https://doi.org/10.37815/rte.v33n2.853

Artículos originales

Machine
learning approach for multidimensional poverty estimation

Enfoque de aprendizaje automático para la estimación de la pobreza
multidimensional

Mario
Ochoa1 https://orcid.org/0000-0002-2283-0203, Ricardo Castro-García2 https://orcid.org/0000-0002-2332-9381, Alexander Arias Pallaroso1, 3 https://orcid.org/0000-0002-6612-4968, Antonia Machado1  https://orcid.org/0000-0003-3856-5659, Dolores Sucozhañay Machado4  https://orcid.org/0000-0003-4930-2176

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

[email-masked], [email-masked]

2Microsoft

[email-masked]

3 Facultad
de Jurisprudencia y Ciencias Políticas y Sociales, Universidad de Cuenca, Cuenca,
Ecuador.

[email-masked]

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

[email-masked]

Sent:               2021/07/11

Accepted:       2021/09/28

Published:      2021/11/30

Resumen

En las ciencias sociales
ha predominado un análisis teórico en sus investigaciones. La escasez de datos,
su dificultad para recolectarlos y almacenarlos, ha sido la principal
limitación para que las ciencias sociales adopten enfoques cuantitativos. Sin embargo,
la gran cantidad de información generada en los últimos años, principalmente a
través del uso de Internet, ha permitido que las ciencias sociales incluyan
cada vez más análisis cuantitativos. Este estudio propone el uso de tecnologías
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 Ecuador
mediante el uso de modelos de regresión de Machine Learning (ML) partiendo de
una cantidad limitada de datos para entrenamiento. Se comparan 10 modelos ML,
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 datos de
prueba. Las estimaciones se comparan con aproximaciones estadísticas del IPM 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, ciencias
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 sciences
to adopt quantitative approaches. However, the large amount of information
generated in recent years, mainly through the use of the Internet, has allowed
the social sciences to include more and more quantitative analysis. This study
proposes the use of technologies such as Machine Learning (ML) are the answers
to solving this data scarcity. The objective is to estimate the
multidimensional poverty index at the personal level in a particular territory
of Ecuador by using Machine Learning (ML) regression models based on a limited
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-validation
and 7.48% with the test data set. The estimates are compared with statistical
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

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 approaches
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 clear
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 research
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 concepts,
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 almost
impossible. At the same time, the computing capacity was limited (Grimmer et
al., 2021; Maldonado, 2019). Nowadays, the social sciences show a strong trend
towards quantitative research. Sociologists have made many efforts to include
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 Internet
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 deductive
approach to an inductive and iterative approach. Allowing to test hypotheses in
a more agile way. Similarly, social networks allow creating studies and social
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 establish
more accurate estimations of social phenomena (Hindman, 2015).

In recent years, technologies
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 learning,
unsupervised learning, and reinforced learning (Chen et al., 2018). Its
applications increasingly have been adopted by fields like economics, political
science, and sociology (Molina & Garip, 2019).

ML has gained popularity 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).

Despite the great benefits of
using modern data analysis in social studies. The adoption of these techniques
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 ML,
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 hand,
the lack of data from minority sectors of the population can cause models to be
trained with a significant bias towards stereotypes, discrimination, and even
racism (Chen et al., 2018). Another barrier that must be overcome is the lack
of experience of data scientists in topics related to causal inference and
complex social data processing (Grimmer, 2015).

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

As part of this effort to
bridge the gap between these two fields of study, this paper uses ML techniques
to improve analyzes of poverty. Our case study focuses on the multidimensional
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 task
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 ENEMDU
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 used
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 variables
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 methodology,
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 section
5. In section 6 some conclusions and future work are stated.

Related work

Social Science 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. Generally,
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 difference
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 data,
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 still
only one source of data, the technical challenges have been raised to be able
to analyze multiple sources to be coupled with the methodologies of the social
sciences (Wallach, 2016).

