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https://doi.org/10.37815/rt= e.v33n2.853

Artículos originales=

 

Machine learning approach for multidimensional poverty estimation<= /o:p>

Enfoque de aprendizaje automático para la estimación de la pobreza multidimensional

Mario Ochoa1 https= ://orcid.org/0000-0002-2283-0203, Ricardo Castro-García<= /span>2= https://orcid.org/0000-0002-233= 2-9381, Alexander Arias Pallar= oso1= , 3 https://orcid.org/0000-0002-661= 2-4968, Antonia Machado= 1= =  https://orcid.org/0000-0003-385= 6-5659, Dolores Sucozhañay Mac= hado4= =  https://orcid.org/0000-0003-493= 0-2176=

 

1 Gr= upo de Investigación en Población y Desarrollo Local Sustentable (PYDLOS), Departamento Interdisciplinario de Espacio y Población (DIEP), Universidad = de Cuenca, Cuenca, Ecuador

mario.esteban= .ochoa@gmail.com, antonia.macha= do@ucuenca.edu.ec

 

2Microsoft

ricardo.castro@microsoft.com

 

3 Fa= cultad de Jurisprudencia y Ciencias Políticas y Sociales, Universidad de Cuenca, <= /span>Cuenca, Ecuador.

alexander.ari= as@ucuenca.edu.ec

 

4 Departamento Interdisciplinario de Espacio y Población (DIEP), Facultad de Ciencias Económicas y Administrativas, Universidad de Cuenca, Cuenca, Ecuador.

dolores.sucozhanay@ucuenca.edu.ec

 

Sent:             =   2021/07/11

Accepted:       2021/09/28

Published:      2021/11/30                          <= span class=3Deop>

Resumen

3D"Cuadro

En las ciencias s= ociales ha predominado un análisis teórico en sus investigaciones. La escasez de da= tos, su dificultad para recolectarlos y almacenarlos, ha sido la principal limitación para que las ciencias sociales adopten enfoques cuantitativos. S= in embargo, la gran cantidad de información generada en los últimos años, principalment= e a través del uso de Internet, ha permitido que las ciencias sociales incluyan cada vez más análisis cuantitativos. Este estudio propone el uso de tecnolo= gías como Machine Learning (ML) para solventar esta escasez de datos. El objetivo es estimar el índice de pobreza multidimensional a nivel de persona en un territorio en particular de Ecuad= or mediante el uso de modelos de regresión de Machine Learning (ML) partiendo = de una cantidad limitada de datos para entrenamiento. Se comparan 10 modelos M= L, tales como modelos lineales, regularizados y ensamblados. Random Forest se desempeña de manera sobresaliente frente a los otros modelos. Se llega a un error del 7,5% en la validación cruzada y del 7,48% con el conjunto de dato= s de prueba. Las estimaciones se comparan con aproximaciones estadísticas del IP= M en una zona geográfica y se obtiene que el IPM promedio estimado por el modelo= en comparación con el promedio informado por los estudios estadísticos difiere= en 1%.

 

Palabras clave: bosques aleatorios, cienci= as sociales, regresión, zona geográfica, datos limitados.

Abstract

In the social sciences, a theoretical analysis = has predominated in its research. The scarcity of data and its difficulty in collecting and storing it, has been the main limitation for the social scie= nces to adopt quantitative approaches. However, the large amount of information generated in recent years, mainly through the use of the Internet, has allo= wed the social sciences to include more and more quantitative analysis. This st= udy proposes the use of technologies such as Machine Learning (ML) are the answ= ers to solving this data scarcity. The objective is to estimate the multidimensional poverty index at the personal level in a particular territ= ory of Ecuador by using Machine Learning (ML) regression models based on a limi= ted amount of data for training. Ten ML models are compared, such as linear, regularized, and assembled models and Random Forest performs outstandingly against the other models. An error of 7.5% was obtained in the cross-valida= tion and 7.48% with the test data set. The estimates are compared with statistic= al approximations of the MPI in a geographical area and it is obtained that the average MPI estimated by the model compared to the average reported by the statistical studies differs by 1%.

 

Keywords: random forest, social sciences, regression, region, limited dataset.=

 

Introduction<= /span>

In recent years, the = social sciences have increasingly chosen to use inductive analysis methodologies in their studies. Contrary to the trend over the years to use deductive approa= ches by default (Grimmer et al., 2021). In the past, most sociological studies adopted the deductive approach due to the recurring problem in the social sciences, the scarcity of data (Chen et al., 2018; Grimmer et al., 2021). Before reviewing or collecting data, the social scientist usually had a cle= ar theory from which to draw propositions that could be testable. From these propositions, the variables of interest were raised and strategies were developed for their measurement, to finally establish hypotheses and a rese= arch design that tested the validity of the theory through the analysis of experimental observations (King et al., 1995; Rudin, 2015. This deductive approach made the researchers miss the opportunity to redefine their concep= ts, develop new theories and outline new hypotheses (Grimmer et al., 2021). In those years, data for social inductive analyzes was difficult to obtain; conducting surveys were expensive and storing large amounts of data was alm= ost impossible. At the same time, the computing capacity was limited (Grimmer et al., 2021; Maldonado, 2019). Nowadays, the social sciences show a strong tr= end towards quantitative research. Sociologists have made many efforts to inclu= de data analysis in their research through statistical techniques such as descriptive statistics (tendency and dispersion analysis), inferential statistics (estimation of confidential interval and significance testing), = and regression analysis (predictions and forecasting) (Rovai et al., 2013).

