Analysis of Principal Nonlinear Components for the Construction of a Socioeconomic Stratification Index in Ecuador
| Autor | Katherine Morales, Miguel Flores, Yasmín Salazar Méndez |
| Cargo | Departamento CITI, Laboratorio Samovar de Telecom SudParis - Institut Polytechnique de Paris. París - Francia. Email: katherine.morales_quinga@telecom-sudparis.eu. - MODES, SIGTI, Department of Mathematics, Escuela Politécnica Nacional. Quito - Ecuador. E-mail: miguel.flores@epn.edu.ec - Department of Quantitative Economics, Escuela Politécnica... |
| Páginas | 43-82 |
43
desarro. soc. 71, primer semestre de 2013, pp. x-xx, issn 0120-3584
Revista
Desarrollo y Sociedad Segundo cuatrimestre 2021
PP. 43-82, ISSN 0120-3584
E-ISSN 1900-7760
88
Analysis of Principal Nonlinear Components for
the Construction of a Socioeconomic Stratification
Index in Ecuador
Katherine Morales1, Miguel Flores2, Yasmín Salazar Méndez3
DOI: 10.13043/DYS.88.2
Abstract
Socio-economic stratification classifies people or groups of people within a
society. Although social stratification is a universal characteristic of human
societies, the criteria considered to classify individuals is not unique and some
methodological approaches are distinguished. In this article, we build an indi-
cator of socioeconomic stratification for Ecuador through a Nonlinear Princi-
pal Components Analysis using data from the 2010 Census. This methodology
allows the incorporation of numerical and categorical variables, and nonlinear
relationships. The main results suggest that the households located in the urban
area show better conditions and greater access to basic services. Also, education
positively affects social and economic conditions of both individuals and the
households. In light of these results, public policy should target education and
public investment in the provision of basic services in rural areas.
Key words: Statistical analysis; social class; social inequality; Ecuador.
JEL classification: C18; D63; I31.
1 Departamento CITI, Laboratorio Samovar de Telecom SudParis - Institut Polytechnique de Paris. París –
Francia. Email: katherine.morales_quinga@telecom-sudparis.eu.
2 MODES, SIGTI, Department of Mathematics, Escuela Politécnica Nacional. Quito – Ecuador. E-mail:
miguel.flores@epn.edu.ec
3 Department of Quantitative Economics, Escuela Politécnica Nacional. Quito – Ecuador. E-mail: yasmin.
salazar@epn.edu.ec
This paper was received on September 23, 2020, revised on February 11, 2021, and finally accepted on
April 11, 2021.
44 Revista
Desarrollo y Sociedad
Segundo cuatrimestre 2021
PP. 43-82, ISSN 0120-3584
E-ISSN 1900-7760
88
Análisis de componentes principales no lineales
para la construcción de un índice de estratificación
socioeconómica para el Ecuador
Katherine Morales4, Miguel Flores5, Yasmín Salazar Méndez6
DOI: 10.13043/DYS.88.2
Resumen
La estratificación socioeconómica clasifica a las personas o grupos de perso-
nas dentro de una sociedad. Si bien la estratificación social es una característica
universal de las sociedades humanas, el criterio considerado para clasificar a los
individuos no es único y se distinguen algunos enfoques metodológicos. En este
artículo, construimos un indicador de estratificación socioeconómica para Ecua-
dor a través de un Análisis de Componentes Principales no Lineales utilizando
datos del Censo de 2010. Esta metodología permite la incorporación de variables
numéricas, categóricas y relaciones no lineales. Los principales resultados sugie-
ren que los hogares ubicados en el área urbana presentan mejores condiciones y
mayor acceso a los servicios básicos. Además, la educación afecta positivamente
las condiciones sociales y económicas tanto de las personas como de los hoga-
res. A la luz de estos resultados, la política pública debe apuntar a la educación
y a la inversión pública para la provisión de servicios básicos en las zonas rurales.
Palabras clave: análisis estadístico; clase social; desigualdad social; Ecuador.
Clasificación JEL: C18; D63; I31.
4 Departamento CITI, Laboratorio Samovar de Telecom SudParis - Institut Polytechnique de Paris. París –
Francia. E-mail: katherine.morales_quinga@telecom-sudparis.eu.