One of the fields of study of the
social sciences, and the one that concerns this study, is poverty. The notion
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 which
poverty is associated with the disposition of monetary income; a second
approach is linked to Rawls’s approach to justice, who raises the notion that
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) different
machine learning algorithms are compared for the classification between a poor
and a non-poor person based on information from the Community Based Monitoring
System (CBMS) in Lagangilang, Abra, Philippines. Information about Health,
Nutrition, Housing, Water and sanitary systems, education, income, employment,
peace, and order, is considered. Algorithms such as Naive Bayes (NB), ID3,
Decision Trees, Logistic Regressions, and K-Nearest Neighbors (KNN) are used.
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 quick
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 Random
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). Sohnesen
& Stender (2017) also, use LASSO and RF to predict poverty using data of a
period of one year. The results indicate that RF is a good predictor of poverty
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 are
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 mining
methods for poverty classification based on censuses and surveys applied to the
population. It is concluded that RF outperforms Logistic Regression and Support
Vector Machine (SVM), in addition to being relatively faster than the other
methods (Korivi, 2016).

In addition to the comparison
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 satellite
imagery data to predict urban poverty in poor countries.

Similarly, Pokhriyal (2019)
uses multiple sources of information to map poverty, establishing relationships
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 obtained
through census information.

On the other hand, Khaefi 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 index of
multidimensional wealth in households. In addition, it uses feature selection
techniques such as Fast correlation-based filter (FCBF), Boruta, and XGBoost.
Finally, five algorithms are applied to estimate the relative multidimensional
wealth index. The algorithms used are SVM, NB, Elastic-net, Neural networks
(NN), and Decision trees. The researchers conclude that CDRs are better suited
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., 2010).
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 worldwide
(Añazco & Pérez, 2016). This index has been incorporated into the annual
Human Development reports developed by the United Nations Development Program
(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 identify
the simultaneous deprivations that the individual experiences in the enjoyment
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 international,
regional or national level (Clausen et al., 2019). Many countries such as
Colombia (Salazar et al., 2011), Mexico (CONEVAL, 2016), Chile (Social, 2015),
El Salvador (Munguía, 2017) measure the MPI based on the methodology proposed
by Alkire and Foster (2011), and adopted by the Economic Commission for Latin
America and the Caribbean (CEPAL) as the standard for the region.

In Ecuador, the MPI is calculated from the sociodemographic information
collected through the ENEMDU household survey. The data is stored in a database
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 unit.
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 overall
results are just a probabilistic approximation based on the expansion factor
from the sampling strategy (Añazco & Pérez, 2016).

Regarding the multidimensional poverty related
to ML in Ecuador, Viscaino Caiche (2019) performs a Statistical Matching
between the variables of the Living Conditions Survey (ECV) and the CPH 2010, to
subsequently estimate the MPI at the regional, provincial and cantonal level.
Using Decision Trees and NN, an explanatory model of poverty is found. Finally,
the Poverty Index is estimated through a Logistic Regression. The results show
that the province with the highest poverty rate is Morona Santiago, while
Galapagos is the province with the lowest poverty rate.

Methodology

The type of study corresponds to a causal cross-sectional
non-experimental quantitative design. Non-experimental designs "are carried
out without the deliberate manipulation of variables and phenomena are observed
in their natural environment to analyze them" (Sampieri Hernández et al,
2014, p. 152). Additionally, cross-sectional causal designs “describe
relationships between two or more categories, concepts or variables at a given
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 that
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 ENEMDU
2010 survey is used to coincide with the temporal context.

The databases are looked up to find common variables. Most of them are
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 found
that the variables related to the DPA coding of the cities, areas, and sectors
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 corresponding
common variable. Thus, the ML can be used with both databases, because their
input variables have the same structure. This process is described in detail 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 ENEMDU
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 common
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, which
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 training
and cross-validation process is performed. This is done for each combination.
After all the combinations are trained and validated, the one with the best
cross-validation performance is chosen as the best model (scikit-learn, 2021).