 

The advent of the Int= ernet and the increase in computational capacity has undoubtedly made the amount = of data go from being scarce to being immensely abundant. In this panorama, the social sciences have had to evolve to adapt to this new reality. The social sciences have moved from concepts of “variables” to the “big data” idea. The methodologies based on observation, description, hypothesis formulation have become insufficient to analyze the current complex reality, driven by data = and permanent virtuality (Maldonado, 2019).

 

This abundant amount = of data has created the opportunity for the social sciences to move from the deduct= ive approach to an inductive and iterative approach. Allowing to test hypothese= s in a more agile way. Similarly, social networks allow creating studies and soc= ial experiments that until a few years ago were logistically impossible (Chen et al., 2018; Grimmer et al., 2021). The development of new and better data analysis algorithms has enabled social science studies to be able to establ= ish more accurate estimations of social phenomena (Hindman, 2015).

 

In recent years, tech= nologies that take advantage of all the possibilities derived from this vast amount = of available data have been developed. As part of these advances, Data Mining = (DM) has been one of the main technologies that benefited most.

 

DM is the science that focuses on extracting information from large data sets through the use of techniques from different disciplines such as ML or statistics (Hand, 2007)= . On the other hand, ML is a field of study that mainly develops algorithms and techniques to build models based on data. Depending on the structure of the data and the techniques used, ML is broadly divided into supervised learnin= g, unsupervised learning, and reinforced learning (Chen et al., 2018). Its applications increasingly have been adopted by fields like economics, polit= ical science, and sociology (Molina & Garip, 2019).

 

ML has gained popular= ity and has great application potential in some social science disciplines. Its algorithms have been applied in tasks such as pattern prediction, characterization of population heterogeneity, causal inference, theory development, and support in experimental decision-making (Chen et al., 2018; Grimmer, 2015; Grimmer et al., 2021; Molina & Garip, 2019).<= /span>

 

Despite the great ben= efits of using modern data analysis in social studies. The adoption of these techniq= ues has been relatively slow compared to other fields (Lazer et al., 2009). Researchers have argued that the “black box” nature of the models used in M= L, which does not allow knowing the internal inference process of the model, is one of the main factors for its rejection (Hindman, 2015). On the other han= d, the lack of data from minority sectors of the population can cause models t= o be trained with a significant bias towards stereotypes, discrimination, and ev= en racism (Chen et al., 2018). Another barrier that must be overcome is the la= ck of experience of data scientists in topics related to causal inference and complex social data processing (Grimmer, 2015).

 

However, social scien= tists could contribute with their expertise in human behavior, to establish a stronger connection between social science and ML to develop applications a= nd tools focused on data generated by social studies (Chen et al., 2018).=

 

As part of this effor= t to bridge the gap between these two fields of study, this paper uses ML techni= ques to improve analyzes of poverty. Our case study focuses on the multidimensio= nal poverty of the city of Cuenca, one of the main cities in Ecuador. However, = the same methodology can be applied to all the cities in the country.

 

The main objective is= to create a model capable of estimating the MPI for each person living in the city, starting from a limited amount of data available for training. The ta= sk of the model is to establish relationships between sociodemographic characteristics of people to estimate the corresponding MPI. In this sense,= the research question is: What machine learning model allows the most accurate estimation of multidimensional poverty at the person level using predictive variables of a sociodemographic nature and with a limited amount of training data?

 

The databases used in= this study corresponds to the National Survey of Employment, Unemployment, and Underemployment (ENEMDU) and Census of Population and Housing (CPH). The EN= EMDU database contains sociodemographic variables and the calculations to obtain= the MPI. However, the data in this database is limited because the survey is carried out following a probabilistic sampling strategy. This database is u= sed for the training and validation process. On the other hand, the CPH database has observations for all the populations but it does not have enough variab= les to calculate de MPI. The model will be applied to this database to obtain an estimation of the MPI for all the population.

 

In section 2, the main concepts and related works about social science, ML, and multidimensional poverty are described. Section 3 explains in detail the followed methodolog= y, including the data preprocessing in section 3.A, the model exploration in section 3.B, and fine-tuning in section 3.C. Following, section 4 presents = the results obtained from the application of the models in the test dataset and= the CPH database. A discussion about the obtained results is carried out in sec= tion 5. In section 6 some conclusions and future work are stated.

 

Related work

Social Scienc= e and Machine Learning

It is important to find a common point where the knowledge of ML and Social Science can be harnessed. However, before finding this common point, it is important to analyze the differences and similarities between these fields to have a better perspective of what they= can contribute to the other. First, the philosophy behind the analysis in these fields is very different. Quantitative sociological studies begin with the proposition of research questions and hypotheses about how the world works = and through theorizations and assumptions around the available data, it tries to explain a social phenomenon or individual and collective behaviors (Rudin, = 2015). On the other hand, in ML the objective is not to explain the phenomena but = to predict an outcome based on the only premise that the data has been obtained independently from an unknown distribution. It can then be said that sociological theory is hypotheses-driven, while ML is data-driven. Generall= y, ML starts with the data to later create a hypothesis, while sociology starts with the hypothesis statement from the beginning (Chen et al., 2018; Rudin, 2015).

 =

Another important differ= ence is the way the models are handled. In quantitative studies in sociology, the model (usually a linear regressor) is theorized and established before analyzing the data. However, in ML, several models are tested to determine = which one best fits the data. Since ML focuses mainly on prediction for unseen da= ta, its models do not provide a causal explanation for the analyzed phenomena, = but rather emphasize adjusting the models and improving the accuracy of the predictions. This is a problem from a sociological point of view where the objective is to explain the whys and hows of observed phenomena (Chen et al= ., 2018; Rudin, 2015).