5 MODES, SIGTI, Department of Mathematics, Escuela Politécnica Nacional. Quito – Ecuador. E-mail:
miguel.flores@epn.edu.ec
6 Department of Quantitative Economics, Escuela Politécnica Nacional. Quito – Ecuador. E-mail: yasmin.
salazar@epn.edu.ec
Este artículo fue recibido el 23 de septiembre del 2020, revisado el 11 de febrero del 2021 y finalmente
aceptado el 11 de abril del 2021.
Katherine Morales, Miguel Flores and Yasmín Salazar Méndez 45
desarro. soc. 88, bogotá, segundo cuatrimestre de 2021, pp. 43-82, issn 0120-3584, e-issn 1900-7760, doi: 10.13043/dys.88.2
1. Introduction
The existence of socioeconomic differences between the members of a society
are inherent to all modern societies in fields such as education, occupation,
income, and prestige, among others (Rodríguez et al. 2020; Leo et al. 2016).
Socio-economic stratification plays a fundamental role in public policy for the
planning, design and implementation of specific programs to reduce social and
economic inequality (Zhou and Wodtke, 2019).
Socio-economic stratification is not without controversy and disagreements
(Fujihara, 2020; Tang, 2017; Haer, 1957), since proposing valid indicators
implies connecting theories and quantitative or qualitative methods, which
allow theories to be operationalized. According to Haug (1977, p. 51), clear
theoretical proposals are the main “obstacle” in the measurement of social
stratification, since these are “complex, contradictory, diverse”. Thus, the cri-
terion considered to classify individuals is not unique and some methodologi-
cal approaches are distinguished. In general, three approaches are prominent:
quantitative, qualitative and mixed approach (Silva, 1981). In the first approach,
which is also used in this article, indicators or classifiers are built using sta-
tistical methods in order to classify individuals, households or housing based
on variables that collect individual, household or housing characteristics. For
example, these variables are considered to be related to the education and
occupation of the head of household, housing characteristics, income level
and purchasing power.
The Principal Components Analysis (PCA) is commonly considered a suitable
method for the construction of indicators as it reduces a large number of
variables to a smaller number of uncorrelated linear combinations of these
variables. These are called principal components and they represent the data
as closely as possible (Mori et al., 2016). However, despite the benefits of the
PCA and its broad-ranging use, this methodology presents a limitation when
it comes to building indicators as the variables must be linearly related and
numerical (Linting et al., 2007).
Given the qualitative and quantitative nature of the variables normally used for
social stratification, the PCA assumptions are not met. Linting et al. (2007) pro-
pose an alternative named Nonlinear Principal Components Analysis (nonlin-
ear PCA) which allows the incorporation of numerical and categorical variables
Analysis of Nonlinear Components for Socioeconomic Stratication Index
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and nonlinear relationships. Variables are quantified by the optimal scaling
process, so that variance is optimized. Optimal scaling is based on the alter-
nating least squares procedure, an iterative process that uses the previous
quantifications to estimate the following quantifications, until converging to
the solution (Krijnen, 2006; Kuroda et al., 2013).
In non-linear PCA, it is important to evaluate the stability of the results
obtained. However, defining stability is a controversial issue already under
discussion. Ferrari and Manzi (2010) argue that stability is an unfinished
issue and that until now no conclusive and definitive results have been pre-
sented. For example in Gi (1990), the stability of an analysis method is defined
as the analysis’ degree of sensitivity to variations in the data or parameters of
the model. According to the same author, a solution is stable if a small change
that is unimportant in the data, the model or technique leads to a small and
unimportant change in the results. In this article, stability is the degree of
sensitivity of the results against changes in the data. Small changes in the
data should lead to changes in the level of the results of the analysis. Efron
and Tibshirani (1993); Linting and Van der Kooij (2007) present an option for
the verification of solution stability by means of non-parametric bootstrap.
In this context, this article builds an indicator for socio-economic stratifica-
tion for Ecuador at provincial level7. In this country, socioeconomic stratifi-
cation plays a fundamental role in public policy, for the planning, design and
implementation of specific programs, to exemplify, the identification of the
beneficiaries of conditional income transfer programs. It is also a tool used
in demography, sociology, political science and marketing, among other areas
of knowledge.
