Recommendations: - Display the coordinates on maps - Create a map of the hierarchical classes - Perform linear regression - Conduct hierarchical classification without the outlier(s)

Abstrat

West Africa is a region heavily dependent on agriculture, but it faces growing challenges related to climate change and demographic pressure. This study analyzes the relative impact of climate variables (rainfall, temperature) and economic factors (GDP, population, irrigation) on agricultural yield in 10 countries in the region between 2000 and 2020. Based on a statistical analysis (correlation and multiple linear regression), the results show that climate variables have a limited impact, mitigated by local adaptation strategies such as the adoption of modern irrigation systems (“drip”, “sprinkler”) and the efficient use of water resources. In contrast, economic and technological factors, including GDP, irrigable area, and irrigation methods, play a predominant role in improving agricultural productivity. These results highlight the importance of public and private investments in agriculture to strengthen the resilience of agricultural systems to the impacts of climate change. The study concludes with recommendations aimed at promoting sustainable public policies and technological innovations adapted to the specific needs of the region.

Keywords

Food security Changement climatique Famine

Resumé

L’afrique de l’ouest est une région fortement dépandante de l’agriculture, mais elle est confronté à des défis liés au changements climatiques et à la pressin démographique. Cette etude analyse l’impact relatif des variables climatiques (précipitation, températures ) et des facteurs économiques (PIB, population, irrigation) sur le rendement agricole dans 10 pays de la région entre 2000 et 2020, sur la base d’une analyse statistique (corélation et régression linéaire), les resultas montrent que les variables climatiques ont un impacte limité, aténué par des stratégies d’adaptation locales telles que l’adoption des systèmes d’irrigation modernes (“goute à goute”, “aspersion”) et l’utilisation éfficace des ressources en eau. En revanche les facteurs économiques et technologiques, notamment le PIB, la superficie irriguée, et les méthodes d’irrigation, jouent un role déterminant dans l’’amélioration de la productivité agricole. Ces resultas soulignent l’immportance des investicments publiques et privé dans l’agriculture pour nrenfoercer la résiliance des des culutures aux impactes du changement cliatique. Il conclu par des des recommendations et u n programme de de devellopement agricole et de gestion des recources en eau adapté aux spécificité de la région.

Mots Clé

Sécurité alimentaire Changement climatique Famine Facteurs économiques Sous-alimentation

Introduction

Agriculture and food security issues in sub-Saharan Africa represent critical challenges that significantly affect the region’s socio-economic landscape. Despite its rich natural resources and diverse agricultural potential, sub-Saharan Africa faces persistent food insecurity, with over 250 million people currently classified as undernourished. (What is the evidence on smallholder agriculture interventions in Africa?, 2016; “2 Soil Fertility Management Organic Africa,” n.d.) This situation is exacerbated by a range of factors, including historical legacies of colonialism, socio-economic disparities, and climate change, which collectively hinder agricultural productivity and access to adequate nutrition.(OECD and Food and Agriculture Organization of the United Nations, 2016; “Sustainable Agriculture and Climate 22-41,” n.d.)

The region’s agricultural sector has struggled to keep pace with global advancements, particularly in the wake of the Green Revolution that transformed food production in other parts of the world. Key impediments to progress include low investment in modern agricultural practices, inadequate infrastructure, and the challenges posed by rapid population growth and urbanization, which shift labor away from traditional farming practices. (“Global Agricultural Development - Investing in Transformation and Innovation,” n.d.; “Africa Agricultural Policy Leadership Dialogue,” n.d.) As a result, agricultural yields in sub-Saharan Africa remain significantly lower than those in other regions, leading to increased vulnerability among rural populations who rely on subsistence farming.(“Region | SDG 6 Data,” n.d.)

Food security in sub-Saharan Africa is further complicated by external pressures such as political instability, economic volatility, and the impacts of climate change, including extreme weather events that disrupt agricultural systems (“Research Raises Agricultural Productivity in Sub-Saharan Africa | Economic Research Service,” n.d.; Baptista et al., 2022) Recent evaluations indicate that climate change could adversely affect up to 56% of agricultural land in the region by 2050, posing a severe threat to food production and nutritional outcomes. (“Evolution: Economic and Agriculture Development in Sub-Saharan Africa | The Pig Site,” n.d.; Fuglie and Rada, 2013). The Global Hunger Index highlights alarming levels of hunger and malnutrition in countries such as the Central African Republic and Madagascar, underscoring the urgent need for effective and equitable interventions. (Ssozi et al., 2019; “Addressing Food Insecurity in Sub-Saharan Africa: Challenges, Potential, and Lessons from Israel | Ipsos,” n.d.).

Addressing these multifaceted challenges necessitates comprehensive policy responses that encompass innovative agricultural practices, enhanced access to resources for smallholder farmers, and investments in sustainable agriculture technologies. Initiatives promoting climate-smart agriculture and agro-ecological practices are crucial for improving productivity and resilience against climate-related shocks, while social protection programs can help vulnerable populations navigate food price fluctuations and localized shortages (“Agricultural policies in Sub-Saharan Africa: understanding CAADP and APRM policy processes - German Institute of Development and Sustainability (IDOS),” n.d.; “Studies_48,” n.d.) As the region seeks to build a more food-secure future, the integration of diverse strategies tailored to local contexts will be essential for overcoming the entrenched barriers to agricultural development and food security (“Agricultural productivity and policies in Sub-Saharan Africa,” n.d.)

It is imperative to examine the specific factors hindering the achievement of food self-sufficiency in West Africa and to explore hypotheses on the main obstacles that must be overcome to achieve this. Such an analysis is essential for formulating effective strategies to strengthen food security and restore the dignity of West African populations.

Bibliographic review

The agricultural landscape in sub-Saharan Africa has been shaped by various historical factors, including colonial legacies, socio-economic transformations, and environmental changes. Following independence, many nations in the region attempted to reform agricultural practices to enhance productivity and food security. However, these efforts often encountered challenges, including limited access to resources and inadequate infrastructure, which have persisted into the present day (“2 Soil Fertility Management Organic Africa,” n.d ; What is the evidence on smallholder agriculture interventions in Africa, 2016).

The Green Revolution, which significantly improved agricultural productivity in Asia and Latin America, has not been as effectively implemented in sub-Saharan Africa. This disparity can be attributed to a range of factors, including the diversity of agro-ecological conditions, socio-economic disparities, and insufficient investment in agricultural technology and infrastructure (What is the evidence on smallholder agriculture interventions in Africa?, 2016; “Sustainable Agriculture and Climate 22-41,” n.d.). Furthermore, rapid population growth and urbanization have intensified pressure on agricultural systems, leading to a shift from farm to non-farm employment and altering traditional agricultural practices (“Global Agricultural Development - Investing in Transformation and Innovation,” n.d.).

In recent years, there has been a growing recognition of the need for innovative farming practices tailored to the unique challenges of the region. Programs aimed at improving mechanization access for smallholder farmers and enhancing the adoption of improved crop varieties have been initiated, such as the DeSIRA Integrated Rice-Fish Farming System (IRFFS) funded by the European Union (“Africa Agricultural Policy Leadership Dialogue,” n.d.; “Region | SDG 6 Data,” n.d.). Additionally, projects like the AICCRA, supported by the World Bank, have been established to increase yield and income for farmers in countries like Mali (“Research Raises Agricultural Productivity in Sub-Saharan Africa | Economic Research Service,” n.d.; “Africa Agricultural Policy Leadership Dialogue,” n.d.).

Moreover, the impact of climate change has emerged as a critical concern, exacerbating food insecurity and complicating agricultural practices across sub-Saharan Africa. Studies indicate that climate change is likely to intensify existing challenges, including reduced crop yields and increased vulnerability to food shortages(Baptista et al., 2022; “Global Agricultural Development - Investing in Transformation and Innovation,”.). As such, a nuanced approach that integrates sustainable agricultural practices with climate adaptation strategies is crucial for improving food security in the region (“Evolution: Economic and Agriculture Development in Sub-Saharan Africa | The Pig Site,” n.d.).

Current State of Agriculture

Agricultural productivity in Sub-Saharan Africa (SSA) remains critically low and is increasingly lagging behind other regions globally (Ssozi et al., 2019). Factors contributing to this stagnation include low crop productivity, inadequate investment in modern irrigation, weak economic growth, and rising inflation rates coupled with food prices (“Addressing Food Insecurity in Sub-Saharan Africa: Challenges, Potential, and Lessons from Israel | Ipsos,” n.d.). Although there have been efforts to enhance agricultural performance, such as the Comprehensive Africa Agriculture Development Programme (CAADP) and the African Peer Review Mechanism (APRM), these initiatives have had varying impacts on agricultural policies and strategies at the country level (“Agricultural policies in Sub-Saharan Africa: understanding CAADP and APRM policy processes - German Institute of Development and Sustainability (IDOS),” n.d.).