 =

In addition, sociology generally generates conclusions based on multiple sources of information. Meanwhile, ML only works with a single data source. That is why applying ML methodologies in social analysis is a great challenge for researchers (Chen= et al., 2018; Rudin, 2015). However, recent studies in the field of ML have focused their efforts on explaining the phenomena, and although there is st= ill only one source of data, the technical challenges have been raised to be ab= le to analyze multiple sources to be coupled with the methodologies of the soc= ial sciences (Wallach, 2016).

 =

One of the fields of stu= dy of the social sciences, and the one that concerns this study, is poverty. The noti= on of poverty is based on a value judgment regarding what are the minimally adequate levels of well-being in societies; it also refers to the degrees of deprivation that are intolerable (Moreno, 2017). There are three approaches= to measuring poverty: the first corresponds to the utilitarian approach in whi= ch poverty is associated with the disposition of monetary income; a second approach is linked to Rawls’s approach to justice, who raises the notion th= at societies must guarantee access to a series of primary goods or basic needs; lastly, there is the capabilities approach whose conceptual basis is articulated around poverty, human freedoms and the multidimensional nature = of poverty (Denis et al., 2010).

 =

Currently, poverty is estimated through socioeconomic household surveys. This approach is costly = and time-consuming to carry out (Devarajan, 2013). However, below are described several studies that make use of ML techniques to enhance the estimation of poverty.

 =

In Talingdan (2019) diff= erent machine learning algorithms are compared for the classification between a p= oor and a non-poor person based on information from the Community Based Monitor= ing System (CBMS) in Lagangilang, Abra, Philippines. Information about Health, Nutrition, Housing, Water and sanitary systems, education, income, employme= nt, peace, and order, is considered. Algorithms such as Naive Bayes (NB), ID3, Decision Trees, Logistic Regressions, and K-Nearest Neighbors (KNN) are use= d. Naïve Bayes classifier outperformed all the four algorithms for predicting households that are poor and non-poor.

 =

Kshirsagar et al. (2017) apply machine learning techniques to generate ProxyMeans Tests (PMT) which are qu= ick surveys that allow estimating the probability that a person is poor or not, based on an approximation through the selection of variables related to poverty. The database used is based on national household surveys in Zambia= . A set of variables is selected, a model is estimated using those variables to predict the poverty level of a household. The model obtained is capable of classifying poor households from non-poor households and is also applicable= to different population segments of the country.

 =

Similarly, Kambuya (2020) applies the Least Absolute Shrinkage and Selection Operator (LASSO) and Ran= dom Forest (RF) models, to improve the variable selection process and the performance of the PMT models. The results show that RF-based PMTs for their selection of variables, reduce the number of poor households classified as non-poor (exclusion error) and increase the accuracy when estimating the poverty rate at the national, urban, and rural levels. While the selection = of variables based on LASSO, present better results compared to RF in terms of reducing the inclusion error (non-poor households classified as poor). Sohn= esen & Stender (2017) also, use LASSO and RF to predict poverty using data o= f a period of one year. The results indicate that RF is a good predictor of pov= erty and obtains more robust estimates compared to Linear Regression estimators.=

 =

Several studies conclude= that RF is one of the best algorithms for estimating poverty. Otok & Seftiana (2014) determines that RF is accurate in identifying poor households that a= re candidates for social assistance programs in Indonesia. Thoplan (2014) uses= RF to estimate poverty in Mauritius, the results showed that RF is the most accurate method for estimating poverty. Mcbride & Nichols (2015) successfully apply RF to improve the precision of PMT compared to linear regressions. They conclude that the RF model can significantly improve PMT performance by 2 to 18%. Another study similarly compares different data mi= ning methods for poverty classification based on censuses and surveys applied to= the population. It is concluded that RF outperforms Logistic Regression and Sup= port Vector Machine (SVM), in addition to being relatively faster than the other methods (Korivi, 2016).

 =

In addition to the compa= rison between methods to determine the most suitable for estimating poverty, there are also studies where different sources of information are used, to find patterns that allow estimating poverty more precisely. For example, Lerman = et al. (2016) obtain indicators of economic income and education based on georeferenced Twitter interaction. Jean et al. (2016) use high-resolution satellite imagery in conjunction with machine learning algorithms to predict poverty in African countries. As well as Piaggesi et al. (2019) use satelli= te imagery data to predict urban poverty in poor countries.<= /span>

 =

Similarly, Pokhriyal (20= 19) uses multiple sources of information to map poverty, establishing relations= hips between poverty and auxiliary data sources, such as cell phone records, satellite images, weather measurements, and Open Street Maps. Poverty is approached as a regression problem where it is sought to estimate a poverty index value for each region, taking as a reference the poverty value obtain= ed through census information.

 =

On the other hand, Khaef= i et al. (2019) identify characteristics obtained from Call Detail Records (CDR), which allow predicting wealth and poverty in New Guinea, combining CDR data with survey data. Techniques such as Principal Component Analysis (PCA) and Multiple Correspondence Analysis (MCA) are used to obtain the relative inde= x of multidimensional wealth in households. In addition, it uses feature selecti= on techniques such as Fast correlation-based filter (FCBF), Boruta, and XGBoos= t. Finally, five algorithms are applied to estimate the relative multidimensio= nal wealth index. The algorithms used are SVM, NB, Elastic-net, Neural networks (NN), and Decision trees. The researchers conclude that CDRs are better sui= ted for generating asset-related indicators and quantile rankings based on the wealth index of individual households. Howerver, they are not suitable for estimating the relative value of the wealth index.=

