed in a single graphical representation, this is called a Biplot. Thus, a Biplot is basically a graph of a matrix $X_{I \times J}$ with row markers $a_1, ..., a_m$ and also column markers $b_1, ..., b_n$ in such a way that the inner product $a_i b_j$ is equal to $x_{ij}$ in $X$ [6].

Matrices $A$ and $B$ are chosen from the SVD of $X$. Let's recall that the SVD of $X$ is defined as $X = U\Lambda V^t$, where $U, V$ are matrices whose column vectors are orthonormal and correspond to the eigenvectors of $XX^t$ and $X^t X$, respectively. $\Lambda$ is a diagonal matrix containing the singular values of $X^t X$ arranged in decreasing order. Depending on how $A$ and $B$ are chosen from this decomposition, a different kind of Biplot is obtained, e.g., the GH-biplot, where $A = U$ and $B^t = VD$; the JK-Biplot, where $A = UD$ and $B^t = V$, and the HJ-Biplot, where $A = UD$ and $B^t = VD$. A more exhaustive review on Biplots methods can be found in [7].

Biplot analysis is a visually descriptive statistical tool, which is a useful tool for the study of the genotype × environment interaction(genotype (G) and the genotype-by-environment interaction (GE)) or any two-ways table, [8]. Gauch in [9] mentions the equivalence of the additive main effects and multiplicative interaction (AMMI) model and genotype main effects (G) and genotype × environment interaction effects (GE) model, known as GGE, and other SVD-based model. Also, he refuted the superiority of GGE, at least in the "which won where" analysis, over AMMI, concluding that GGE is for any research purpose superior to AMMI. However, [10] shows that GGE biplot is better than AMMI1 graph, which is the most known AMMI model. In fact, they state that the view of the “which won where” in GGE biplot is better than the AMMI1, since it explains more G+GE and it is of an easier construction and visualization. Moreover, that GGE is an effective tool for test-environment evaluation, which has not been a research topic in AMMI analysis. Additional information on this context can be found in [11].

In order to analyze the data, we will use the GGE Biplot approach [12], [13], [14], [15], [8]; that consists of a set of Biplots, by which important questions concerning individuals (rows) and variables (columns) in a data matrix can be addressed visually. For the implementation, we will use the R package GGEBiplotGUI [11]. The GGEBiplotGUI package provides a graphical user interface for the construction of, interaction with, and manipulation of GGE Biplots in R [16]. Although this software uses a multivariate statistical
<table><caption>Tab. 1: Model selection prompt options in the GGEBiplotGUI.</caption><thead><tr><th rowspan="2">SVP</th><th colspan="2">Model Elements</th></tr><tr><th>Centered By</th><th>Scaled (Divided) By</th></tr></thead><tbody><tr><td>JK-(Row<br>Metric Preserving)</td><td>0. No centering</td><td></td></tr><tr><td>GH-(Column<br>Metric Preserving)</td><td>1. Global-Centered<br>E+G+GE</td><td>0. No scaling</td></tr><tr><td>HJ-(Dual<br>Metric Preserving)</td><td>2. Tester-Centered<br>G+GE</td><td>1. Std Deviation<br>(SD)</td></tr><tr><td>SQ-Symmetrical</td><td>3. Double-Centered GE</td><td></td></tr></tbody></table>

technique that is frequently used to study the relationship between genotype and environment in the context of agriculture, it also is a powerful tool to study data presented in a two-way table [11]. Another reason for this choice is the simplicity of its graphical interface and the variety of analytical tools it presents. Considering all these elements, we used this package to elaborate Biplots based on the data presented in Tables 4, 5 and 6.

Using the package according to the indicated by Frutos & Galindo in the reference manual [16], the interface presents a selection of model prompt. Here, the user selects the best options for the GGE biplot graph. These options are shown in Table 1. The configuration of the model according to these options will be shown in the description of each of the GGE biplots in the Results section. For all the biplots presented in the Results section, the data was Tester-Centered G+GE. In [17], it is stated that one of the merits of the GGE biplot model is that it can graphically show “who (which cultivar)-won-where (in which locality)” in a set of data [18].