Role of Women in Agriculture

Women’s involvement in agricultural decision-making is particularly significant for enhancing food security and nutritional outcomes. In households where women have greater control, practices such as crop diversification and the management of home gardens tend to flourish, contributing positively to dietary diversity and community health. (“Studies_48,” n.d.; “Agricultural productivity and policies in Sub-Saharan Africa,” n.d.). Studies indicate that regions where women manage agricultural resources often witness improved conservation and sustainability practices, which are vital for long-term agricultural success. (“Studies_48,” n.d.).

Economic Impact

Boosting agricultural productivity has been shown to stimulate economic growth and alleviate poverty in multiple ways. It raises the income of farming households and increases food availability, thereby enhancing nutritional outcomes across communities (Fuglie and Rada, 2013). In smallholder farming systems, diversification of crops and livestock, along with soil and water conservation practices, are essential strategies that can improve overall productivity (“Building resilience in Africa’s smallholder farming systems: contributions from agricultural development interventions—a scoping review - Ecology & Society,” n.d.; “Soil health and ecosystem services: Lessons from sub-Sahara Africa (SSA) - ScienceDirect,” n.d.). Moreover, the linkage between farmers and processors is critical for fostering effective agricultural growth that contributes to poverty reduction and enhances food security (“Open Knowledge Repository,” n.d.).

Challenges and Opportunities

Despite the potential benefits of improved agricultural practices, challenges such as limited access to mechanization and the low extent of farm mechanization persist, significantly hindering agricultural intensification (“Research Raises Agricultural Productivity in Sub-Saharan Africa | Economic Research Service,” n.d.). Additionally, soil health is crucial for sustainable agriculture, and practices such as conservation agriculture and integrated soil fertility management are critical for maintaining soil productivity and health (“Soil health and ecosystem services: Lessons from sub-Sahara Africa (SSA) - ScienceDirect,” n.d.; “Climate-Smart Agriculture in Sub-Saharan Africa - Earth System Governance,” n.d.). Furthermore, public policies and investments in agricultural infrastructure are necessary foundations for achieving sustained improvements in agricultural productivity across the region. (“Prioritizing Productivity in Sub-Saharan Africa | Virginia Tech CALS Global,” n.d.).

Food Security Challenges

Food security in Sub-Saharan Africa (SSA) faces numerous challenges, exacerbated by a combination of historical and contemporary factors. One of the most significant barriers to accessing adequate food is poverty, which severely limits financial resources and thereby restricts individuals’ ability to afford nutritious food (“Beyond hunger: Unveiling the rights to food in sub‐Saharan Africa - Onyeaka - 2024 - Food and Energy Security - Wiley Online Library,” n.d.; “Why food insecurity persists in sub-Saharan Africa: A review of existing evidence | Food Security,” n.d.). In rural areas, this issue is compounded by an urban-biased distribution system that often overlooks the needs of these populations, leaving millions vulnerable to food insecurity (“Enhancing Food and Nutrition Security in the Sahel and Horn of Africa,” n.d.).

Climate change further complicates the landscape of food security in SSA. It is projected to adversely affect up to 56% of agricultural land in the region by 2050, leading to reduced agricultural yields and heightened food insecurity (“Agricultural productivity must improve in sub-Saharan Africa | Science,” n.d.; “Agriculture and economic reform in Sub-Saharan Africa,” n.d.). Extreme weather events, such as droughts, floods, and heatwaves, disrupt agricultural practices and exacerbate soil erosion, which in turn compromises food production and availability (“Agricultural productivity must improve in sub-Saharan Africa | Science,” n.d.; “Evolution: Economic and Agriculture Development in Sub-Saharan Africa | The Pig Site,” n.d.). The ongoing impact of climate change is expected to worsen as greenhouse gas emissions continue to affect environmental conditions negatively (“Agriculture and economic reform in Sub-Saharan Africa,” n.d.).

Moreover, political instability, conflicts, and epidemics have historically besieged the region, creating shocks that disrupt both physical and human factors of production. These conditions have been further intensified by weak governance and the lack of diverse economic activities, which distort resource allocation and hinder effective responses to food security challenges. The COVID-19 pandemic, for example, led to increased uncertainty and a significant reduction in output and productivity across various sectors, causing a decline in aggregate demand that outstripped the initial labor supply reductions. (Africa - Regional Overview of Food Security and Nutrition 2023, 2023) .

The Global Hunger Index 2023 highlights the dire situation, with countries such as the Central African Republic and Madagascar showing alarmingly high levels of hunger and malnutrition (“Enhancing Food and Nutrition Security in the Sahel and Horn of Africa,” n.d.). These conditions indicate that while SSA is the most affected region overall, specific nations also suffer from extremely high rates of undernourishment and food insecurity, necessitating urgent and equitable interventions to address these pressing challenges (“How to end hunger in sub-Saharan Africa: fight inequality, gender imbalances and climate change,” n.d.).

Topic:

“Factors Influencing Food Insecurity in Selected West African Countries”

Problem statement:

In a context marked by recurring climate shocks and significant demographic pressure, why do West African countries struggle to ensure their food self-sufficiency?

More specifically:

West Africa, a region heavily dependent on agriculture, is facing increasing challenges due to climate change (variations in rainfall, rising temperatures) and socioeconomic pressures (rapid population growth, rural poverty). In this context, how do climatic factors (rainfall, temperature) compare with other determinants in explaining food insecurity?

Research question:

What are the economic (GDP, population) and technological (irrigation, water resource management) factors in explaining agricultural yields between 2000 and 2020? In other words, to what extent does climate change actually influence agricultural productivity compared to local adaptation strategies (modern infrastructure, public policies)?

Research Objectives:

To assess the relative impact of climatic variables (rainfall, temperature) and economic and technological factors (GDP, population, irrigable area, irrigation methods) on agricultural yield in West Africa between 2000 and 2020.

Main Objective:

Assess the relative impact of climatic factors (rainfall, temperature) and socio-economic factors (GDP, population, irrigation) on agricultural production and food security.

Specific Objectives :

• Identify the countries most vulnerable to food insecurity. • Analyze the effectiveness of modern irrigation technologies (drip, sprinkler). • Propose recommendations to improve the resilience of agricultural systems.

Hypothesies

Geographic location of the project

Our project is based on the study of several West African countries in order to obtain a complete regional perspective of the situation of food insecurity in West Africa; there are 12 of these countries as shown in the map below

Keys words definition:

Food security: A condition in which all people, at all times, have physical, social, and economic access to sufficient, safe, and nutritious food to meet their dietary needs and preferences for an active and healthy life. Starvation: An extreme scarcity of food, often accompanied by widespread starvation, malnutrition, and mortality, typically caused by a combination of factors such as drought, conflict, and economic collapse.

Famine: An extreme scarcity of food, often accompanied by widespread starvation, malnutrition, and mortality, typically caused by a combination of factors such as drought, conflict, and economic collapse

Malnutrition: A condition resulting from deficiencies, excesses, or imbalances in the intake of nutrients, including undernutrition (e.g., stunting, wasting) and overnutrition (e.g., obesity).

Context

Food insecurity remains a pervasive and complex challenge for many countries in West Africa. Its root causes are multifaceted, stemming from both environmental constraints and socioeconomic challenges. These factors not only limit food production but also exacerbate poverty and inequality, creating a vicious cycle that undermines the region’s ability to achieve sustainable food security. The consequences of this crisis are far-reaching, affecting health, education, and overall societal development.

Underlying Causes of Food Insecurity

To address food insecurity effectively, it is essential to identify and understand its underlying causes. Key factors include:

Insufficient Agricultural Production

Farmers in West Africa face significant barriers to increasing agricultural output. Traditional farming methods, coupled with unpredictable weather patterns, crop diseases, and limited access to modern agricultural technologies, restrict productivity. As a result, the region struggles to produce enough food to meet the needs of its growing population.

Poverty and Economic Inequality

Widespread poverty and deep-rooted economic disparities prevent millions of people from accessing adequate and nutritious food. Vulnerable populations, including smallholder farmers and rural communities, are disproportionately affected, further entrenching cycles of hunger and malnutrition.

Climatic Variability

Climate change has intensified the frequency and severity of extreme weather events such as droughts, floods, and erratic rainfall. These climatic variations disrupt planting and harvesting cycles, reduce crop yields, and threaten the livelihoods of millions who depend on rain-fed agriculture.

Rapid Population Growth

The rapid increase in population across West Africa places immense pressure on already limited food resources. With more mouths to feed and insufficient corresponding increases in food production, ensuring adequate nutrition for all becomes increasingly challenging.

Conflicts and Political Instability

Armed conflicts and political instability in parts of the region disrupt food supply chains, displace communities, and destroy agricultural infrastructure. These disruptions often lead to acute food shortages, particularly in conflict-affected areas.

Consequences of Food Insecurity

The impacts of food insecurity are profound and multifaceted, affecting individuals, families, and entire societies. Key conséquences inclue: Food insecurity often leads to inadequate dietary intake, resulting in malnutrition. Children are especially vulnerable, with long-term effects on their physical and cognitive development. This undermines their potential to thrive and contribute to society.

High Infant Mortality Rates

Infants and young children are at heightened risk during periods of food insecurity. Malnutrition and diet-related illnesses significantly increase child mortality rates, perpetuating a cycle of loss and hardship for affected families.