 =

Multidimensional Poverty

Multidimensional poverty is an approach to assess poverty that arises from the question that well-being is associated with income and consumption Añazco & Pérez (2016); under this perspective analysis, it is necessary= to evaluate social welfare from new non-monetary dimensions (Denis et al., 201= 0). Therefore, poverty for this approach represents a situation of insufficient realization of certain capacities considered elementary (Añazco & Pérez, 2016). The multidimensional poverty index (MPI) is a methodology developed = by Alkire and Foster in 2007 and from its formulation it has become the most widely used statistical practice to measure multidimensional poverty worldw= ide (Añazco & Pérez, 2016). This index has been incorporated into the annual Human Development reports developed by the United Nations Development Progr= am (UNDP) from 2010 to the present. The multidimensional poverty index allows identifying the simultaneous deprivations that the individual experiences in the enjoyment of their rights (Quinde Rosales, Bucaram Leverone, Saldaña Vargas, & Martínez Murillo, 2020).

 

The Multidimensional Poverty Index (MPI) makes it possible to identi= fy the simultaneous deprivations that the individual experiences in the enjoym= ent of their rights (Rosales et al., 2020).

 

Studies in Latin America regarding multidimensional poverty have been directed towards a basic set of dimensions such as education, health, employment, social protection, housing conditions, and basic services. These are consistent with the findings of participatory studies at the internatio= nal, regional or national level (Clausen et al., 2019). Many countries such as Colombia (Salazar et al., 2011), Mexico (CONEVAL, 2016), Chile (Social, 201= 5), El Salvador (Munguía, 2017) measure the MPI based on the methodology propos= ed by Alkire and Foster (2011), and adopted by the Economic Commission for Lat= in America and the Caribbean (CEPAL) as the standard for the region.

 

In Ecuador, the MPI is calculated from the sociodemographic informat= ion collected through the ENEMDU household survey. The data is stored in a data= base that contains the answers of each respondent. Then, based on data related to education, health services, access to food and water, and social security, = the MPI is calculated for each individual and then extended to the familiar uni= t. This survey is applied only to the main cities of the country which implies that many regions within the country and cities are not considered. Besides, this survey follows a probabilistic sampling strategy. Therefore, the overa= ll results are just a probabilistic approximation based on the expansion factor from the sampling strategy (Añazco & Pérez, 2016).

 

Regarding the multidimensional poverty rela= ted to ML in Ecuador, Viscaino Caiche (2019) performs a Statistical Matching between the variables of the Living Conditions Survey (ECV) and the CPH 201= 0, to subsequently estimate the MPI at the regional, provincial and cantonal leve= l. Using Decision Trees and NN, an explanatory model of poverty is found. Fina= lly, the Poverty Index is estimated through a Logistic Regression. The results s= how that the province with the highest poverty rate is Morona Santiago, while Galapagos is the province with the lowest poverty rate. <= /a>

 

Methodology

The type of study corresponds to a causal cross-sectional non-experimental quantitative design. Non-experimental designs "are ca= rried out without the deliberate manipulation of variables and phenomena are obse= rved in their natural environment to analyze them" (Sampieri Hernández et a= l, 2014, p. 152). Additionally, cross-sectional causal designs “describe relationships between two or more categories, concepts or variables at a gi= ven time based on the cause-effect relationship” (Sampieri Hernández et al, p. 158); In this sense, in the different evaluated models of machine learning,= a series of predictive variables of a sociodemographic nature are included th= at affect multidimensional poverty.

 

This study starts with the collection of the databases ENEMDU and CPH 2010. Using the Political Administrative Division (DPA), which is a codification strategy that assigns an identifier for each city, area, and sector in the country. The data of Cuenca city is extracted from both databases.

 

Due to the CPH is carried out every 10 years, and the 2020 version is not yet available. Therefore, the 2010 version is used. In addition, the EN= EMDU 2010 survey is used to coincide with the temporal context.

 

The databases are looked up to find common variables. Most of them a= re related to socio-demographic information, such as education, housing, employment, marital status, age, sex, etc. 33 common variables were found. = In the process of identifying common variables between the databases, it was f= ound that the variables related to the DPA coding of the cities, areas, and sect= ors were present in both databases and had the same coding. However, they were = not included as common variables to avoid the model having a bias towards the geographic location of the observation.

 

Each of these variables has its structure. The objective is to have = the same structure between corresponding common variables, so the next step is = to process them to change their original structure to match with the correspon= ding common variable. Thus, the ML can be used with both databases, because their input variables have the same structure. This process is described in detai= l in section 3.A.1.

 

The input features of the machine learning models must have specific characteristics to facilitate the training process. Therefore, categorical = and numerical features must be preprocessed. The method is described in detail = in section 3.A.2. After this procedure, 140 input features were obtained.=

 

Once the data is ready, the 3440 available observations from the ENE= MDU database, are split into training and test datasets, with a ratio of 80% training and 20% test, following a random sampling strategy.

 

Ten ML models, from simple linear regressors to ensemble models like= RF, were trained to find the most suitable for estimating the MPI using the com= mon variables as input features. This process is explained in detail in section 3.B.

 

The models with good performance are further tested adjusting their hyperparameters using a GridSearch = strategy, w= hich tries to find the best combination of parameter’s values from given distributions, testing every single combination. This is achieved by first = picking a combination of hyper-parameters. Then, with those hyperparameters, a trai= ning and cross-validation process is performed. This is done for each combinatio= n. After all the combinations are trained and validated, the one with the best cross-validation performance is chosen as the best model (scikit-learn, 202= 1).

 

Finally, the best model can be used to estimate the MPI using the CPH common variables as input features. Thus, we have the MPI for every observa= tion in the CPH database, without any region excluded.