## 3 Results

Figure 1 indicates the absolute frequency of reports of the different types of criminal activities indicated in Table 3 from January of 2014 until July 2020. Evidently, the national emergency caused by coronavirus disease dramatically affected the number of reports in all categories of criminal activity. During April 2020, the overall number of reports is significantly lower than that of any other month. The total amount of April's reports represent just the 7.68% of the total cases reported during January of the same year.
<table><caption>Tab. 2: Codes for Ecuador provinces</caption><tr><td>A</td><td>Azuay</td><td>B</td><td>Bolivar</td><td>U</td><td>Cañar</td></tr><tr><td>C</td><td>Carchi</td><td>X</td><td>Cotopaxi</td><td>H</td><td>Chimborazo</td></tr><tr><td>O</td><td>El Oro</td><td>E</td><td>Esmeraldas</td><td>G</td><td>Guayas</td></tr><tr><td>I</td><td>Imbabura</td><td>L</td><td>Loja</td><td>R</td><td>Los Rios</td></tr><tr><td>M</td><td>Manabí</td><td>S</td><td>Pastaza</td><td>N</td><td>Napo</td></tr><tr><td>V</td><td>Morona Santiago</td><td>P</td><td>Pichincha</td><td>T</td><td>Tungurahua</td></tr><tr><td>Z</td><td>Zamora Chinchipe</td><td>K</td><td>Sucumbios</td><td>Q</td><td>Orellana</td></tr><tr><td>J</td><td>Santo Domingo</td><td>Y</td><td>Santa Elena</td><td>W</td><td>Galapagos</td></tr></table>

<table><caption>Tab. 3: Codes of Delinquency and Crime</caption><tr><td>H</td><td>Total homicides</td><td>PR</td><td>People Robbery</td></tr><tr><td>TP</td><td>Theft of property</td><td>MT</td><td>Motorcycle Theft</td></tr><tr><td>AT</td><td>Automobile Theft</td><td>DT</td><td>Domiciliary Theft</td></tr><tr><td>EUT</td><td>Economic Unit Theft</td><td>R</td><td>Rape</td></tr><tr><td>TRD</td><td>Transit related deaths</td><td></td><td></td></tr></table>