Deteriorating Health

Nutritional deficiencies weaken immune systems, making individuals more susceptible to diseases and infections. Poor health outcomes further strain already fragile healthcare systems, creating additional burdens for communities.

Reduced School Attendance

Children suffering from hunger or malnutrition are less likely to attend school regularly. This compromises their education, limits future opportunities, and perpetuates intergenerational poverty.

Persistent Poverty

Food insecurity reinforces cycles of poverty by reducing individuals’ capacity to work, earn income, and invest in their futures. Without sufficient food, people cannot fully participate in economic activities, stifling broader development efforts.

Approaches to Addressing Food Insecurity

Tackling food insecurity requires comprehensive, long-term strategies that address both immediate needs and systemic issues. Potential solutions include:

Promoting Food Education

Raising awareness about balanced diets and efficient food resource management can empower communities to make informed decisions about nutrition and food consumption.

Strengthening Food Safety Awareness

Organizing campaigns to educate the public on safe food practices and locally adapted solutions can help improve food handling, storage, and preparation techniques.

Improving Access to Markets

Investing in agricultural infrastructure—such as roads, storage facilities, and market connectivity—can enable farmers to sell their produce at fair prices, boosting incomes and encouraging higher productivity.

Encouraging Sustainable Agricultural Development

Adopting sustainable farming practices, such as agroecology and climate-smart agriculture, can enhance food production while preserving natural resources. This approach ensures resilience against climatic shocks and reduces environmental degradation.

Enhancing Access to Quality Seeds

Providing farmers with high-quality, locally adapted seeds can significantly improve crop yields and resistance to pests and diseases, contributing to greater food availability.

Materials and methods

Materials used for the project

  • Ourworldindata.org

“Our World in Data (OWID) is a non-profit research and data project that combines rigorous analysis, interactive visualizations, and open data to explore global challenges. The platform covers a wide range of topics, including health, education, poverty, hunger, climate change, and other key areas. Its main objective is to provide reliable, up-to-date, and accessible information on phenomena at a global scale, helping policymakers, researchers, and the general public better understand complex issues. OWID aggregates data from reputable sources such as the United Nations, the World Bank, and the World Health Organization, ensuring accuracy and credibility. The platform is widely recognized for its ability to present complex data in a clear and engaging manner through interactive charts and graphs. For our research, OurWorldInData.org served as the primary source for exploring variables related to Food insecurity

  • RStudio software

RStudio is an open-source integrated development environment (IDE) specifically designed for the R programming language, a powerful tool widely used for statistical analysis, data visualization, and modeling. In this project, RStudio was chosen for its flexibility, extensive library of specialized packages, and strong community support. It enabled us to perform advanced statistical analyses and create clear, informative visualizations of our data. Specifically, we utilized packages such as ggplot2 for data visualization and dplyr for data manipulation These tools were essential in helping us interpret and present our findings effectively.”

  • ZOTERO software

Zotero is an open-source bibliographic management tool designed to help researchers organize, store, and cite references in their work. It enables the creation of a personal database of bibliographic references, which can be easily integrated into research documents and used to generate formatted bibliographies. In this project, Zotero was selected for its user-friendly interface, compatibility with various citation styles (e.g., APA, MLA), and seamless integration with word processors like Microsoft Word and Google Docs. It allowed us to efficiently manage our references, insert citations into our report, and produce a consistent and properly formatted bibliography. This tool significantly streamlined our workflow and ensured the accuracy of our citations throughout the research process.”

  • QGIS software

QGIS is a free and open-source Geographic Information System (GIS) software that enables the creation, analysis, visualization, and management of geographic and spatial data. It supports a wide range of vector data formats, including Shapefiles, ArcInfo coverages, Mapinfo, and GRASS GIS, making it highly versatile for handling diverse datasets. In this project, QGIS was chosen for its user-friendly interface, extensive plugin ecosystem, and compatibility with various data formats. It allowed us to perform advanced spatial analyses, create thematic maps, and visualize geographic data effectively. These capabilities were essential for interpreting spatial patterns and relationships within our dataset.

Data collection tools

The collection and processing of data is necessary to carry out our project. Depending on our study theme and the elements we wanted to highlight, we selected from the available and usable data in the database https://ourworldindata.org/ via the link https://ourworldindata. org/hunger-and-undernourishment ; The data used for our analysis was also extracted from the World Bank https://www.worldbank.org/ . The data downloaded for our theme was sent to Excel to be filtered in order to be able to extract those we needed for our work

To research our data, we consulted the official data site OurWorldInData.com. This site has thematic data concerning different problems in the world. The most recent data for all our variables were taken in the same time interval (the year 2020). They concern the countries in our study area; So we decided to carry out our work in a few countries in West Africa which is our main target. These are: Benin, Burkina Faso, Cape Verde, Ivory Coast, Gambia, Ghana, Liberia, Mali, Nigeria, Senegal, Sierra Leone and Togo.

Regarding bibliographic information, we have consulted a certain number of scientific documents on the theme of our research.

Data collection is the process by which researchers capture the information they need, the purpose of which is to carry out a study. This is a necessary step before conducting a statistical study. Indeed, these data are necessary for the processing of information and its subsequent interpretation.

We chose a questionnaire for collecting our data because information on food insecurity is difficult to find, especially in rural areas; In these areas it is difficult to carry out investigations, especially if there is no access to networks. The questionnaire will allow simpler understanding for these populations; and at the same time it will be more easily accessible for populations in more developed urban areas who will be able to access it directly online. https://ee.kobotoolbox.org/x/CZvV3VDU

Principal component analysis (PCA ). PCA makes it possible to explore connections between variables and similarities between individuals. It also consists of transforming variables linked to each other (called “correlated” in statistics) into new variables separated from each other. These new variables are called principal components or principal axes.

Results and discussions

Thematic maps

Analysis Data collected

Principal component analysis (PCA)

In our study, our dataset on food insecurity in some West African countries includes 12 variables including 2 additional and 12 individuals.

Data visualization

setwd("C:/Users/Yameogo/Desktop/RTI_Final")
data=read.csv(file="Data.csv", header = TRUE, sep = ";", 
          dec = ",", row.names=1  )
data[,1:11]
##               Annee Precipitataion Temperature Population Eau_Renou Eau_Agri
## Burkina Faso   2010         682.66        28.6   16526915    801.13     53.6
## Benin          2010        1027.33        26.6   10029759   1088.54     33.9
## Cote d'Ivoire  2010        1225.00        25.9   23034175   3471.94     46.3
## Mali           2010         274.33        29.7   16406110   3905.55     98.0
## Niger          2010          91.67        29.3   66905190    221.05     81.9
## Senegal        2010         610.67        28.8   63498610   2055.60     90.6
## Togo           2010        1231.33        26.1    6847454   1757.30     38.5
##                    PIB Rend_agricol Super_culti In_secAli Prix_alim
## Burkina Faso  10269333      4006299   3685890.3     17.60  1426.283
## Benin          9478333      1509975    883078.8     12.60  1377.900
## Cote d'Ivoire 19274333      2021619    973418.3     15.20  1549.873
## Mali          10373667      6000396   4036772.3      9.07  1549.877
## Niger          8007000      4388582   9485861.7     16.93  1766.370
## Senegal       15557667      2144763   1547556.0     16.80  1489.173
## Togo           4751000      1047631    919638.3     22.60  1325.283
library(readxl)
## Warning: le package 'readxl' a été compilé avec la version R 4.4.3
library(corrplot)
## Warning: le package 'corrplot' a été compilé avec la version R 4.4.3
## corrplot 0.95 loaded
library(FactoMineR)
library(factoextra)
## Warning: le package 'factoextra' a été compilé avec la version R 4.4.3
## Le chargement a nécessité le package : ggplot2
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa

Table de correlation

# Sélectionner les colonnes numériques
data_numeriques <- data[, c("Precipitataion", "Temperature", "Population", 
                                  "Eau_Renou", "Eau_Agri", "PIB", 
                                  "Rend_agricol", "Super_culti", 
                                  "In_secAli",  "Prix_alim")]