 

Data preprocessing

Recoding

To have the same structure between the common variables on the ENEMDU and CPH database, many variables must be recoded. Table 1<= /span> shows an example for a variable that represents the educational level. It c= an be noticed that option 3 from both databases, which represents the kinder garden, is merged with option 4 that represents primary education. Option 8: “Ciclo Postbachillerato” from the ENEMDU database is merged with option 7: “Superior no Universitario” of the new coding proposal. Also, the order in = the options for both databases is changed to match the proposed recodification.=

 

The same strategy is applied to all the variables that have a differ= ent structure from their correspondent common counterpart.

 

It is important to mentions that during this process it was found th= at some of the variables contained an assigned category (number 99) for when t= he respondent cannot answer the question. One might think that these values do= not represent relevant information and should be discarded from the analysis. However, the fact that the respondent does not answer may have deeper connotations. For example, if the respondent is not able to answer “how many rooms are destined only for resting?” it may imply an overcrowding situatio= n. That is why null values must also be taken into account as a source of information. Therefore, when recoding the variables, there must be a coding= for these values.

 

Table = 1=

Recoding Variable “Level of Instruction”<= o:p>

ENEMDU

CPH

 

Variable

Options

Variable

Options

New coding<= o:p>

What is the highest level of instruction you attend or attended?

1.0: ‘None’,=

2.0: ‘Literacy Center’,=

3.0: ‘Preschool’,

4.0: ‘Primary school’,<= /span>

5.0: ‘Highschool’,

6.0: ‘Basic education’,=

7.0: ‘Middle education’,

8.0: ‘Post-Baccalaureate Cycle’,

9.0: ‘Higher education’,

10.0: ‘Postgraduate’,

99.0: ‘It is ignored’

Level of instruction

1.0: ‘None’,

2.0: ‘Literacy Center’,=

3.0: ‘kinder garden’,

4.0: ‘Primary school’,<= /span>

5.0: ‘Basic education’,=

6.0: ‘Highschool’,

7.0: ‘Middle education’,

8.0: ‘Non-university superior’,

9.0: ‘University Superior’,

10.0: ‘Postgraduate’

1.0: ‘None’,=

2.0: ‘Literacy Center’,=

3.0: ‘Primary school’,<= /span>

4.0: ‘Basic education’,=

5.0: ‘Highschool’,

6.0: ‘Middle education’,

7.0: ‘Non-university superior’,

8.0: ‘University Superior’,

9.0: ‘Postgraduate’

Source: The authors

Sources: ENEMDU(2010), CPH (2010)

 

 = ;

Data Conditioning

This study considers= two kinds of variables: numerical variables and categorical variables. Each of = them needs their conditioning to simplify its representations and help in the training process because most training algorithms are optimized to use only numbers as input features, they could binary or decimal points (Géron, 2019= ).

 

For numerical features such as the age or the number of bedrooms in a house, the conditioning is called feature scaling. This is done because mos= t ML models do not perform well when their input has different scales. There are= two common methods to scale the features. 1) mix-max scaling and 2) standardization.

 

mix-max scaling (a.k.a. normalization) consists of shifting and rescaling the values so that they range from 0 to 1. This is achieved by subtracting the minimum value and dividing the maximum minus the minimum. Standardization on the other hand first subtracts the mean (to have a zero-= mean distribution) and then divides the result by its standard deviation (to have unit variance) (Géron, 2019).

In this study, the standardization is used through the StandardScaler function of the sklearn library.

 

For categorical features, many strategies can be applied. The most popular are Ordinal Encoding and One Hot Encoding. Both strategies convert a categorical variable into numbers. Ordinal Encoding assigns a number for ea= ch category. This can be used with ordered categories such as bad, average, go= od, excellent. Not all the categorical variables represent an ordered list. In = that case, the One Hot Encoding must be used. This strategy creates one binary variable for each category, being 1 only the binary variable that correspon= ds with the category that represents. Table 2<= !--[if gte mso 9]> 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F005200= 65006600380036003500390039003100370031000000 shows an example of the= One Hot Encoding strategy.

 

Table 2<= /span>

One hot Encoding

Categorical Variable

One Hot Encoding=

Values

Cat A

Cat B

Cat C

Cat D

A

1

0

0

0

D

0

0

0

1

C

0

0

1

0

B

0

1

0

0

Source: The authors.

 

It can be noticed that one categorical variable with four categories= is transformed into 4 binary variables. For all the categorical variables in o= ur study, the One Hot Encoding strategy is used through the OneHotEncoder function of the sklearn library. After the feature conditioning proc= ess, we pass from 33 to 140 variables

 

Model Exploration

To evaluate each model, a performance criterion must be chosen. This criterion usually represents the distance between two vectors (a.k.a. norm), the vector of prediction, a= nd the target vector. For regression models, the most common criterion is the Euclidean distance, which is calcu= lated by the Root Mean Square Error (RMSE), also called the l2 norm. RMSE assigns a higher weight for larger err= ors. Another distance measure is the Man= hattan norm calculated by the Mean Absolute Error (MAE), also called the l1 norm. The higher the= norm index, the more focus is on large errors and neglects small ones. That is w= hy the RMSE is more sensitive to outliers than the MAE, but when there are jus= t a few outliers RMSE is preferred (Géron, 2019).

 

For this study RMSE is used because the aim is to penalize large prediction errors, the outliers are quite rare, and because it uses the same units as the dependent variable (MPI). So, the results are easy to compare.=

 

Below, the process for training a Linear Regressor is shown. The same steps are followed for all the other models.