<figure><img src="image_2.png" /><figcaption>Fig. 1: Line graph for the absolute number of monthly reports of occurrences related to citizen insecurity in Ecuador from January 2014 to July 2020.</figcaption></figure>
<table><caption>Tab. 4: Ecuador Insecurity in January of 2020</caption><thead><tr><th></th><th>A</th><th>B</th><th>U</th><th>C</th><th>X</th><th>H</th><th>O</th><th>E</th><th>G</th><th>I</th><th>L</th><th>R</th><th>M</th><th>V</th><th>N</th><th>S</th><th>P</th><th>T</th><th>Z</th><th>K</th><th>Q</th><th>J</th><th>Y</th><th>Total</th></tr></thead><tbody><tr><th>H</th><td>1</td><td>0</td><td>1</td><td>2</td><td>2</td><td>1</td><td>7</td><td>1</td><td>52</td><td>2</td><td>0</td><td>7</td><td>8</td><td>1</td><td>0</td><td>0</td><td>19</td><td>2</td><td>0</td><td>2</td><td>1</td><td>2</td><td>3</td><td>114</td></tr><tr><th>PR</th><td>94</td><td>3</td><td>18</td><td>9</td><td>34</td><td>55</td><td>146</td><td>91</td><td>1171</td><td>42</td><td>25</td><td>146</td><td>132</td><td>6</td><td>9</td><td>10</td><td>794</td><td>51</td><td>3</td><td>21</td><td>14</td><td>57</td><td>43</td><td>2974</td></tr><tr><th>TP</th><td>81</td><td>3</td><td>10</td><td>2</td><td>22</td><td>33</td><td>12</td><td>3</td><td>204</td><td>7</td><td>11</td><td>10</td><td>19</td><td>2</td><td>0</td><td>2</td><td>307</td><td>22</td><td>2</td><td>3</td><td>0</td><td>11</td><td>11</td><td>777</td></tr><tr><th>MT</th><td>14</td><td>0</td><td>4</td><td>0</td><td>5</td><td>7</td><td>64</td><td>24</td><td>250</td><td>3</td><td>2</td><td>77</td><td>51</td><td>3</td><td>3</td><td>1</td><td>108</td><td>0</td><td>0</td><td>14</td><td>14</td><td>30</td><td>31</td><td>697</td></tr><tr><th>AT</th><td>4</td><td>2</td><td>1</td><td>2</td><td>13</td><td>7</td><td>12</td><td>5</td><td>176</td><td>1</td><td>2</td><td>21</td><td>29</td><td>2</td><td>2</td><td>0</td><td>163</td><td>7</td><td>1</td><td>3</td><td>4</td><td>29</td><td>1</td><td>487</td></tr><tr><th>DT</th><td>49</td><td>5</td><td>14</td><td>3</td><td>11</td><td>19</td><td>44</td><td>48</td><td>203</td><td>24</td><td>19</td><td>26</td><td>69</td><td>14</td><td>10</td><td>14</td><td>203</td><td>22</td><td>3</td><td>14</td><td>14</td><td>30</td><td>31</td><td>889</td></tr><tr><th>EUT</th><td>37</td><td>3</td><td>7</td><td>4</td><td>12</td><td>11</td><td>26</td><td>12</td><td>88</td><td>14</td><td>0</td><td>20</td><td>25</td><td>2</td><td>0</td><td>1</td><td>172</td><td>7</td><td>4</td><td>4</td><td>6</td><td>13</td><td>9</td><td>477</td></tr><tr><th>R</th><td>29</td><td>7</td><td>9</td><td>5</td><td>7</td><td>15</td><td>39</td><td>28</td><td>61</td><td>11</td><td>11</td><td>14</td><td>28</td><td>25</td><td>6</td><td>9</td><td>97</td><td>10</td><td>3</td><td>10</td><td>5</td><td>21</td><td>4</td><td>454</td></tr><tr><th>TRD</th><td>5</td><td>0</td><td>2</td><td>1</td><td>4</td><td>6</td><td>6</td><td>17</td><td>39</td><td>3</td><td>6</td><td>14</td><td>13</td><td>3</td><td>1</td><td>1</td><td>32</td><td>3</td><td>1</td><td>4</td><td>2</td><td>6</td><td>4</td><td>173</td></tr></tbody><tfoot><tr><th>Total</th><td>314</td><td>23</td><td>66</td><td>28</td><td>110</td><td>154</td><td>356</td><td>229</td><td>2244</td><td>107</td><td>76</td><td>335</td><td>374</td><td>58</td><td>31</td><td>38</td><td>1895</td><td>124</td><td>17</td><td>75</td><td>60</td><td>207</td><td>121</td><td>7042</td></tr></tfoot></table>