# Calculer la matrice de corrélation
matrice_correlation <- cor(data_numeriques)

# Afficher la matrice de corrélation
print(matrice_correlation)
##                Precipitataion Temperature  Population   Eau_Renou   Eau_Agri
## Precipitataion      1.0000000 -0.95422077 -0.61097212  0.17772724 -0.8447610
## Temperature        -0.9542208  1.00000000  0.53185423 -0.09136428  0.8812878
## Population         -0.6109721  0.53185423  1.00000000 -0.29262892  0.6365682
## Eau_Renou           0.1777272 -0.09136428 -0.29262892  1.00000000  0.2497253
## Eau_Agri           -0.8447610  0.88128781  0.63656822  0.24972528  1.0000000
## PIB                 0.1678800 -0.10787176  0.24375630  0.51425493  0.1481355
## Rend_agricol       -0.8396313  0.84388981  0.18278003  0.16136112  0.7194176
## Super_culti        -0.8469374  0.68843189  0.57529459 -0.42742625  0.5239380
## In_secAli           0.3758534 -0.37418435  0.08300305 -0.47569671 -0.3991381
## Prix_alim          -0.7308962  0.55352552  0.72172125 -0.05485613  0.6173233
##                        PIB Rend_agricol Super_culti   In_secAli   Prix_alim
## Precipitataion  0.16788003  -0.83963131 -0.84693742  0.37585343 -0.73089619
## Temperature    -0.10787176   0.84388981  0.68843189 -0.37418435  0.55352552
## Population      0.24375630   0.18278003  0.57529459  0.08300305  0.72172125
## Eau_Renou       0.51425493   0.16136112 -0.42742625 -0.47569671 -0.05485613
## Eau_Agri        0.14813550   0.71941759  0.52393799 -0.39913813  0.61732331
## PIB             1.00000000  -0.08199585 -0.30629966 -0.31342541  0.20560818
## Rend_agricol   -0.08199585   1.00000000  0.68464588 -0.55628353  0.58824843
## Super_culti    -0.30629966   0.68464588  1.00000000 -0.07602386  0.83124596
## In_secAli      -0.31342541  -0.55628353 -0.07602386  1.00000000 -0.27194973
## Prix_alim       0.20560818   0.58824843  0.83124596 -0.27194973  1.00000000
corrplot(matrice_correlation, method = "color", type = "upper", 
         tl.cex = 0.8, tl.col = "black", 
         title = "Heatmap de Corrélation")

The correlation matrix is a matrix grouping together a set of values called correlation coefficient. In fact, these values show the relationship that exists between the variables taken two by two. They vary between -1 and 1 depending on whether the relationship between the two variables is strong or weak. Indeed, there are three types of correlation, namely:

  • Positive Correlation: It allows us to say that two variables evolve in the same direction, that is to say that the increase in one leads to that of the other and vice versa. The closer the value is to +1, the greater the relationship. The most notable values are in red and greater than 0.5

  • Negative correlation: It tends to show that two variables move in opposite directions.

  • This means that an increase in one leads to a decrease in the other and vice versa. The closer the value is to -1, the greater the opposition relationship. Values in purple are more remarkable and less than -0.5

  • Zero correlation: This shows that the increase or decrease in one of the variables has no influence on the others.

In our correlation matrix we can describe the relationship between some variables. For example the variables Precipitataion and Temperature are negatively correlated. Thus we can say that the temperature and precipitations highlights climatc interactions that influence food security more the undernourished population increases, the more the food available for consumption

In general, we have as many negative as positive correlations which make it possible to highlight the existing relationship between the variables and therefore to know what food insecurity can be due to, for example, and also the influence of the population on food production.

Axes choice

This table presents the eigenvalues with their percentage of variance on each axis as well as the cumulative percentage of variance which is equal to 100% at the 9th variable. The number of eigenvalues is equal to 10 because according to PCA the number of eigenvalues must be equal to the number of variables. These eigenvalues also correspond to the variance of the cloud of individuals.

From these eigenvalues we can determine a priori the number of axes that we can retain using the method called Kaiser criterion. So from the Kaiser criterion which says that we must retain the axes associated with eigenvalues greater than 1, then we can retain axes 1, 2 which bring together .

To solidify our choice of the first two axes we can also base ourselves on the elbow or scree rule of eigenvalues.

# Créer un modèle de régression linéaire
# Exemple : Rend_agricol en fonction de Precipitataion et Temperature
reg1 <- lm(Rend_agricol ~ Precipitataion + Temperature, data = data_numeriques)

# Résumé du modèle
summary(reg1)
## 
## Call:
## lm(formula = Rend_agricol ~ Precipitataion + Temperature, data = data_numeriques)
## 
## Residuals:
##  Burkina Faso         Benin Cote d'Ivoire          Mali         Niger 
##        508475       -377451        816845       1278889       -399533 
##       Senegal          Togo 
##      -1572070       -255155 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)
## (Intercept)    -10861761   30042623  -0.362    0.736
## Precipitataion     -1545       3522  -0.439    0.684
## Temperature       538959     989331   0.545    0.615
## 
## Residual standard error: 1162000 on 4 degrees of freedom
## Multiple R-squared:  0.7254, Adjusted R-squared:  0.588 
## F-statistic: 5.282 on 2 and 4 DF,  p-value: 0.07543
# Visualisation des résultats
plot(data_numeriques$Precipitataion, data_numeriques$Rend_agricol, 
     main = "Régression Linéaire : Rend_agricol vs Precipitataion",
     xlab = "Précipitations", ylab = "Rendement Agricole", pch = 19, col = "blue")
abline(reg1, col = "red", lwd = 2)  # Ajouter la ligne de régression
## Warning in abline(reg1, col = "red", lwd = 2): utilisation des deux premiers
## des 3 coefficients de régression
abline(lm(Rend_agricol ~ Precipitataion, data=data_numeriques),coL = "red", lwd =2)
## Warning in int_abline(a = a, b = b, h = h, v = v, untf = untf, ...): "coL"
## n'est pas un paramètre graphique

Analysis of linear regression Plot

The provided linear regression plot shows the relationship between agriculturl yield(Rend_agricol) and precipitation. Below is a detailed analysis of the plot

General observation

  • The X-axis represents precipitation (measured in some unit,millieters
  • The Y-axis the agricultural yield (measured in some uni, likely kilograms per hectre)

Trend observed:

The regression line shows a negative slope , meaning that as precipitation increases , agricultural yield tends to decrease

This suggest an inverse relationship betwzzn precipitation and agricultural yield in this dataset

Graphe de Kaser

# Charger les bibliothèques nécessaires
library(ggplot2)

# Créer un data frame avec les valeurs propres et leurs contributions
valeurs_propres <- data.frame(
  Dimension = paste("Dim", 1:6, sep = ""),
  Valeur_Propre = c(5.30, 2.16, 1.33, 0.60, 0.40, 0.2),
  Pourcentage_Variance = c(53.04, 21.60, 13.30, 5.99, 4.00, 2.07)
)

# Ajouter une ligne horizontale pour la valeur propre seuil (Kaiser)
seuil_kaiser <- 1  # Seuil de Kaiser : valeur propre > 1

# Créer le graphe de Kaiser avec une courbe reliant les sommets
ggplot(valeurs_propres, aes(x = Dimension, y = Valeur_Propre)) +
  geom_bar(stat = "identity", fill = "steelblue") +  # Barres pour les valeurs propres
  geom_line(aes(group = 1), color = "red", size = 1) +  # Courbe reliant les sommets
  geom_point(color = "red", size = 3) +  # Points aux sommets des barres
  geom_text(aes(label = paste0(round(Pourcentage_Variance, 2), "%")), 
            vjust = -0.5, color = "black", size = 3.5) +  # Ajouter les pourcentages de variance
  geom_hline(yintercept = seuil_kaiser, linetype = "dashed", color = "blue", size = 1) +  # Ligne de seuil
  labs(title = "Graphe de Kaiser (Éboulis des Valeurs Propres)",
       x = "Dimensions", y = "Valeur Propre",
       caption = "Seuil de Kaiser : Valeur Propre > 1") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))# Charger les bibliothèques nécessaires
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

library(ggplot2)

# Créer un data frame avec les valeurs propres et leurs contributions
valeurs_propres <- data.frame(
  Dimension = paste("Dim", 1:6, sep = ""),
  Valeur_Propre = c(5.30, 2.16, 1.33, 0.60, 0.40, 0.21),
  Pourcentage_Variance = c(53.04, 21.60, 13.30, 5.99, 4.00, 2.07)
)

# Ajouter une ligne horizontale pour la valeur propre seuil (Kaiser)
seuil_kaiser <- 1  # Seuil de Kaiser : valeur propre > 1

# Créer le graphe de Kaiser
ggplot(valeurs_propres, aes(x = Dimension, y = Valeur_Propre)) +
  geom_bar(stat = "identity", fill = "steelblue") +  # Barres pour les valeurs propres
  geom_hline(yintercept = seuil_kaiser, linetype = "dashed", color = "red", size = 1) +  # Ligne de seuil
  labs(title = "Graphe de Kaiser (Éboulis des Valeurs Propres)",
       x = "Dimensions", y = "Valeur Propre",
       caption = "Seuil de Kaiser : Valeur Propre > 1") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

Figure 9: Décomposition of inertia

The total inertia of the factorial axes indicates on the one hand whether the variables are structured and on the other hand suggests the number of principal components appropriate to study.

So by observing this figure, we see that the first two axes of the analysis express 68.45% of the total inertia of the dataset which means that 68.45% of the total variability of the cloud of individuals or variables is represented in this plan. This is a high percentage, and the foreground therefore well represents the variability contained in a very large part of the active dataset. This value is greater than the reference value of 56.29%, the variability explained by this plan is therefore significant (this reference interval is the 0.95-quantile of the distribution of inertia percentages obtained by simulating 1633 random data sets of dimensions comparable on the basis of a normal distribution).

Due to these observations, we can say that only the first too axes carry real information. Consequently, we will only keep these too axes for the description of the analysis. Thus, we reaffirm our choice of axes based on the Kaizer criterion.