 

1. Train the linear regressor with default hyperparameters from the python library sklearn as shown in Table 3<= /span>.

 

Table 3<= /span>

Linear Regressor Hyper-Parameters=

Hyper Parameter<= /i>

Value

fit intercept

True

normalize

False

positive

False

Source: The = authors

 =

2. Calculate the RMSE. In theory, the MPI can have values between 0 = and 1. Under this condition, an RMSE of 0.0855, as shown in Table 4<= !--[if gte mso 9]> 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F005200= 65006600380036003500390039003200370038000000 , is equal to a relative= error of 8.55%. However, the real range of the MPI in the dataset is between 0 and 0.7917. So, the relative error is 10.80%. The second approach is better bec= ause considers the real data, and avoid overestimating the performance of the mo= del.

 

Table 4<= /span>

Training Performance Measures of = the Linear Regressor

RMSE

Range

% error<= /p>

0.0855

0.7917

10.80%

Source: The = authors

 

3. Generate a scatter plot to visualize the predictions on the train= ing set as shown in Figure 1= . As the da= taset is sorted according to the survey sampling strategy it would be very difficult= to visualize. For that reason, the samples are sorted in ascending order. The target MPI from the training dataset is plotted in green and the MPI estima= ted by the linear regression is plotted in red.

 =

Figure <= /span>1<= /span>

Estimated MPI vs Target MPI with = the Linear Regressor from the Training Dataset

3D"Gráfico,

Source: The authors<= /o:p>

 <= /p>

4. Perform cross-validation with 10 folds. The cross-validation meth= od with 10 folds equally divides the dataset into 10 small datasets following a random sampling strategy. Then, the first nine datasets are used to train t= he model, while the 10th remaining dataset is used to test the performance. The process is repeated until each dataset has been used for testing. The RMSE = for each fold is calculated. The mean of all the RMSE is calculated to obtain an overall performance measurement that considers each iteration of the cross-validation process. Also, the relative error is calculated from the r= ange of the MPI in the dataset.

 

Table 5estimators: The number of trees in the forest.

max depth: The maximum depth of the tree.<= o:p>

max features: The number of features to consider when looking for the best split.

bootstrap: The sampling strategy. If False, the whole dataset is used to build each tree. If true, a bootstrap strategy= is applied.

 

There are many other hyper-parameters, but those were not considered= in this study.

With these hyper-parameters, an exploration grid is created. This gr= id contains all the possible combinations that can be explored by the search algorithm.

 =

Figure 2

Source: The = authors

 

As mentioned in section 3, the GridSearch = strategy is= used to explore the possible combinations of hyper-parameters. The exploration grid= is shown in Table 6<= !--[if gte mso 9]> 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F005200= 65006600380036003500390039003500300032000000 .

 

Table 6<= /span>

Hyper-parameters Exploration Grid=

Hyper-parameter<= /i>

Values

n estimators=

10, 50, 100, 500, 1000<= /span>

max depth

5, 10, 50, 100, 500, 1000

max features=

10, 50, 100, 140=

bootstrap

True, False<= /p>

Source: The = authors

According to the number of values for each hyper-parameter in the exploration grid, there are 240 possible combinations. All of them are test= ed by the GridSearch algorithm. In addition, with each combination, 10-fold cross-validation is performed. So, the training process is executed 2400 ti= mes. The combination with the best performance is chosen as the best model. The = best combination of hyperparameters is shown in Table 7.

 

Table 7<= /span>

Best Combination of Hyper-Paramet= ers

n estimators=

max features=

max depth

bootstrap

1000

50

500

False

Source: The = authors

 

The performance is measured through the mean RMSE of the 10-fold cross-validation and the percentage of error based on the MPI range, as sho= wn in Table 8.

 

Table 8<= /span>

Performance Measures of the best = Random Forest Model

Mean RMSE

Range

% error<= /p>

0.0594

0.7917

7.50%

Source: The = authors

 <= /p>

It can be noticed that after adjusting the hyper-parameters the cross-validation performance of the model was improved, going from an error= of 8.95% to 7.50%.

 

 

Results

Table 9 shows the = results obtained from all the tested models. It can be noticed that Linear Regressor has a consistent performance along with training and cross-validation. Howe= ver, the error is around 11%, which is considered under-fitted. Polynomial Regressor, is overfitted because the cross-validation error is much higher = than the training error. This can be solved using a regularized model such as Ri= dge Regressor, Bayesian Regressor, or Elastic-Net. The Ridge Regressor shows be= tter performance on the cross-validation but is still overfitted. Bayesian Regre= ssor has a good performance overall and shows consistency between training and cross-validation performance. Elastic-net shows consistency between training and cross-validation but is still under-fitted with an error of 11%.

 =

Continuing with other mo= dels, Linear SVM is under-fitted with an error of around 20%. For no Linear SVM, = two kernels were tested. 1) Polynomial Kernel with a degree of 3 and 2) Radial basis function (RBF) Kernel. SVM with Polynomial kernel shows good performa= nce but it is still considered under-fitted with a cross-validation error of 10= %. Similarly, SVM with RBF kernel has an error of 10% on the cross-validation.= On the other hand, the Decision Tree is also highly overfitted with 0.5% of training error and 11% of the cross-validation error. Finally, Random Forest shows the best cross-validations performance among all of them. It is quite overfitted with a training error of around 3% and a cross-validation error = of 8.95% but this can be solved by adjusting the hyper-parameters. Thus, Random Forest is chosen as the best model, Figure 2 shown the = plot from this model.