The contribution of this article, alongside the socio-economic stratification
indicator, is that it is obtained through the non-linear PCA method. To the
best of our knowledge, there are no studies using this methodology and our
aim is mainly empirical.
The data used correspond to the Population and Housing Census (2010). The
selected variables are related to characteristics of the head of household, the pos-
7 In Ecuador, a province is a political-administrative division made up of two or more cantons. A canton
is the second level administrative division. The country has 24 provinces and 221 cantons.
Katherine Morales, Miguel Flores and Yasmín Salazar Méndez 47
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session of household goods and the characteristics of the housing. For the sta-
bility analysis of the results obtained from the non-linear PCA, the bootstrap
method mentioned in the previous paragraph is applied.
The article is organized as follows. After this introductory part, Section 2 con-
tains a brief literature review. Section 3 describes the database and methodol-
ogy used. In Section 4 the results are presented and discussed. Finally, Section
5 shows the conclusions of the work.
2. Brief Literature Review
Social stratification consists in classifying people or groups of people in a
society (Kerbo, 2017). Although, academically, European social scientists such
as Max Weber, Karl Marx, Wilhelm Dilthey, Émile Durkheim are recognized as
the pioneers in the study of stratification and social class (Lemos, 2012), the
idea of classifying individuals dates back to advanced ancient societies. For
example, Kamakura and Mazzon (2013) mention the social classes of Athens
(citizens, , and slaves), Sparta (spartiates, perioecis and helots) and Ancient
Rome (patricians, noble plebeians and plebeian gentes) to argue that the exis-
tence of well-established social classes with clearly defined characteristics to
differentiate them extends to antiquity. The same authors state that this clas-
sificatory notion is still used today but with different terminology.
Although the construction of groups implicitly implies the legitimacy of the
differences in the distribution —of wealth, goods or income—, ignoring indi-
vidual heterogeneity would create a false illusion of equality and temporal
stability of socio-economic conditions (Kerbo, 2017). It is an undeniable fact
that the unequal distribution of goods favors a group that concentrates not
only on wealth, but also on power, and leaves those who are not as important
a part in this division at a disadvantage.
Even though from a normative point of view the acceptable level of inequal-
ity, as well as the deliberate delimitation of social and economic groups, are
debatable, these facts are usually associated with social and political con-
flicts, which can even put democratic systems at risk (Acemoglu et al., 2015).
In some way, the study of socio-economic stratification ratifies the existence
of these differences (see Fujihara, 2020; Wu, 2019; Wright, 2005; Featherman
Analysis of Nonlinear Components for Socioeconomic Stratication Index
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and Hauser, 1976), however, the transparency of the imbalances in the dis-
tribution of goods and wealth provides information that allows reflection on
the desirable structure of a society in terms of social and economic inequality.
It also, depending on its members’ level of aversion to inequity, offers instru-
ments to reduce inequality, to a greater or lesser extent.
3. Data and Methodology
3.1 Data
3.1.1. Description of the database
The data used in this article correspond to the Population and Housing Cen-
sus (2010) conducted by the INEC, which provides the following general
information: Ecuador, at the census date, had 14,483,499 inhabitants. At
household level there were 3,815,527 households and 3,810,548 heads of
household. The difference between household and house is that the word
household is used to designate a person or a group of people who live under
the same roof and share the food expenses, while the house is the space
where people live, which is separated by walls or other elements covered
by a roof (INEC, 2012).
The information used in this paper relates to 3,802,566 households, in con-
junction with information on housing and the heads of households. Variables
at individual, household and housing level had to be used to make sure that
the segmentation conducted collects as much information about Ecuadorian
households as possible. In terms of provinces, Table 1 shows that the prov-
ince with the most households in Ecuador is Guayas, with 958,965 households
(25.22%), followed by Pichincha with 727,838 households (19.14%).
For the selection of variables, the initial criterion consisted of considering those
variables8 that present the least amount of missing data, between 0% and
10%. However, in these cases, a simple imputation process was carried out;
8 The variables of the initial stage will not necessarily be part of the definitive model. In the following
sections, the variables selected for the execution of the algorithm and creation of the indicator
are presented.
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that is, the missing values of a variable were replaced by the average value
of the units observed in the variable.