<table><caption>Tab. 5: Ecuador Insecurity in April of 2020 during the national emergency state declared due to the COVID-19 outbreak.</caption><thead><tr><th></th><th>A</th><th>B</th><th>U</th><th>C</th><th>X</th><th>H</th><th>O</th><th>E</th><th>G</th><th>I</th><th>L</th><th>R</th><th>M</th><th>V</th><th>N</th><th>S</th><th>P</th><th>T</th><th>Z</th><th>K</th><th>Q</th><th>J</th><th>Y</th><th>Total</th></tr></thead><tbody><tr><th>H</th><td>1</td><td>1</td><td>1</td><td>0</td><td>0</td><td>1</td><td>3</td><td>1</td><td>40</td><td>3</td><td>1</td><td>8</td><td>3</td><td>2</td><td>0</td><td>0</td><td>8</td><td>1</td><td>0</td><td>5</td><td>1</td><td>1</td><td>2</td><td>83</td></tr><tr><th>PR</th><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>29</td><td>11</td><td>28</td><td>5</td><td>0</td><td>21</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>95</td></tr><tr><th>TP</th><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>2</td><td>2</td><td>3</td><td>3</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>13</td></tr><tr><th>MT</th><td>3</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>22</td><td>3</td><td>26</td><td>0</td><td>0</td><td>21</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>77</td></tr><tr><th>AT</th><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>4</td><td>0</td><td>16</td><td>0</td><td>0</td><td>3</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>24</td></tr><tr><th>DT</th><td>1</td><td>0</td><td>0</td><td>2</td><td>1</td><td>2</td><td>8</td><td>8</td><td>9</td><td>4</td><td>0</td><td>8</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>43</td></tr><tr><th>EUT</th><td>0</td><td>2</td><td>0</td><td>1</td><td>2</td><td>2</td><td>10</td><td>0</td><td>25</td><td>6</td><td>0</td><td>10</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>58</td></tr><tr><th>R</th><td>4</td><td>0</td><td>1</td><td>1</td><td>0</td><td>2</td><td>7</td><td>7</td><td>12</td><td>2</td><td>2</td><td>4</td><td>5</td><td>8</td><td>3</td><td>2</td><td>11</td><td>3</td><td>1</td><td>4</td><td>2</td><td>4</td><td>0</td><td>85</td></tr><tr><th>TRD</th><td>2</td><td>0</td><td>0</td><td>0</td><td>1</td><td>4</td><td>0</td><td>2</td><td>23</td><td>1</td><td>2</td><td>3</td><td>5</td><td>1</td><td>0</td><td>0</td><td>9</td><td>2</td><td>1</td><td>0</td><td>1</td><td>4</td><td>2</td><td>63</td></tr><tr><th>Total</th><td>13</td><td>4</td><td>3</td><td>4</td><td>4</td><td>14</td><td>85</td><td>35</td><td>182</td><td>22</td><td>5</td><td>79</td><td>13</td><td>11</td><td>3</td><td>2</td><td>28</td><td>6</td><td>2</td><td>9</td><td>4</td><td>9</td><td>4</td><td>541</td></tr></tbody></table>

From the data used in Figure 1, a GGE biplot was used to visualize the time evolution of the type of reports of criminal activity between June of 2019 to June of 2020. In Figure 2 a Biplot of the type of criminal activity (as a variable) and each month in the before mentioned time period (as observations) is presented. The goodness of fit of the axes in Figure 2 reaches 94.24%, so, the first two axes account for 94.24% of total inertia. In this Biplot, it is clear that the months of March and April of 2020 are very different from those before and after the start of the virus outbreak in Ecuador and that the distance between March and April to the rest of the months elucidates a clear transition in the amount and type of reports of criminal activity in the country.