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 observation
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
shows an example for a variable that represents the educational level. It can
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 different
structure from their correspondent common counterpart.

It is important to mentions that during this process it was found that
some of the variables contained an assigned category (number 99) for when the
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 situation.
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”

ENEMDU

CPH

Variable

Options

Variable

Options

New coding

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’,

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’,

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’,

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 most 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 each
category. This can be used with ordered categories such as bad, average, good,
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 corresponds
with the category that represents. Table 2 shows an example of the One
Hot Encoding strategy.

Table 2

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 our
study, the One Hot Encoding strategy is used through the OneHotEncoder function of the sklearn
library.
After the feature conditioning process,
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, and the
target vector. For regression models, the most common criterion is the Euclidean distance, which is calculated
by the Root Mean Square Error (RMSE), also called the l2 norm. RMSE assigns a higher weight for larger errors.
Another distance measure is the Manhattan
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 why
the RMSE is more sensitive to outliers than the MAE, but when there are just 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.

Table 3

Linear Regressor Hyper-Parameters

Hyper Parameter

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, 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 because
considers the real data, and avoid overestimating the performance of the model.

Table 4

Training Performance Measures of the
Linear Regressor

RMSE

Range

% error

0.0855

0.7917

10.80%

Source: The authors

3. Generate a scatter plot to visualize the predictions on the training
set as shown in Figure 1. As the dataset 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 estimated
by the linear regression is plotted in red.

Figure 1

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

Source: The authors

4. Perform cross-validation with 10 folds. The cross-validation method
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 the
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 range
of the MPI in the dataset.

Table 5

Cross-validation Performance Measures of
the Linear Regressor

Mean RMSE

Range

% error

0.0905

0.7917

11.43%

Source: The authors

To be able to compare the models, it is necessary to define the concepts
of underfitting and overfitting. This allows understanding the overall
performance of the model and permits the proposal of some solutions to improve
it.

Comparison
between models

When a model is
underfitting means that is not capable to make good estimations, mainly for two
reasons. 1) The features do not provide enough information or 2) the model is
not powerful enough. To fix the underfitting problem we can select a more
powerful model, feed the training algorithm with better features, or reduce the
constraints of the model (Géron, 2019). On the other hand, when a model is
overfitting means that the model is capable to make good estimations, but only
with the same data with which it was trained. When trying to estimate with
different data the performance is bad. To determine if the model is overfitting
it is necessary to compare the performance with training data vs the performance
with unseen data. As the unseen data is not available, a way to estimate its
performance is through a cross-validation process. If the training performance
is much better than the cross-validation performance, the model is overfitting.
Overfitting happens when the model is too complex to the amount or the
noisiness of the data. To fix this problem we can simplify the models,
constrain them (also called regularization), reduce the noise in the data, or
feed more training data (Géron, 2019).

At this stage, multiple
ML models are evaluated and compared by overfitting or underfitting analysis to
identify the model that best performs in the task of estimating the MPI. The
tested models are:

·       Linear Regressor

·       Polynomial Regressor

·       Ridge Regressor

·       Bayesian Regressor

·       Elastic-net Regressor

·       Linear SVM

·       SVM, kernel: Polinomial
(d=3)

·       SVM, Kernel: RBF

·       Decision Tree

·       Random Forest

The performance of each
of these models is evaluated in section 4.

Fine Tuning

Fine Tuning is the process where the hyper-parameters are adjusted to
obtain the best possible model (Géron, 2019). First, it is necessary to
determine the hyper-parameters available to tweak from the model.

For this case, Random Forest was chosen as the best model. So, its
hyper-parameters are (scikit-learn, 2021):

n estimators: The number of trees in the forest.

max depth: The maximum depth of the tree.

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 grid
contains all the possible combinations that can be explored by the search
algorithm.