3.1.2. Categorization of variables
The nonlinear PCA method makes it possible to analyze a set of data with qualita-
tive and quantitative variables; however, as the objective of this article is to obtain
an indicator of households’ social stratification in the provinces, the variables are
Table 1. Number of households and participation of Ecuador’s provinces in the 2010
census
Province Households Participation
Galápagos 7236 0.19%
Pastaza 19818 0.52%
Zamora Chinchipe 21371 0.56%
Napo 22462 0.59%
Orellana 31495 0.83%
Morona Santiago 33352 0.88%
Sucumbíos 43056 1.13%
Carchi 44136 1.16%
Bolívar 47723 1.25%
Cañar 58627 1.54%
Santa Elena 76194 2.00%
Santo Domingo de los Tsáchilas 95221 2.50%
Imbabura 103009 2.71%
Cotopaxi 103137 2.71%
Loja 116892 3.07%
Chimborazo 125407 3.30%
Esmeraldas 129539 3.41%
Tungurahua 140536 3.70%
El Oro 163290 4.29%
Azuay 188331 4.95%
Los Ríos 201933 5.31%
Manabí 343088 9.02%
Pichincha 727838 19.14%
Guayas 958965 25.22%
Source: Authors based on Data from the Population and Housing Census (2010)
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categorized in an ordinal way, which refers to changing the original scale of the
variables in the Table 2, by turning them into ordinal variables. The categories
are classified under the criteria of possession of goods and access to services
that each category represents; i.e., the first category “1” is assigned to the low-
est value categories under the criteria mentioned above, while the last category
is assigned to the ones that present the best characteristics.
Table 2. Selected preliminary variables
Variable Abbreviation Scale Categories
Population
Education of the head of household P23 Nominal 11
Type of educational center P22 Nominal 4
Private insurance P07 Nominal 2
Can read and write P19 Nominal 2
Households
Type of hygienic service of household H03 Nominal 3
Shower H04 Nominal 3
Landline telephone H07 Nominal 2
Cell phone H08 Nominal 2
Internet H09 Nominal 2
Computer H10 Nominal 2
Cable television H11 Nominal 2
House possession H15 Nominal 7
Number of exclusive bedrooms for sleeping H01 Numerical -
Number of people in the house TP1 Numerical -
Last payment of electricity H12 Numerical -
The way they drink water H06 Nominal 5
Housing
Area URH Nominal 2
Ceiling material V01 Nominal 6
Wall material V03 Nominal 7
Floor covering material V05 Nominal 7
Source of water V07 Nominal 5
The way they get water V08 Nominal 4
WC V09 Nominal 5
(Continued)
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Table 2. Selected preliminary variables
Variable Abbreviation Scale Categories
Garbage disposal V13 Nominal 5
Main entrance path VAP Nominal 6
Electrical power service V10 Nominal 4
Type of housing VTV Nominal 7
Ceiling condition V02 Nominal 3
Condition of the walls V04 Nominal 3
Condition of the floor covering V06 Nominal 3
Electric meter V11 Nominal 3
Number of light bulbs in house V12A, V12B Numerical -
Source: Authors based on Data from the Population and Housing Census (2010)
For example, if we take the variable area of Table 2, we assign “1” to rural
area and “2” to urban area, since the rural area generally has less access to
services than the urban area. In tables 3 and 4, the preliminary variables are
presented with their respective categories.
Furthermore, in some cases, it was necessary to create the variables based on
the census information; for example, the case of variable overcrowding, which
was constructed from the general information of the household and the head of
the household. Overcrowding refers to the relationship between the number
of people in a house (TP1) and the space or number of available rooms (H01)
(See Table 2). Since poor people’s access to resources is limited, the housing
facilities they occupy tend to be less appropriate than those available for non-
poor people, “1” is assigned to yes and “2” to no.
3.2. Methodology
The first version of the Nonlinear Principal Components Analysis (nonlinear
PCA) method was described by Guttman (1941). Other contributions to this
methodology were made in later years by Kruskal (1964), Shepard (1966) and
Kruskal and Shepard (1974).