From what is shown in Figures 1 and 2, it was interesting to make a comparative exploratory analysis of a pre-outbreak month of the studied period, a post-outbreak month, and the month of April; which was the first entire month that Ecuador was under the state of emergency declared due to the pandemic. Since the number of infected people and population compliance
<table><caption>Tab. 6: Ecuador Insecurity in June of 2020 after the national emergency state declared due to the COVID-19 outbreak.</caption><thead><tr><th></th><th>A</th><th>B</th><th>U</th><th>C</th><th>X</th><th>H</th><th>O</th><th>E</th><th>G</th><th>I</th><th>L</th><th>R</th><th>M</th><th>V</th><th>N</th><th>S</th><th>P</th><th>T</th><th>Z</th><th>W</th><th>K</th><th>Q</th><th>J</th><th>Y</th><th>Total</th></tr></thead><tbody><tr><th>H</th><td>1</td><td>1</td><td>1</td><td>0</td><td>5</td><td>1</td><td>8</td><td>7</td><td>46</td><td>1</td><td>1</td><td>12</td><td>8</td><td>1</td><td>0</td><td>1</td><td>12</td><td>3</td><td>0</td><td>0</td><td>0</td><td>0</td><td>3</td><td>0</td><td>112</td></tr><tr><th>PR</th><td>33</td><td>2</td><td>9</td><td>4</td><td>5</td><td>16</td><td>72</td><td>51</td><td>534</td><td>14</td><td>11</td><td>94</td><td>57</td><td>0</td><td>3</td><td>2</td><td>267</td><td>19</td><td>2</td><td>0</td><td>10</td><td>3</td><td>38</td><td>20</td><td>1266</td></tr><tr><th>TP</th><td>55</td><td>0</td><td>7</td><td>2</td><td>6</td><td>13</td><td>3</td><td>3</td><td>135</td><td>8</td><td>6</td><td>4</td><td>4</td><td>1</td><td>1</td><td>1</td><td>173</td><td>18</td><td>1</td><td>0</td><td>1</td><td>0</td><td>7</td><td>1</td><td>450</td></tr><tr><th>MT</th><td>17</td><td>4</td><td>3</td><td>0</td><td>3</td><td>4</td><td>44</td><td>20</td><td>199</td><td>5</td><td>1</td><td>104</td><td>29</td><td>1</td><td>0</td><td>1</td><td>87</td><td>5</td><td>0</td><td>0</td><td>7</td><td>13</td><td>20</td><td>5</td><td>572</td></tr><tr><th>AT</th><td>4</td><td>0</td><td>0</td><td>0</td><td>2</td><td>4</td><td>6</td><td>2</td><td>147</td><td>4</td><td>4</td><td>20</td><td>21</td><td>1</td><td>1</td><td>1</td><td>103</td><td>2</td><td>0</td><td>0</td><td>2</td><td>2</td><td>26</td><td>1</td><td>353</td></tr><tr><th>DT</th><td>18</td><td>2</td><td>11</td><td>0</td><td>4</td><td>2</td><td>21</td><td>38</td><td>126</td><td>9</td><td>17</td><td>23</td><td>26</td><td>9</td><td>11</td><td>6</td><td>84</td><td>9</td><td>2</td><td>3</td><td>4</td><td>10</td><td>15</td><td>30</td><td>480</td></tr><tr><th>EUT</th><td>13</td><td>1</td><td>1</td><td>2</td><td>3</td><td>4</td><td>19</td><td>8</td><td>63</td><td>8</td><td>2</td><td>13</td><td>5</td><td>1</td><td>0</td><td>2</td><td>96</td><td>8</td><td>1</td><td>0</td><td>5</td><td>4</td><td>16</td><td>0</td><td>275</td></tr><tr><th>R</th><td>8</td><td>9</td><td>6</td><td>1</td><td>4</td><td>15</td><td>14</td><td>7</td><td>52</td><td>6</td><td>6</td><td>14</td><td>11</td><td>18</td><td>2</td><td>7</td><td>41</td><td>9</td><td>1</td><td>2</td><td>7</td><td>8</td><td>12</td><td>3</td><td>263</td></tr><tr><th>TRD</th><td>3</td><td>0</td><td>2</td><td>1</td><td>6</td><td>9</td><td>2</td><td>7</td><td>29</td><td>5</td><td>2</td><td>5</td><td>10</td><td>4</td><td>1</td><td>0</td><td>27</td><td>3</td><td>1</td><td>0</td><td>0</td><td>1</td><td>2</td><td>3</td><td>123</td></tr></tbody><tfoot><tr><th>Total</th><td>152</td><td>19</td><td>40</td><td>10</td><td>38</td><td>68</td><td>189</td><td>143</td><td>1331</td><td>60</td><td>50</td><td>289</td><td>171</td><td>36</td><td>19</td><td>21</td><td>890</td><td>76</td><td>76</td><td>8</td><td>36</td><td>41</td><td>139</td><td>63</td><td>3894</td></tr></tfoot></table>

to social distancing policies varied depending on the province, a GGE Biplot analysis of reports of criminal activity in each Province of Ecuador was carried out. Since the GGE Biplot GUI software is commonly applied in the context of agriculture, Provinces were understood as the “environment” in which we studied the reports of different types of criminal activity (“genotypes”). This analogous way of proceeding pretty simplified the interpretation of the results obtained through the graphical interface.

Figure 3 shows the GGE Biplots for the reports of criminal activity in each province in Ecuador in January, April, and June of 2020. An important characteristic to notice is that the data is not scaled in either of the Biplots. This was done to highlight the main differences between the structures and geometry of the Biplots for these two months. Since the priority is studying the variation explained by the provinces, a Biplot based on the column metric preserving decomposition (GH) was employed. Notice that this yields overall goodness of fit of 99.3%, 85.93%, and 97.5% for January, April, and June respectively.

One of the most evident differences in the criminal activity in these three months we are studying has to do with the variation of each province. In Figure 3 we can see that during January and June of 2020, the Provinces that showed the highest variations corresponded to the two most populated provinces: Guayas and Pichincha. The rest of the provinces show very similar but much lower variation. In contrast to this, in April, the first entire month of the national emergency, we can observe some relevant differences.