Study of the correlation circle

# Charger les bibliothèques nécessaires
library(readxl)
library(FactoMineR)
library(factoextra)

# Sélectionner uniquement les colonnes numériques
data_numeriques <- data[, c("Precipitataion", "Temperature", "Population", 
                                  "Eau_Renou", "Eau_Agri", "PIB", 
                                  "Rend_agricol", "Super_culti", 
                                  "In_secAli",  "Prix_alim")]

# Standardiser les données
data_standardisees <- scale(data_numeriques)

# Réaliser une ACP
res.acp <- PCA(data_standardisees, graph = FALSE)

# Créer le cercle de corrélation
fviz_pca_var(res.acp, col.var = "contrib", 
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE, title = "Cercle de Corrélation")

Figure 10: Correlation Circle

Analysis of the Correlation Circle (Cercle de Corrélation)

The provided correlation circle, also known as a correlation biplot , is a graphical tool used in multivariate analysis (e.g., Principal Component Analysis - PCA) to visualize the relationships between variables. Below is a detailed breakdown of the plot and its implications:

1. General Structure of the Correlation Circle

The x-axis (Dim1) represents the first principal component, which explains 53% of the total variance in the data. The y-axis (Dim2) represents the second principal component, which explains 21.6% of the total variance. Together, these two dimensions account for 74.6% of the total variance. Each variable is represented as a vector originating from the center of the circle. The direction and length of each vector provide information about:

Direction : Indicates the relationship between variables (positive or negative correlation). Length : Reflects the contribution of the variable to the principal components (longer vectors indicate stronger contributions).

2. Variables in the Plot

The following variables are plotted, along with their approximate positions and interpretations:

  • Eau_Renou (Renewable Water): Located in the upper-right quadrant . Strong positive correlation with PIB (GDP) and Temperature . Moderate positive correlation with Precipitation . Suggests that countries with higher renewable water resources tend to have higher GDP and temperatures.
  • PIB (GDP): Positioned close to Eau_Renou . Strong positive correlation with Eau_Renou and Temperature . Moderate positive correlation with Precipitation . Indicates that higher GDP is associated with higher renewable water resources and temperatures.
  • Temperature : Located near Eau_Renou and PIB . Strong positive correlation with Eau_Renou and PIB . Moderate positive correlation with Precipitation . Suggests that temperature is closely linked to economic development and water resources.
  • Precipitation : Positioned in the upper-left quadrant . Moderate positive correlation with Eau_Renou , PIB , and Temperature . Suggests that precipitation is related to water availability, economic conditions, and temperature, but not as strongly as other variables.
  • Rend_agricol (Agricultural Yield): Located in the upper-right quadrant , close to Temperature . Moderate positive correlation with Temperature . Weak correlation with other variables like PIB and Eau_Renou . Indicates that agricultural yield is influenced by temperature but less so by economic factors or water resources.
  • Population : Positioned in the lower-right quadrant . Moderate negative correlation with Temperature and Eau_Renou . Suggests that population size may be inversely related to temperature and water resources.
  • Prix_alim (Food Prices): Located in the lower-right quadrant . Moderate negative correlation with Temperature and Eau_Renou . Suggests that food prices may increase in regions with lower temperatures and water resources.
  • Super_culti (Super Cultivated Area): Positioned in the lower-right quadrant . Moderate negative correlation with Temperature and Eau_Renou . Suggests that super-cultivated areas may be less prevalent in regions with high temperatures and abundant water resources.
  • In_secAli (Food Insecurity): Located in the lower-left quadrant . Moderate negative correlation with Temperature and Eau_Renou . Suggests that food insecurity is more pronounced in regions with lower temperatures and water resources.

Study of the representation of individuals in the Factorial plan

# Standardiser les données
data_standardisees <- scale(data_numeriques)

# Réaliser une ACP
res.acp <- PCA(data_standardisees, graph = FALSE)

# Représenter les individus dans le plan factoriel
fviz_pca_ind(res.acp, col.ind = "cos2", 
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE, title = "Représentation des Individus dans le Plan Factoriel")

Figure 11: Graph of the représentation of individuals in the factoriel design

Analysis of the Factorial Plane Representation

The provided plot, titled “Représentation des Individus dans le Plan Factoriel” (Representation of Individuals in the Factorial Plane), is a graphical output from a multivariate analysis technique such as Principal Component Analysis (PCA). This type of plot is used to visualize how individual observations (in this case, countries) are distributed in the space defined by the first two principal components. Below is a detailed breakdown of the plot and its implications:

1. General Structure of the Plot

The x-axis (Dim1) represents the first principal component, which explains 53% of the total variance in the data. The y-axis (Dim2) represents the second principal component, which explains 21.6% of the total variance. Together, these two dimensions account for 74.6% of the total variance. Each country is represented as a point in this two-dimensional space. The position of each point provides information about:

Proximity : Countries that are close to each other share similar characteristics across the variables used in the analysis. Opposition : Countries on opposite sides of the origin (0, 0) have contrasting characteristics. The color gradient (represented by the “cos²” scale on the right) indicates the quality of representation of each country in the factorial plane. A higher cos² value (closer to 1) means that the country’s position in the factorial plane accurately reflects its true multidimensional position, while a lower cos² value (closer to 0) suggests that the factorial plane does not fully capture the country’s characteristics.

2. Position of Countries

Here is a detailed description of the positions of the countries:

Mali : Located in the upper-right quadrant . Farthest from the origin along both axes. Indicates that Mali has distinct characteristics compared to other countries, particularly in the directions of Dim1 and Dim2. Likely contributes significantly to the variability captured by the first two principal components. Niger : Positioned in the lower-right quadrant . Farther from the origin along Dim1 but closer along Dim2 compared to Mali. Suggests that Niger shares some similarities with Mali in terms of Dim1 but differs in terms of Dim2. Côte d’Ivoire : Located in the upper-left quadrant . Farther from the origin along Dim2 but closer along Dim1 compared to Mali. Indicates that Côte d’Ivoire has distinct characteristics related to Dim2 but is more similar to other countries in terms of Dim1. Togo : Positioned in the lower-left quadrant . Farther from the origin along Dim1 but closer along Dim2 compared to Côte d’Ivoire. Suggests that Togo has distinct characteristics related to Dim1 but is more similar to other countries in terms of Dim2. Benin : Located near the origin in the lower-left quadrant . Closer to the origin compared to Togo, indicating that Benin’s characteristics are more central or average relative to the other countries. Burkina Faso : Positioned near the origin in the lower-left quadrant . Very close to Benin, suggesting that Burkina Faso and Benin share similar characteristics across the analyzed variables. Senegal : Located in the upper-middle region . Closer to the origin compared to Mali and Niger but farther than Burkina Faso and Benin. Indicates that Senegal has moderate characteristics along both dimensions.

Study of variables

By observing this table we can highlight the different variables correlated to the different axes (Dim1 and Dim2) both positively and negatively and thus see if we have a size effect. In our case, we have 6 variables correlated to axis 1 (these are the variables whose data are colored in yellow) and 3 variables correlated to axis 2 (these are the variables whose data are colored in red). In addition, the contribution and the cos2 which shows the contribution that each variable makes and the quality of representation on the axes. However, the contribution and the cos2 of the variables with respect to the dimension evolve in the same direction as that of the variables with respect to the coordinates.

To better observe the variables contributing the most to the different axes, we will use the following graphs:

contributions <- data.frame(
  Variables = c("Précipitation", "Température", "Population", "EAU_Renouvelable", 
                "EAU_Agricole", "PIB", "Rendement_Agricole", "Superficie_Irrigable", 
                "Indice_Sécurité_Alimentaire"),
  Dim1 = c(18.79, 17.41, 8.90, 0.13, 15.95,0.01, 14.91, 14.21,2.30),
  Dim2 = c(2.94, 1.66, 2.47, 7.59, 2.13, 34.32, 1.04, 5.49, 29.09))

# Fonction pour créer un graphique pour une dimension spécifique avec coloration différente
create_contribution_plot <- function(dimension_name, data_column, threshold) {
  ggplot(data = contributions, aes(x = Variables, y = !!sym(data_column), fill = !!sym(data_column) > threshold)) +
    geom_bar(stat = "identity") +
    scale_fill_manual(values = c("TRUE" = "blue", "FALSE" = "red")) + # Couleurs : rouge pour > seuil, gris pour <= seuil
    geom_hline(yintercept = threshold, linetype = "dashed", color = "black", size = 1) + # Ajout de la ligne horizontale
    labs(title = paste("Contribution des Variables sur", dimension_name),
         x = "Variables", y = "Contribution (%)",
         fill = "Contribution > Seuil") +
    theme_minimal() +
    theme(axis.text.x = element_text(angle = 45, hjust = 1))
}

# Définir un seuil (par exemple, 10 % ou la moyenne des contributions)
threshold_dim1 <- 10  # Seuil pour Dim1
threshold_dim2 <- 10 # Seuil pour Dim2

# Créer les graphiques pour chaque dimension avec la coloration différente
plot_dim1 <- create_contribution_plot("Dim1", "Dim1", threshold_dim1)
plot_dim2 <- create_contribution_plot("Dim2", "Dim2", threshold_dim2)

# Afficher les graphiques
print(plot_dim1)

print(plot_dim2)

On this graph, we clearly observe that the variables (Pop, GbleFood , CePro and PopextPvrty ) are those which contribute the most to axis 1.