The nonlinear PCA is presented as a generalization of the PCA, since it makes
it possible to incorporate qualitative variables, with ordered and unordered
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Table 3. Preliminary Variables
Electrical power service
1 None
2 Power generator
3 Electric network company
4 Solar panel
Electric meter
1 None
2 Shared
3 Exclusive use
Type of housing
1Choza (Construction with adobe or straw walls, dirt floor
and thatched roof)
2
Covacha (Construction with rustic materials such as
branches, cardboard, asbestos, cans or plastic, with wood
or dirt floors)
3Rancho (Rustic construction covered with palm or straw,
with cane walls and with cane or earth wood floor)
4 Room in tenement house
5 Apartments in a house or a building
6 House-Villa
7 Other atypical housing
Ceiling condition
1 Poor
2 Good
3 Regular
Type of educational centre
1 Mainly state-run
2 Nobody studies
3 Mainly private
Private insurance
1 Nobody in household
2 Some people
3 All
Condition of the walls
1 Poor
2 Good
3 Regular
Condition of the floor covering
1 Poor
2 Good
3 Regular
Can read and write
1 No
2Yes
Private insurance
1 No
2Yes
Overcrowding
1 No
2Yes
Last payment of electricity
1 Lower than 5
2 From 5 to 9
3 From 10 to 14
4 From 15 to 20
5 From 21 to 29
6 From 30 to 39
7 From 40 to 49
8 From 50 to 59
9 From 60 to 69
10 More than 70
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Table 4. Preliminary Variables
Education of the head of household
1 None
2 Literacy center
3 Pre-school
4 Primary
5 Secondary
6 Higher (non-university)
7 Higher (university)
8 Postgraduate
Type of WC
1 Exclusive
2 Shared
3 None
Shower
1 Exclusive
2 Shared
3 None
Landline telephone
1Yes
2 No
Cell phone
1Yes
2 No
Internet
1Yes
2 No
Computer
1Yes
2 No
Cable television
1Yes
2 No
Area
1 Urban
2 Rural
Floor covering material
1 Other materials
2 Dirt
3 Cane
4 Brick or concrete
5 Ceramics, tile, marble
6 Untreated plank
7 Boarding, parquet or floating floor
Source of water
1 Other (rain)
2 Delivery
3 River, slope, ditch
4 Well
5 Public network
How do they get water
1 Not by pipeline
2 By pipeline outside the building
3By pipeline outside the house and inside
the building
4 By pipeline inside the house
WC
1 None
2 Latrine
3 Direct discharge into the sea or river
4 Connected to septic tank
5 Connected to cesspit
6 Connected to public network
Garbage disposal
1 Other
2 Burying
3 They burn it
4 They throw it into the river or stream
5They throw it into vacant or irregular lands
6 By garbage collection vehicle
(Continued)
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categories (ordinal, nominal), and to discover and treat nonlinear relationships
between variables. Mori et al. (2016) present nonlinear PCA as the result of
minimizing two loss functions, rank and homogeneity analysis, both of which
are the subject to restrictions, in conjunction with the optimal scaling. In
order to find the solution, one has to minimize several parameters of the
loss function simultaneously using the alternating least squares technique
(Mori et al., 2016).
Young (1981) expresses that optimal scaling is a quantification technique that
assigns numerical values to the categories of the variables, under the restric-
tions of the analysis level of the variable (numerical, ordinal and nominal)
and turns them into a vector of optimal scale. On the other hand, while mini-
mizing the loss function, the solution must be found with several parameters
simultaneously. The Alternating Least Squares (ALS) algorithm is used as a tool
to solve this minimization problem. The ALS algorithm is an iterative process
based on the alternation, where first the loss function for the first parameter
is minimized while the remainder is kept fixed, and then the loss function for
Table 4. Preliminary Variables
Ceiling material
1 Other materials
2 Straw, thatch
3 Tile or shingle
4 Zinc sheet
5 Asbestos
6 Concrete
Wall material
1 Other materials
2 Uncoated cane
3 Coated cane
4 Wood
5 Adobe or clay
6 Brick
7 Concrete
Main entrance path
1 Other
2 River, sea, lake road
3 Pathway, chaquiñan (trails in Ecuador)
4 Dirt road or ballast
5 Paved stone
6 Cobbled, paved or concrete
Number of light bulbs
1 5 or less
2 From 6 to 10
3 From 11 to 15
4 from 16 to 20
5 From 21 to 25
6 From 26 to 30
7 From 31 to 35
8 From 36 to 40
9 More than 41
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the second parameter is minimized, keeping the remainder fixed, etc. (Krijnen,
2006; Kuroda et al., 2013).