 =

 =

Table 9

Comparison of Models Performance with Training data set

 

Training

Cross-Validation

Model

RMSE

% error

Mean RMSE

% error

Linear Regressor

0.0911

11.5

0.0904

11.42

Polynomial Regressor

0.0117

1.48

1.6552

209.07

Ridge Regressor

0.0135

1.70

0.0758

9.57

Bayesian Regressor

0.0518

6.55

0.0742

9.36

Elastic-net Regressor

0.0901

11.38

0.0923

11.65

Linear SVM

0.1651

20.86

0.1653

20.88

SVM, kernel: Polinomial (d=3D3)

0.0683

8.63

0.0807

10.19

SVM, Kernel: RBF

0.0693

8.75

0.0809

10.22

Decision Tree

0.0046

0.58

0.0874

11.04

Random Forest

0.0288

3.64

0.0709

8.95

Source: The authors

 =

As mentioned above, the = main purpose of this study is to estimate the MPI through an ML model using sociodemographic variables as inputs. With the trained model, now we can estimate the MPI for new unseen data. We expect an error similar to the one obtained with the cross-validation process.

 =

Usually, the only way to evaluate the final performance of the model is through the reserved test dataset. This is described in section 4.A. However, in this particular case= , it is available another way to evaluate the performance based on the comparison between the overall MPI indexes of the ENEMDU database as the ground truth = and the overall MPI indexes calculated from the estimated MPI of the CPH databa= se. This is described in detail in section 4.B.

 =

Test Dataset

Using the reserved 20% o= f the data to evaluate the final performance of the model has the advantage of ha= ving the target value of MPI to be compared with. So, we can plot the estimated = MPI vs the target MPI, as shown in Figure 3.

 =

The measures of RMSE and= the percentage of error, between the estimated MPI and the target MPI from the = test dataset, are shown in Table 10.

 =

Table 10

Performance Measures with the test Dataset

Mean RMSE

Range

% error

0.0592

0.7917

7.48%

Source: The authors

Overall MPI

When the model is used with the CPH database, we do not have the expected value to compare with. Therefore, the RMSE and the percentage of e= rror cannot be calculated.

 

However, the performance can be approximately meas= ured if the overall results between the estimated MPI from the CPH database and = the target MPI from the ENEMDU database are compared. 4 indexes that represent a summary of the multidimensional poverty in a region can be calculated. These 4 indexes are:

 

      =   MPR: Multidimensional Poverty Ratio. The percentage of the population with Multidimensional Pover= ty. MPI >=3D 0.33.

      =   EMPR: Extreme Multidimensional Poverty Ratio. The percentage of the population with Extre= me Multidimensional Poverty. MPI ><= span style=3D'mso-bookmark:_Toc38966068'>=3D 0.5.

      =   A: The average MPI among= the population with Multidimensional Poverty.

      =   MPI: The average MPI in = the region.

 =

Figure  3=

Estimated MPI vs Target MPI with the test Dataset

3D"Gráfico,

Source: The authors<= /o:p>

 =

For Cuenca city, = Table 11 shows a co= mparison between the target indexes from the ENEMDU database vs the estimated indexes from the CPH database using the tuned RF model.

 =

Table 11

Target vs Estimated Multidimensional Poverty in Cuenca=

 =

ENEMDU

CPH=

 =

 =

Negat= ive

Positive

Negat= ive

Positive

Diffe= rence

MPR

74.53= %

25.47= %

74.25= %

25.75= %

0.28%=

EMPR<= /span>

88.41= %

11.59= %

95.15= %

4.85%=

6.74%=

A=

0.487= 7

0.424= 5

0.063=

MPI=

0.124= 2

0.109= 2

0.015=

Source: The authors

 =

It can be n= oticed, that the estimated indexes are very similar to the target indexes. The difference in MPR is only 0.28%, which means that the model estimates almost the same value of MPI close to the multidimensional poverty threshold (0.33= ). The difference in EMPR (6.74%) shows that the model estimated considerably higher values of MPI close to the extreme multidimensional poverty threshold (0.5). About the average MPI among the population with multidimensional pov= erty (A), the difference is only 0.0028, which represents 7.95% of the MPI range. Overall MPI in the region differs by 0.015, which is 1.89% of the range.

 =

Discussion

All the analysis and res= ults of this study move around the data, so its preprocessing is essential for t= he study. This preprocessing not only covers technical aspects such as the cleaning of the database, the imputation of missing values, or the conditio= ning of variables but also has a strong component of theoretical concepts that m= ust be taken into account to maintain or discard important features.=

 =

Tal= king about those theoretical concepts, it is identified that the possibility of measuring the MPI through the ML, opens the range of possibilities to conti= nue rethinking the established concepts according to social dynamics and its contemporary problems, integrating multiple variables of analysis that make visible no only those aspects that have traditionally been measured, but ot= hers that determine “poverty” in different contexts and are from a more subjecti= ve nature, such as the level of access to justice, the level of social cohesio= n of a territory, or the time devoted to activities considered a priority for people.

 =

When analyzing the targe= t MPI values (plotted in green) in Figure= 1 it can be = seen that the statistical calculation that yields these values works through thresholds. That is why when ordering the data ascendingly, steps defined w= ith a constant value of MPI can be observed. This calculation methodology hides= the random component of the observations. On the other hand, however, the featu= res used as inputs for the training process maintain the typical random nature = of a survey. For this reason, it is quite difficult for the models to generate estimates close to the target values. This may be one of the reasons why RF performs better than other models. Since RF, internally uses decision trees= and they work precisely with thresholds for regression tasks.=

 =

Another model that perfo= rmed well is the Bayesian Regressor. However, when adjusting its hyper-parameter= s, the improvement was not significant. That is why a deep fine-tuning analysis has not been included.