The first one has to do that the variation in all the provinces was reduced significantly, making the province markers concentrate towards the center of the Biplot. Although all the variances were globally reduced, the Provinces of
<figure><img src="image_3.png" /><figcaption>Fig. 2: GGEBiplot for the same data used for Figure 1 with scaled data, test-centered G+GE and symmetrical SVD decomposition (SQ).</figcaption></figure>

Guayas, El Oro, Los Rios, Pichincha, and Esmeraldas show a higher variation relative to the rest of the provinces. Pichincha, despite being the second most populated province in the country, changed from 2nd place to 4th in terms of explained variation.

The provinces of Guayas and Pichincha were examined in more detail since they together concentrate more than 40% of Ecuador's total population. Both Provinces were examined using the environment examination tool of the GGEBiplotGUI. It provided the orthogonal projections of the markers of each type of report for criminal activity onto the axis defined by the province vector. In this way, we were able to graphically show the most and least common crimes in each province in the two months studied.

In the case of the Guayas, Figure 4 indicates that during January and, June the most commonly reported illegal activity in the province was people
<figure><img src="image_4.png" /><figcaption>Fig. 3: GGBiplots for the data of Tables 4, 5 and 6 with non-scaled data, test-centered G+GE and column metric preserved (GH) SVD.</figcaption></figure>

robbery. This changed by month of April, where homicides became more common. Also, notice that people robbery is in second place during April.

<figure><img src="image_5.png" /><figcaption>Fig. 4: Examination of insecurity reports in Guayas in 2020.</figcaption></figure>

The examination of Pichincha unveils some significant changes from January to April and back to June. During January and June of 2020, Figure 5 indicates that the most commonly reported offense to citizen security was people robbery with a high positive correlation. This change shows a notorious difference when compared to the examination of Pichincha during April, where people robbery becomes the least reported criminal activity in the province. The most common offense in Pichincha in April shifts towards homicide, followed by transit-related deaths, automobile theft, and rape.
<figure><img src="image_6.png" /><figcaption>Fig. 5: Examination of insecurity reports in Pichincha in 2020.</figcaption></figure>

As shown in Tables 4, 5 and 6, people robbery is the most common report of criminal activity in all of the studied months. Thus, an individual examination was carried out to understand if the distribution of such cases somehow changed due to the national emergency, that started in March of 2020. In Figure 6 we can see that in the months of January and June of 2020, the two provinces where most cases of people robbery were reported correspond to Guayas and Pichincha. Interestingly, in April of the same year, after the social distancing measures were dictated, the provinces with the highest indices of this offense were the coastal provinces of El Oro, Los Rios, Guayas, and Esmeraldas. During this month of emergency, Pichincha passed from being the Province with the second-highest score on people robbery to the one with the lowest, and in June returned to its previous state.

After studying the most commonly reported criminal activity, it is natural to perform a similar examination to the second most frequent criminal activity indicated in Tables 4, 5 and 6. In the case of January, this corresponds to domiciliary theft. Figure 7 shows that Azuay is the Province that shows the highest proportion of theft of property compared to other criminal activities. Moreover, Guayas is the province with the lowest incidence for this type of crime. In the case of the month of April, the second most common report of criminal activity was rape. The Province, where the greatest proportion of rapes occurred, was Pichincha, while the lowest corresponded again to Guayas. Finally, during June, motorcycle theft was the most representative insecurity report with Guayas as the main environment in which it occurred.

Finally, to identify if there exist regions of various provinces that can
<figure><img src="image_7.png" /><figcaption>Fig. 6: Examination of people robbery by province in 2020.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 7: Examination of the monthly second most relevant report type by province in 2020.</figcaption></figure>

be characterized by their criminal activity reports, we use GGEBiplotGUI's *which-won-where/what* tool. The resulting figure is indicated in Figure 8. During the months of January and June, we can see that the region where the prevailing criminal activity is people robbery contains all of the provinces. This was expected since we can see that people robbery was by far the most commonly reported criminal activity in Ecuador during regular months (see Figure 1). Now, in Figure 8 the same has been done during the virus lockdown month of April 2020. Notice that the geometry of the convex hull formed by the row markers creates a substantially different partition of provinces in the Biplot. From this, we can identify three groups of Provinces defined by their criminal activity reports. The first group, characterized by homicides
and transit-related deaths, is located at the upper part of the Biplot and contains Provinces like Guayas, Pichincha, Manabí, Sucumbios, etc. The second group, identified mainly by reports of people robbery, is formed by El Oro, Los Rios, Esmeraldas, and Imbabura. Lastly, we identified a third group characterized by theft of property and domiciliary theft. The province of Carchi is part of this last group.