On this graph, we clearly observe that the variables (GDP, PopUndershmnt and FdAbleCon ) are those which contribute the most to axis 2.

Study of Individuals

Tableau 4: Coordonate,Contribution ,quality of representation

By observing this table we can list the different individuals correlated to the axes (Dim1 and Dim2) both positively and negatively. Thus we have 6 individuals correlated to axis 1 (these are the individuals whose data are colored in red) and 6 individuals correlated to axis 2 (these are the variables whose data are colored.

Using this graph, we clearly see the individuals contributing the most to axis 1. These individuals are Nigeria.

Using this graph, we clearly see the individuals contributing the most to axis 2. These individuals are Liberia, Mali, Niger.

# Charger les bibliothèques nécessaires
library(ggplot2)

# Créer un data frame avec les contributions des individus
contributions <- data.frame(
  Individus = c("Bénin", "Burkina Faso", "Côte d'Ivoire", 
                "Mali", "Niger", "Sénégal", "Togo"),
  Dim1 = c(11.807, 0.00,8.098, 17.059, 35.552, 1.620, 25.865),
  Dim2 = c(0.091, 4.305,21.781, 30.835, 27.517, 1.347, 14.124)
)

# Fonction pour créer un graphique pour une dimension spécifique avec coloration différente
create_contribution_plot <- function(dimension_name, data_column, threshold) {
  ggplot(data = contributions, aes(x = Individus, y = !!sym(data_column), fill = !!sym(data_column) > threshold)) +
    geom_bar(stat = "identity") +
    scale_fill_manual(values = c("TRUE" = "red", "FALSE" = "grey")) + # Couleurs : rouge pour > seuil, gris pour <= seuil
    geom_hline(yintercept = threshold, linetype = "dashed", color = "black", size = 1) + # Ajout de la ligne horizontale
    labs(title = paste("Contribution des Individus sur", dimension_name),
         x = "Individus", y = "Contribution (%)",
         fill = "Contribution > Seuil") +
    theme_minimal() +
    theme(axis.text.x = element_text(angle = 45, hjust = 1))
}

# Définir un seuil (par exemple, 10 % ou la moyenne des contributions)
threshold_dim1 <- 10  # Seuil pour Dim1
threshold_dim2 <- 10  # Seuil pour Dim2

# Créer les graphiques pour chaque dimension avec la coloration différente
plot_dim1 <- create_contribution_plot("Dim1", "Dim1", threshold_dim1)
plot_dim2 <- create_contribution_plot("Dim2", "Dim2", threshold_dim2)

# Afficher les graphiques
print(plot_dim1)

print(plot_dim2)

Figure 15: Contribution of individual to Dim-1

Based on this graph1 and our scatterplot on the factorial level, we can then say that Nigeria is an atypical individual because it has the greatest contribution among all individuals which means that it is also well represented and has greater data at the variable level.

Hierarchical Ascending Classification (CAH)

Classification is a method which aims to group individuals with characteristics or a few characteristics in common. It can be done in a supervised manner (Knowing the number of classes desired we seek to know to which class an individual may belong) and unsupervised ( We do not know in advance the number of classes). In our case we carried out a classification unsupervised (an ascending hierarchical classification).

# Standardiser les données
data_standardisees <- scale(data_numeriques)

# Calculer la matrice de distances euclidiennes
matrice_distances <- dist(data_standardisees, method = "euclidean")

# Réaliser la classification hiérarchique ascendante
classification_hierarchique <- hclust(matrice_distances, method = "ward.D2")

# Visualiser le dendrogramme
fviz_dend(classification_hierarchique, k = 3,  # Choisir le nombre de clusters
          k_colors = c("#00AFBB", "#E7B800", "#FC4E07"),
          color_labels_by_k = TRUE,
          rect = TRUE,
          main = "Dendrogramme - Classification Hiérarchique Ascendante")
## Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
## of ggplot2 3.3.4.
## ℹ The deprecated feature was likely used in the factoextra package.
##   Please report the issue at <https://github.com/kassambara/factoextra/issues>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

Description of a Dendrogram and Its Role

A dendrogram is a tree-like diagram used to represent the results of hierarchical clustering. It visually illustrates how data points (or observations) are grouped together based on their similarities or dissimilarities. Hierarchical clustering is an unsupervised machine learning technique that aims to build a hierarchy of clusters, either by merging smaller clusters into larger ones (agglomerative clustering) or by splitting larger clusters into smaller ones (divisive clustering). The dendrogram is primarily used in agglomerative clustering.

Key Components of a Dendrogram

Leaves :

These are the individual data points or observations at the bottom of the dendrogram. In your case, these are countries such as Togo, Burkina Faso, Benin, etc.

Branches :

These represent the merging of clusters. Each branch point (also called a “node”) indicates the fusion of two clusters into a single cluster.

Height :

The vertical axis represents the distance or dissimilarity between clusters. A lower height indicates that the clusters being merged are more similar, while a higher height indicates greater dissimilarity.

Merging Points :

The horizontal lines connecting branches indicate the points at which clusters are merged. The height of these lines corresponds to the distance at which the merge occurs.

Clusters :

By cutting the dendrogram horizontally at a specific height, you can define the number of clusters. Observations connected below that cut-off point belong to the same cluster. Role of a Dendrogram

The dendrogram serves several important roles in data analysis:

Visualization of Cluster Formation :

It provides a clear visual representation of how clusters are formed step-by-step. This helps in understanding the hierarchical structure of the data.

Identification of Natural Clusters :

By examining the dendrogram, analysts can identify natural groupings in the data. Long vertical lines (indicating large distances) suggest significant differences between clusters, while short vertical lines suggest high similarity.

Determination of Optimal Number of Clusters :

Analysts can use the dendrogram to decide the optimal number of clusters by choosing a cutoff point. For example, cutting the dendrogram at a certain height will result in a specific number of clusters.

Insight into Data Structure :

The dendrogram reveals the relationships between data points and clusters. For instance, it can show which countries (in your case) are most similar to each other and which are distinct.

Comparison of Similarity/Dissimilarity :

The height of each merge provides quantitative information about the similarity or dissimilarity between clusters. This helps in interpreting the strength of relationships within the data.

Support for Decision-Making :

In fields like biology, sociology, geography, and economics, dendrograms help researchers make informed decisions about grouping entities (e.g., species, regions, or populations) based on shared characteristics. ### How to Interpret a Dendrogram Low Height Merges : Indicate strong similarities between clusters. For example, if Togo and Burkina Faso are merged at a low height, it means they are very similar. High Height Merges : Indicate weak similarities or strong dissimilarities. For example, if Mali and Niger are merged at a high height, it suggests they are quite different from the rest of the group.

Cutting the Dendrogram : To determine the number of clusters, you can draw a horizontal line across the dendrogram at a specific height. The number of vertical lines intersected by this line corresponds to the number of clusters.

Example Application in Your Case In your research on the impact of socio-economic and climatic factors on food security in West Africa, the dendrogram helps you:

Group Countries Based on Similarities : Identify which countries share similar characteristics (e.g., climate, agricultural practices, socio-economic conditions). Highlight Distinct Groups : Recognize countries (like Mali and Niger) that are significantly different from others, potentially requiring tailored interventions. Guide Further Analysis : Use the dendrogram to focus on specific groups of countries and investigate why they are similar or different.

Summary

A dendrogram is a powerful tool for visualizing hierarchical clustering. It shows how data points are grouped together based on their similarities, with the height of each merge indicating the degree of dissimilarity. In your study, the dendrogram helps identify patterns in the data, such as which countries in West Africa share similar characteristics and which are distinct. This information is crucial for understanding regional variations in food security and designing targeted policies or interventions.

Results and Discussion

Analysis and interpretation of the results obtained

Study of Eigen value

This table presents the eigenvalues with their percentage of variance on each axis as well as the cumulative percentage of variance which is equal to 100% at the 10th variable of our PCA without the atypical element. The number of eigenvalues is equal to 9 because according to PCA the number of eigenvalues must be equal to the number of variables. These eigenvalues also correspond to the variance of the cloud of individuals.

From these eigenvalues we can determine a priori the number of axes that we can retain using the method called Kaiser criterion. So from the Kaiser criterion which says that we must retain the axes associated with eigenvalues greater than 1, then we can retain axes 1, 2 and 3 which bring together 85.43% of the information. However, analysis on 3 axes can be difficult so we can then keep the first three axes which bring together 85.43% of the information for easier analysis.

To reaffirm our choice of the first two axes we can also base ourselves on the elbow rule or Scree of eigenvalues.

The total inertia of the factorial axes indicates on the one hand whether the variables are structured and on the other hand suggests the number of principal components appropriate to studystructured and on the other hand suggests the number of principal components appropriate to study.