3.2.1. Bootstrap Method
In the context of the nonlinear PCA, the nonparametric bootstrap procedure
is employed to evaluate the stability of the nonlinear PCA solution (Linting
and Van der Kooij, 2007). This procedure incorporates the random bootstrap
with replacement, which is based on the original sample called principal sam-
ple and consists of obtaining B bootstrap samples from the principal sample
(Efron, 1997; Efron and Tibshirani, 1993). The bootstrap samples obtained are
balanced; that is, it is guaranteed that the initial observations appear exactly
B times in the B samples (Linting and Van der Kooij, 2007; Davison et al., 1986).
Subsequently, the analysis (CATPCA algorithm) is performed for each of the
bootstrap samples, which results in B values for the quantifications of catego-
ries of the variables. B bootstrap values for each of the nonlinear PCA results
are obtained, forming a bootstrap distribution, from which a confidence interval
can be calculated. These same confidence intervals are used to analyze the
stability of the results (Linting and Van der Kooij, 2007; Markus, 1994; Efron
and Tibshirani, 1993). In this work, the confidence intervals will be obtained
for the outputs of the algorithm, i.e. for the optimal quantifications for the
categories of the variables.
The quantifications of the categories of selected variables and the bootstrap
samples along with the quantifications of the principal sample are recorded
in order to create the confidence intervals (a confidence interval is associ-
ated with a level of confidence at (1) 100%). Linting and Van der Kooij (2007)
present the construction of the confidence intervals for the quantifications
obtained through percentiles.
In the context of nonlinear PCA, the quantifications with small intervals,
obtained from bootstrap samples indicate how stable the optimal quantifi-
cations are; in other words, if the quantifications of the bootstraps samples
are not very different, the solution is considered stable (Linting and Van der
Kooij, 2007).
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This study employed the CATPCA algorithm, included in the SPSS statistical
program, which was introduced in version 10 of SPSS in mid-1999 (Meulman
et al., 1999). The patch used in this work is IBM-SPSS 23 and the complete
algorithm is followed by Mori et al. (2016); Washed (2004); Fernando (2014).
4. Results and Discussion
4.1. Results
4.1.1. Selection of variables
The CATPCA algorithm is applied for each province with the preliminary vari-
ables defined in the previous section (See Table 3 and Table 4). This is done
in order to maximize the variance explained by each principal component
within each province. Using this criterion, several similarities are identified
when analyzing the variables that contribute most to the variance of the first
component, and a pattern is found within the 24 provinces. Table 5 presents
some selected variables.
Table 5. Selection of variables
Variable Abbreviation Level of analysis Categories
Education of the head of household P23 Ordinal 8
Landline telephone H07 Ordinal 2
Computer H10 Ordinal 2
Area URH Ordinal 2
Wall material V03 Ordinal 7
Floor covering material V05 Ordinal 7
Main entrance path VAP Ordinal 6
Number of light bulbs in House FO Ordinal 9
Condition of the walls V04 Ordinal 3
Condition of the floor covering V06 Ordinal 3
4.1.2. Result analysis
Based on the selection of variables described in the previous section and once
the sample design was obtained for each of the analyzed provinces, the CAT-
PCA algorithm was performed to acquire the optimal quantifications of the
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categories of variables and to analyze the variance explained by the compo-
nents. At this point, the bootstrap procedure is applied with B=1000, followed
by the presentation of a stability analysis of the results.
Variance analysis
The results obtained include the variance that is recorded for the first (% Vari-
ance C1) and second (% Variance C2) components, along with the total vari-
ance (% Total) (See Table 6). It was also concluded that the variance explained
by the two principal components ranges between 45% and 59%. The province
whose first component explains the highest percentage of the data is Loja, with
47.73%, and the province that has the lowest variance is Galápagos, with 27.99%.
For Pichincha, the first component has a variance of 35.73% and for Guayas, a
value of 39.63%. The variance calculated for the second component is observed
to be greater than 10% in all provinces.
To determine the reliability in the internal consistency of components, the
Cronbach alpha coefficient9 of the first (ACC1) and second component (ACC2)
is used (See table 6).