Figure 2

Estimated MPI vs Target MPI with the
Random Forest Regressor from the Training Dataset

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.

Table 6

Hyper-parameters Exploration Grid

Hyper-parameter

Values

n estimators

10, 50, 100, 500, 1000

max depth

5, 10, 50, 100, 500, 1000

max features

10, 50, 100, 140

bootstrap

True, False

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 tested
by the GridSearch algorithm. In addition, with each combination, 10-fold
cross-validation is performed. So, the training process is executed 2400 times.
The combination with the best performance is chosen as the best model. The best
combination of hyperparameters is shown in Table 7.

Table 7

Best Combination of Hyper-Parameters

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 shown
in Table 8.

Table 8

Performance Measures of the best Random
Forest Model

Mean RMSE

Range

% error

0.0594

0.7917

7.50%

Source: The authors

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. However,
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 Ridge
Regressor, Bayesian Regressor, or Elastic-Net. The Ridge Regressor shows better
performance on the cross-validation but is still overfitted. Bayesian Regressor
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 models,
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 performance
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=3)

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 database.
This is described in detail in section 4.B.

Test
Dataset

Using the reserved 20% of the
data to evaluate the final performance of the model has the advantage of having
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 error
cannot be calculated.

However, the performance can be approximately measured
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 Poverty. MPI >= 0.33.

–
EMPR: Extreme
Multidimensional Poverty Ratio. The percentage of the population with Extreme
Multidimensional Poverty. MPI >= 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

Source: The authors

For Cuenca city, Table 11 shows a comparison
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

Negative

Positive

Negative

Positive

Difference

MPR

74.53%

25.47%

74.25%

25.75%

0.28%

EMPR

88.41%

11.59%

95.15%

4.85%

6.74%

A

0.4877

0.4245

0.063

MPI

0.1242

0.1092

0.015

Source: The authors

It can be noticed,
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 poverty
(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 results
of this study move around the data, so its preprocessing is essential for the
study. This preprocessing not only covers technical aspects such as the
cleaning of the database, the imputation of missing values, or the conditioning
of variables but also has a strong component of theoretical concepts that must
be taken into account to maintain or discard important features.

Talking
about those theoretical concepts, it is identified that the possibility of
measuring the MPI through the ML, opens the range of possibilities to continue
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 others
that determine “poverty” in different contexts and are from a more subjective
nature, such as the level of access to justice, the level of social cohesion of
a territory, or the time devoted to activities considered a priority for
people.

When analyzing the target 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 with
a constant value of MPI can be observed. This calculation methodology hides the
random component of the observations. On the other hand, however, the features
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 performed
well is the Bayesian Regressor. However, when adjusting its hyper-parameters,
the improvement was not significant. That is why a deep fine-tuning analysis
has not been included.

On the other hand, it can be
noted that the models with the worst performance are those of a linear nature.
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 made by
the model with the CPH data against the indices calculated statistically from
the ENEMDU database. Although the indices of the ENEMDU cannot be considered 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 model.
If the indices calculated based on our estimates are similar to those estimated
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 (0.33)
but its accurate decrease is close to the Extreme Multidimensional Poverty
threshold (0.5).

Currently, there are just 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 numerical
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 model.
On the other hand, our regression model has an approximate accuracy of 93%.

Conclusions

This study has shown that through 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 poverty
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 complex
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 interventions
on the less favored territories. as well as long-range policies that make it
possible to achieve a model of sustained territorial equity.

The robustness 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 become
more precise in their theories and engineering becomes more humane.

After this first approach between data analysis techniques and the
social sciences, it can be noted that joint work allows carrying out researches
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 perform
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 cannot
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 each
variable and knowledge of their meaning, tasks that for now cannot be executed
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 result of
the research project entitled "Unreported crime figure: Links between
multidimensional poverty and the human right of access to justice", funded
by the Research Directorate of the University of Cuenca (DIUC) in the period
2019 -2021, Cuenca, Ecuador.

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