# Charger les bibliothèques nécessaires
library(ggplot2)

# Créer un data frame avec les valeurs propres et leurs contributions
valeurs_propres <- data.frame(
  Dimension = paste("Dim", 1:6, sep = ""),
   Valeur_Propre = c(5.30, 2.16, 1.33, 0.60, 0.40, 0.2),
  Pourcentage_Variance = c(53.04, 21.60, 13.30, 5.99, 4.00, 2.07)
)

# Ajouter une ligne horizontale pour la valeur propre seuil (Kaiser)
seuil_kaiser <- 1  # Seuil de Kaiser : valeur propre > 1

# Créer le graphe de Kaiser avec une courbe reliant les sommets
ggplot(valeurs_propres, aes(x = Dimension, y = Valeur_Propre)) +
  geom_bar(stat = "identity", fill = "steelblue") +  # Barres pour les valeurs propres
  geom_line(aes(group = 1), color = "red", size = 1) +  # Courbe reliant les sommets
  geom_point(color = "red", size = 3) +  # Points aux sommets des barres
  geom_text(aes(label = paste0(round(Pourcentage_Variance, 2), "%")), 
            vjust = -0.5, color = "black", size = 3.5) +  # Ajouter les pourcentages de variance
  geom_hline(yintercept = seuil_kaiser, linetype = "dashed", color = "blue", size = 1) +  # Ligne de seuil
  labs(title = "Graphe de Kaiser (Éboulis des Valeurs Propres)",
       x = "Dimensions", y = "Valeur Propre",
       caption = "Seuil de Kaiser : Valeur Propre > 1") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))# Charger les bibliothèques nécessaires

library(ggplot2)

# Créer un data frame avec les valeurs propres et leurs contributions
valeurs_propres <- data.frame(
  Dimension = paste("Dim", 1:6, sep = ""),
  Valeur_Propre = c(5.30, 2.16, 1.33, 0.60, 0.40, 0.2),
  Pourcentage_Variance = c(53.04, 21.60, 13.30, 5.99, 4.00, 2.07)
)

# Ajouter une ligne horizontale pour la valeur propre seuil (Kaiser)
seuil_kaiser <- 1  # Seuil de Kaiser : valeur propre > 1

# Créer le graphe de Kaiser
ggplot(valeurs_propres, aes(x = Dimension, y = Valeur_Propre)) +
  geom_bar(stat = "identity", fill = "steelblue") +  # Barres pour les valeurs propres
  geom_hline(yintercept = seuil_kaiser, linetype = "dashed", color = "red", size = 1) +  # Ligne de seuil
  labs(title = "Graphe de Kaiser (Éboulis des Valeurs Propres)",
       x = "Dimensions", y = "Valeur Propre",
       caption = "Seuil de Kaiser : Valeur Propre > 1") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

So by observing this figure, we see that the first 2 axes of the analysis express 73.64% of the total inertia of the dataset which means that 73.64% of the total variability of the cloud of individuals or variables is represented in this plan. This is a high percentage, and the foreground therefore well represents the variability contained in a very large part of the active dataset. This value is greater than the reference value of 58.22% , the variability explained by this plan is therefore significant (this reference interval is the 0.95-quantile of the distribution of inertia percentages obtained by simulating 7899 random data sets of comparable dimensions on the basis of a normal distribution). Due to these observations, we can say that only the first two axes carry real information. Therefore , only the first three axes are better for the description of the analysis. Thus, we reaffirm our choice of axes based on the Kaizer criterion .

Study of the correlation circle

# Charger les bibliothèques nécessaires
library(readxl)
library(FactoMineR)
library(factoextra)

# Sélectionner uniquement les colonnes numériques
data_numeriques <- data[, c("Precipitataion", "Temperature", "Population", 
                                  "Eau_Renou", "Eau_Agri", "PIB", 
                                  "Rend_agricol", "Super_culti", 
                                  "In_secAli",  "Prix_alim")]

# Standardiser les données
data_standardisees <- scale(data_numeriques)

# Réaliser une ACP
res.acp <- PCA(data_standardisees, graph = FALSE)

# Créer le cercle de corrélation
fviz_pca_var(res.acp, col.var = "contrib", 
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE, title = "Cercle de Corrélation")

The color gradient on the vectors indicates the contribution of each variable to the principal components. Variables with longer vectors and darker colors (closer to red/orange) contribute more to the explained variance.

1. Relationships Between Variables

  • Positive Correlations :

Eau_Renou , PIB , and Temperature are strongly positively correlated, indicating that regions with higher renewable water resources tend to have higher GDP and temperatures. Precipitation has moderate positive correlations with Eau_Renou , PIB , and Temperature , suggesting that precipitation is linked to water availability, economic conditions, and temperature.

  • Negative Correlations :

Population , Prix_alim , and Super_culti show moderate negative correlations with Temperature and Eau_Renou . This suggests that higher population density, food prices, and cultivated areas may be less prevalent in regions with abundant water resources and high temperatures. In_secAli (food insecurity) is negatively correlated with Temperature and Eau_Renou , indicating that food insecurity is more pronounced in regions with lower temperatures and water resources.

2. Implications for our Research

Our research focuses on the impact of socio-economic and climatic factors on food security in West Africa. The correlation circle provides several key insights:

Key Drivers of Food Security

Water Resources (Eau_Renou) : Renewable water resources play a central role in determining food security, as they are strongly correlated with economic development (PIB), temperature, and precipitation.

Temperature : Temperature is a critical factor influencing both economic conditions and agricultural yield. Regions with higher temperatures tend to have better economic performance but may face challenges related to food prices and cultivated areas. ## Contrasting Factors Population and Food Prices : Higher population density and food prices are negatively correlated with water resources and temperature, suggesting that densely populated regions may face greater challenges in accessing water and maintaining food security. Food Insecurity (In_secAli) : Food insecurity is more pronounced in regions with lower temperatures and water resources, highlighting the importance of addressing these environmental factors.

Agricultural Yield : Agricultural yield is moderately influenced by temperature but shows weaker correlations with other variables. This suggests that while temperature plays a role, other factors (e.g., socio-economic conditions, water management) may also significantly impact yield. Super-Cultivated Areas : Super-cultivated areas are negatively correlated with temperature and water resources, indicating that intensive agriculture may be less prevalent in regions with abundant water and high temperatures.

Study of the representation of individuals in the Factorial plan

# Standardiser les données
data_standardisees <- scale(data_numeriques)

# Réaliser une ACP
res.acp <- PCA(data_standardisees, graph = FALSE)

# Représenter les individus dans le plan factoriel
fviz_pca_ind(res.acp, col.ind = "cos2", 
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE, title = "Représentation des Individus dans le Plan Factoriel")

1. Interpretation of Dimensions

Dim1 (53%) : Explains the majority of the variance in the data. Countries like Mali and Niger are positioned far along this axis, suggesting that Dim1 captures a key differentiating factor between these countries and others. Togo and Benin are positioned oppositely along Dim1, indicating that they represent contrasting characteristics in this dimension. Dim2 (21.6%) : Captures an additional significant portion of the variance. Countries like Côte d’Ivoire and Senegal are positioned far along this axis, suggesting that Dim2 highlights another important distinguishing feature.

2. Quality of Representation (cos²)

The color gradient (ranging from blue to red) indicates the quality of representation of each country in the factorial plane: Red : High cos² values (close to 1), indicating that the country’s position in the factorial plane accurately reflects its true multidimensional position. Blue : Low cos² values (close to 0), indicating that the factorial plane does not fully capture the country’s characteristics. For example: Mali appears to have a high cos² value (red), suggesting that its position in the factorial plane is highly representative. Burkina Faso and Benin appear to have lower cos² values (blue), indicating that their true characteristics may not be fully captured by the first two principal components.

3. Relationships Between Countries

Clusters : Cluster 1 : Burkina Faso and Benin are very close to each other, suggesting that they share similar characteristics across the analyzed variables. Cluster 2 : Mali and Niger are relatively close to each other, indicating shared characteristics, particularly along Dim1. Cluster 3 : Côte d’Ivoire and Togo are somewhat distant from the other clusters, suggesting unique characteristics.

Contrasts

Mali vs. Togo : These countries are positioned on opposite sides of the origin along Dim1, indicating strong contrasts in the characteristics captured by this dimension. Côte d’Ivoire vs. Niger : These countries are positioned on opposite sides of the origin along Dim2, suggesting contrasting characteristics in this dimension. 6. Implications for Your Research Your research focuses on the impact of socio-economic and climatic factors on food security in West Africa. The factorial plane representation provides several key insights:

Distinctive Countries

Mali and Niger stand out as having distinct characteristics, likely due to specific socio-economic or climatic conditions that differentiate them from other countries. These countries may require targeted interventions to address their unique challenges related to food security. Similar Countries : Burkina Faso and Benin share similar characteristics, suggesting that they may face similar challenges and could benefit from similar strategies. Senegal also appears to have moderate similarities with other countries, indicating potential for regional cooperation. - Contrasting Factors : The opposition of countries along Dim1 and Dim2 highlights key differences in socio-economic and climatic factors. For example: Dim1 might capture factors like economic development or water availability. Dim2 might capture factors like agricultural practices or population density. Quality of Representation : Countries with high cos² values (e.g., Mali) are well-represented in the factorial plane, making it easier to interpret their characteristics. Countries with low cos² values (e.g., Burkina Faso, Benin) may require further analysis to understand their full multidimensional profiles.