 =

On the other hand, it ca= n be noted that the models with the worst performance are those of a linear natu= re. This is an important observation since most sociological studies start with linear models to explain the phenomena, which would be an error in the case= of multidimensional poverty.

 =

The performance obtained= by RF, both in the cross-validation (7.5%) and in the test dataset (7.48%) is considered acceptable given that, from a theoretical point of view, multidimensional poverty is a complex phenomenon that can have several edges and variables that have not been considered in this study.

 =

Finally, it is necessary= to analyze the comparison of the indices calculated based on the estimates mad= e by the model with the CPH data against the indices calculated statistically fr= om the ENEMDU database. Although the indices of the ENEMDU cannot be considere= d a ground truth, since they are calculated by applying the expansion factor of= the survey, they can give us an approximation about the performance of our mode= l. If the indices calculated based on our estimates are similar to those estim= ated statistically, it can be said that the model is fulfilling its purpose of estimating, as precisely as possible, the MPI for the entire population of a specific region. When observing the results, it can be seen that this is the case, the difference of the average value of MPI in the entire region is 0.= 015, a difference of only 1.86 % of the range. However, it has to be noted that = the model is very accurate close to the Multidimensional Poverty threshold (0.3= 3) but its accurate decrease is close to the Extreme Multidimensional Poverty threshold (0.5).

 =

Currently, there are jus= t a few studies that address the estimation of multidimensional poverty using machine learning techniques. The study that most closely resembles ours is = the one carried out by Viscaino Caiche (2019), where it performs a statistical matching between the variables of the Living Conditions Survey (ECV) and the CPH 2010. Unlike our study that uses regression models to estimate a numeri= cal value of IPM, Viscaino Caiche (2019) uses decision trees, neural networks, = and logistic regression to obtain a classification model between rich and poor. Obtaining a precision of 80.84% for the decision tree model, 83.65% for the artificial neural network model, and 83.55% for the logistic regression mod= el. On the other hand, our regression model has an approximate accuracy of 93%.=

 

Conclusions

This study has shown that throug= h ML techniques, substantial aspects such as the territorialization of MPI over a meso and micro-scale is a reality, which contributes decisively to the development of science in the area of ​​human well-being and the decision making in public policy.

 

In Ecuador, multidimensional pov= erty has been estimated only in large territorial areas and has not reached the canton level due to the lack of precise information on aspects inherent to = said estimation. The application of the Random Forest model that has been tested= in this study has given the possibility of estimating the MPI of individuals at the sector level in the Cuenca canton, which implies a substantial advance = for the visibility of poverty in its multiple dimensions as one of the most com= plex social problems in the country. In addition, the model has managed to cover= the MPI both in the urban area and in the rural area, which will help to analyze the impact of the differences underlying the provision of services and the = guarantee of rights in the territories as a substantive input for making decisions of= the decentralized autonomous governments.

 

This research finding is also relevant insofar as it manages to establish multidimensional poverty levels= and identify extreme multidimensional poverty, with which the target populations can be taken into account to focus affirmative actions and urgent intervent= ions on the less favored territories. as well as long-range policies that make it possible to achieve a model of sustained territorial equity.

 

The robustnes= s of the Random Forest model and its application in the estimation of MPI proven through the validation of accuracy with other similar models will allow it = to be applied in different latitudes with the same success, which is why it constitutes a basic tool for academia and public management.

 

In the information age, the social sciences not only have the opportunity, but also the obligation to adopt new technologies in their research. It is well known that interdisciplinary work has led to great advances as a society. It is time for the social sciences to work together = with other sciences. Not only between sciences of the same family, such as statistics and economics but also with sciences such as engineering to bring technical advances to the social field and in the same way social advances = to technical fields. In this way, both fields benefit. The social sciences bec= ome more precise in their theories and engineering becomes more humane.<= span lang=3DEN style=3D'font-size:12.0pt;mso-bidi-font-size:11.0pt;color:#202124; mso-ansi-language:EN'>

After this first approach between data analysis techniques and the social sciences, it can be noted that joint work allows carrying out resear= ches that would be very difficult separately. As seen in the results, the ML has great potential as support in studies of a social nature. Mitigating one of= the main problems of the social sciences such as the scarcity of data.

 

It is important to mention that ML algorithms are only tools, which = by themselves will not solve the problems of the social sciences. ML will perf= orm well as long as there is strong theoretical support and it is applied to appropriate research problems. The theory of social sciences should be the guide for the research design and the interpretation of the results. A guide that the data alone will never provide.

 

The tasks of data cleaning, model training, and prediction of the MPI can be automated since they are nothing more than programming codes that are executed sequentially. However, there is a large part of this work that can= not be automated since it requires the exclusive intervention of a person, specifically in the task of identifying and recoding common variables. These tasks require a sense of association between the information provided by ea= ch variable and knowledge of their meaning, tasks that for now cannot be execu= ted by a computer.

 

There is still a long way to go in this bridge formed between these sciences, the scarcity of data is not the only problem to be solved and multidimensional poverty is not the only variable of interest. It is still difficult to analyze all the information found in this infinite source of information such as social networks. Phenomena such as xenophobia, racism, misogyny, violence, security, public policies, among others, are issues that can be addressed from data science in conjunction with social sciences. This cooperative work must be maintained. Therefore, universities, companies, and society, in general, must promote this type of multidisciplinary study.

 

Acknowledgments

This work is the resu= lt of the research project entitled "Unreported crime figure: Links between multidimensional poverty and the human right of access to justice", fu= nded by the Research Directorate of the University of Cuenca (DIUC) in the period 2019 -2021, Cuenca, Ecuador.

 

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=  

 

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