<figure><img src="image_9.png" /><figcaption>Fig. 8: Which won where/what plots for citizen insecurity reports from the studied months in 2020.</figcaption></figure>

# 4 Discussion and Conclusions

From all of the results presented in the last section, we have some evidence to understand, from a statistical standpoint, the shift in criminal activity in Ecuador's province due to the COVID-19 pandemic. It is clear from Figures 1 and 2 that not just the number of reports of criminal activity reduced dramatically after the emergency state was dictated, but also that the trends in the proportion of the type of reported crimes changed significantly. In Figure 3 it is evident that in Pichincha the social distancing measures altered its usual criminal activity. The total reported cases in the province decreased in Provinces such as El Oro and Los Rios. The most reasonable explanations for this could be the greater compliance with the social distancing politics of Pichincha's population or a greater vigilance of Pichincha's security authorities concerning the before-mentioned coastal provinces.

In the case of the Guayas province, although in the last section we presented some changes in its criminal activities from January to April, it did
not present such notable changes as the Pichincha province did. For example, in Table 5 Guayas is still the province with the highest criminal activity reports in Ecuador, and in Figure 3 we can see that it is the one that explains the most variation regardless of the emergency state. This could be a result of the lack of compliance with the measures dictated due to the emergency. In spite of this, it is also important to remark that both provinces (Guayas and Pichincha) faced different starting conditions since Guayas was the first province to report a positive COVID-19 case in Ecuador, and by April of 2020 was the province with the highest number of people infected by the virus.

The curfew imposed by the national Emergency Operations Committee also had a remarkable effect on the frequency of certain types of crimes. For example, in Pichincha and more specifically in Quito, people robbery dropped to the least common illegal activity (Figure 6) since most people stayed home during the month of April avoiding a possible COVID-19 infection. In the same province, however, rape increased significantly becoming the most commonly reported crime during the lockdown month (Figure 7). This change in the trend does not come as a surprise since the perpetrators of mugging cannot operate if their victims do not leave their houses, while rapists usually target members of their household as their victims.

A final observation is on the grouping of provinces that was done using GGEBiplotGUI's *Which Won Where/What* tool. In the month of January and, June all of the Provinces presented people robbery as their most representative criminal activity. The circumstances within the context of the COVID-19 in April 2020 in Ecuador motivated a diversification in the type of criminal activities in different provinces. In Figure 8, we can see that people robbery persisted as the most frequent crime in the coastal Provinces of El Oro, Los Rios, and Esmeraldas. Two of these provinces, namely El Oro and Los Rios, were the most affected by the virus right behind Guayas during April. The persistence of the same trends of criminality in these provinces could suggest a lack of compliance with the social distancing measures. The group that contained Guayas, Pichincha, Manabí, and others presented homicide as the most common report of criminal activity. This fact is unexpected since, during the emergency state, it was expected that the cases of homicides would have similar behavior to that observed for people robbery since the victims would have less exposure to perpetrators.

Throughout all the results just presented, it is clear that although trends in insecurity reports changed drastically during the first month of the emer-
gency state, the latest data suggests a return to pre-pandemic trends. The transition in criminal activity, which we have presented in this text between January and, April does not persist into June in the “new normality” paradigm. The biplots from Figure 3 and the frequencies in Figure 1 elucidate the return to the same pre-pandemic patterns.

As a proposal for further studies, a MANOVA analysis could be included to group provinces by similarities in their criminal activities and to make a comparison between this and the *Which Won Where/What* approach presented in Figure 8. This kind of research could help authorities and officials to make informed decisions that ultimately benefit the whole country's population.

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