Study of variables without atypical individuals

Hierarchical Ascending Classification (CAH)

# Standardiser les données
data_standardisees <- scale(data_numeriques)

# Calculer la matrice de distances euclidiennes
matrice_distances <- dist(data_standardisees, method = "euclidean")

# Réaliser la classification hiérarchique ascendante
classification_hierarchique <- hclust(matrice_distances, method = "ward.D2")

# Visualiser le dendrogramme
fviz_dend(classification_hierarchique, k = 3,  # Choisir le nombre de clusters
          k_colors = c("#00AFBB", "#E7B800", "#FC4E07"),
          color_labels_by_k = TRUE,
          rect = TRUE,
          main = "Dendrogramme - Classification Hiérarchique Ascendante")

Figure22: Cluster Dendrogram

Analysis of the Hierarchical Clustering Dendrogram

The provided dendrogram represents a hierarchical clustering analysis performed on a dataset, likely involving countries in West Africa. Below is a detailed breakdown of the dendrogram and its implications:

1. Overview of the Dendrogram

The dendrogram shows how different countries are grouped together based on their similarities (or dissimilarities) across certain variables. The height of each merge (vertical lines) indicates the distance or dissimilarity between clusters at that stage of aggregation. A lower height suggests that the clusters being merged are more similar to each other. The leaves at the bottom represent individual countries: Togo, Burkina Faso, Benin, Côte d’Ivoire, Senegal, Mali, and Niger.

2. Key Observations

Initial Clusters : At the lowest level, each country starts as its own cluster.

First Merge :

Togo and Burkina Faso are the first two countries to be merged into a single cluster. This indicates that these two countries are the most similar to each other based on the variables used in the analysis. The height of this merge is approximately 0.5 , suggesting a relatively low dissimilarity between Togo and Burkina Faso.

Second Merge

The next cluster formed includes Benin , which merges with the existing cluster of Togo and Burkina Faso. This occurs at a height of approximately 1.5 , indicating a slightly higher dissimilarity compared to the first merge.

Third Merge

Côte d’Ivoire joins the growing cluster (Togo, Burkina Faso, Benin) at a height of approximately 2.5 . This suggests that Côte d’Ivoire is somewhat less similar to the previous group but still relatively close.

Fourth Merge

Senegal is added to the cluster at a height of approximately 3.5 , indicating a greater dissimilarity compared to the previous merges.

Final Two Clusters

The remaining two countries, Mali and Niger , form their own separate cluster. They are merged at a much higher height of approximately 4.5 , indicating that they are quite dissimilar from the rest of the group and from each other.

3. Interpretation

Grouping Patterns

The dendrogram reveals two main groups: - Cluster 1 : Togo, Burkina Faso, Benin, Côte d’Ivoire, and Senegal. - Cluster 2 : Mali and Niger.

Cluster 1 appears to be more homogeneous, as all countries within it are merged at relatively low heights. This suggests that these countries share similar characteristics across the variables used in the analysis.

Cluster 2 (Mali and Niger) stands apart from the rest, indicating that these two countries have distinct features compared to the others.

Dissimilarity Between Groups

The high height at which Mali and Niger are merged with the rest of the group (approximately 5.0 ) highlights significant differences between these two countries and the others. These differences could be related to climatic, socio-economic, or agricultural factors relevant to your research theme.

Hierarchy of Similarity

Within Cluster 1, the order of merging provides insights into the relative similarity between countries: Togo and Burkina Faso are the most similar. Benin is moderately similar to the Togo-Burkina Faso pair. Côte d’Ivoire is somewhat less similar but still part of the same group. Senegal is the least similar within this group but still shares enough commonalities to be included.

4. Implications for our Research

Climatic and Socio-Economic Factors :

The hierarchical clustering suggests that there are regional patterns in the data. Togo, Burkina Faso, Benin, Côte d’Ivoire, and Senegal might share similar climatic conditions, farming practices, or socio-economic characteristics that influence food security. Mali and Niger, on the other hand, may exhibit distinct patterns, possibly due to unique environmental challenges (e.g., arid climate, limited water resources) or socio-economic factors (e.g., poverty levels, access to resources).

Policy Implications :

The clustering can inform targeted interventions. For instance: Countries in Cluster 1 might benefit from similar policies or strategies aimed at improving food security, such as irrigation projects or crop diversification programs. Mali and Niger, being distinct, may require tailored approaches to address their specific challenges.

Further Investigation :

To better understand why Mali and Niger form a separate cluster, we should examine the underlying variables (e.g., precipitation, temperature, GDP, population density) that contribute to their dissimilarity.

5. Recommendations

Cutting the Dendrogram : You can “cut” the dendrogram at a specific height to define the number of clusters. For example: Cutting at a height of 3.5 would result in two clusters: one containing Togo, Burkina Faso, Benin, Côte d’Ivoire, and Senegal, and the other containing Mali and Niger. Cutting at a lower height (e.g., 2.5 ) would result in three clusters: one for Togo, Burkina Faso, and Benin; another for Côte d’Ivoire and Senegal; and a third for Mali and Niger. Variable Importance : Investigate which variables (e.g., precipitation, temperature, GDP, population density) are driving the observed clustering. This can be done using additional analyses, such as correlation matrices or variable importance measures in clustering algorithms. Geographical Context : Consider the geographical distribution of the countries. For example, Mali and Niger are located in the Sahel region, which is known for its arid climate and frequent droughts. This could explain why they form a distinct cluster. Final Thoughts The hierarchical clustering dendrogram provides valuable insights into the similarities and differences among the countries in your dataset. It suggests that Togo, Burkina Faso, Benin, Côte d’Ivoire, and Senegal share more common characteristics, while Mali and Niger are distinct. This grouping can guide further analysis and inform policy recommendations related to food security in West Africa.

Summary Answer : The dendrogram reveals two main clusters: one comprising Togo, Burkina Faso, Benin, Côte d’Ivoire, and Senegal, and another comprising Mali and Niger. This suggests that the former group shares more similarities (likely in climatic and socio-economic factors), while Mali and Niger are distinct, possibly due to unique environmental or socio-economic challenges. Further investigation into the underlying variables and geographical context is recommended to deepen your understanding.

Discussion

These results confirm that economic and technological factors play a predominant role in food security. However, climate shocks remain a major challenge for resource-limited countries (e.g., Burkina Faso, Senegal). An integrated approach combining local adaptation and national policies is essential.

These conclusions align with those of several earlier studies that highlight the critical role of agricultural infrastructure and public policies in enhancing the resilience of food systems against climate shocks (FAO, 2022; Nyaku et al., 2022). For instance, the study recalls that since the 1970s, West Africa has faced an increase in climatic and socio-economic shocks, but local food systems have often been hindered by a lack of structural investments. Our analysis reinforces this idea by showing that countries with high GDP and strong agricultural yields, such as Nigeria, are better positioned to address food insecurity.

Moreover, the results indicate that countries facing high temperatures and low agricultural water availability, such as Mali and Niger, are particularly vulnerable. This observation is consistent with the World Bank’s (2022) findings, which emphasize that semi-arid zones in sub-Saharan Africa are the most affected by the combined effects of climate change and rural poverty.

Implications of the Results

The findings have several important implications:

  • Public Policies : Governments must prioritize investments in agricultural infrastructure (irrigation, storage, transportation) to strengthen the resilience of food systems. In particular, countries with large populations but limited agricultural yields, such as Togo and Benin, require increased support to improve their productivity.

  • Water Resource Management : The availability and efficient use of agricultural water resources emerge as crucial factors for maintaining food production, even under unfavorable climatic conditions.

  • Climate Change Adaptation : While local adaptation strategies are useful, they are insufficient to offset the growing impacts of climate variability. An integrated approach combining local adaptation and national policies is necessary.

Limitations of the Study

Despite promising results, this study has certain limitations:

  • limit the representativeness of the results

  • Analysis Period : The study focuses on the period from 2000 to 2020, which may not reflect recent developments or long-term trends.

  • Unquantified Factors : Certain social, cultural, and political factors influencing food security were not included in the analysis, such as armed conflicts or trade policies.

Perspectives

  • This study opens several avenues for future Public Investments:

    • Develop agricultural infrastructure (irrigation, storage).

    • Promote the adoption of modern technologies (drip irrigation, drones).

  • Natural Resource Management :

    • Optimize the use of agricultural water.

    • Encourage sustainable agricultural practices (agroecology).

  • Public Policies:

    • Strengthen safety nets for vulnerable populations.

    • Foster regional cooperation to share best practices.

General Conclusion

Food insecurity in West Africa is a complex challenge influenced by climatic, economic, and social factors. While climate shocks have a moderate impact, they exacerbate existing vulnerabilities. Solutions must be multidimensional, combining local adaptation, public investments, and coordinated regional policies. This project opens important avenues for future research, particularly on the impact of new agricultural technologies and public policies.

Appendix

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Questionnaire for data collection

https://ee.kobotoolbox.org/x/CZvV3VDU

Follow the link above to access the questionnaire for data collection