The value of the Cronbach alpha coefficient in all provinces is greater than 0.7;
thus, it can be concluded that the first component is reliable, depending on
how well the information is represented. The Cronbach alpha coefficient of the
eigenvalue associated with the total eigenvalue presents values greater than
0.8; that is, when the two components are used, the total reliability increases.
It is also important to mention that the total variance explained in the first
results of the execution of the CATPCA algorithm with the preliminary vari-
ables (See Tables 4 and 3), is lower in all provinces with respect to the results
obtained in this section with the final variables. This is due to the selection of
the final variables under the criterion of greatest contribution.
Table 7 presents the analysis of the explained variance for selected variables in
the first component for each province. For example, the education variable for
9 The Cronbach alpha coefficient is a value that allows to measure internal consistency, in other words,
it indicates how well the information of multiple variables is represented in a single indicator. The
coefficient takes values between 0 and 1. The value of the coefficient will be greater the greater
the correlation between the variable is. The closer the index gets to end 1, the better the reliability of
proposed variables selection, considering an acceptable reliability from 0,70 (Cortina, 1993)
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the head of the household (P23) in the province of Chimborazo shows greater
variance, with a value of 52%, in Morona Santiago, this variable has a value
of 25.09%. On the other hand, in Galápagos, the landline telephone variable
(H07) has the lowest recorded variance with 12.09%, while in Bolívar, it rep-
resents 47.40%. In the province of Sucumbíos, the landline telephone variable
(H10) presents the lowest value compared to the rest of the provinces which
can be explained by the fact that access to a telephone network in the East-
ern provinces is rather poor- with a value of 38.79%, and in Loja 46.75%. The
Table 6. Cronbach’s Alpha-Variance
Province % Variance
C1
% Variance
C2 % Total ACC1 ACC2
Azuay 43.21 10.84 54.05 0.85 0.09
Bolívar 41.85 12.23 54.08 0.85 0.20
Cañar 37.90 13.73 51.63 0.82 0.30
Carchi 38.45 12.87 51.32 0.82 0.24
Cotopaxi 41.92 12.33 54.25 0.85 0.21
Chimborazo 46.31 13.07 59.37 0.87 0.26
El Oro 32.98 12.42 45.40 0.77 0.22
Esmeraldas 37.46 12.60 50.06 0.81 0.23
Guayas 39.63 12.71 52.34 0.83 0.24
Imbabura 42.12 11.99 54.11 0.85 0.19
Loja 47.73 10.90 58.62 0.88 0.09
Los Ríos 34.90 13.95 48.86 0.79 0.32
Manabí 39.85 12.88 52.73 0.83 0.25
Morona Santiago 38.07 14.73 52.80 0.82 0.36
Napo 39.83 12.93 52.76 0.83 0.25
Pastaza 36.19 15.22 51.41 0.80 0.38
Pichincha 35.73 12.27 48.00 0.80 0.21
Tungurahua 40.43 13.43 53.86 0.84 0.28
Zamora Chinchipe 38.30 13.01 51.31 0.82 0.26
Galápagos 27.99 14.14 42.13 0.71 0.33
Sucumbíos 36.97 12.92 49.89 0.81 0.25
Orellana 36.22 12.92 49.15 0.80 0.25
Santo Domingo de los Tsáchilas 33.33 14.80 48.13 0.78 0.36
Santa Elena 33.23 14.05 47.28 0.78 0.32
Source: Authors based on Data from the Population and Housing Census (2010)
Katherine Morales, Miguel Flores and Yasmín Salazar Méndez 59
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area (URH) of house location in Santa Elena has a value of 8.3% and 59.88%
in Chimborazo. The wall material (V03) in Sucumbíos has the highest value
(61.03%), while Tungurahua has the lowest (10.92%). Santa Elena presents
a variance of 26.63% and Chimborazo a 64.26%. In Galápagos, the main
entrance path variable (VAP) presents a variance of 6.89%; owing to the fact
that in this province, the main entrance road for over 65% of the dwellings
Table 7. Explanation of variance of the variables in the first component
Province P23 H07 H10 URH V03 V05 VAP FO V04 V06
Azuay 0.4566 0.2118 0.4193 0.4763 0.4431 0.4456 0.4782 0.4386 0.4616 0.4895
Bolívar 0.4680 0.4740 0.3620 0.5040 0.2970 0.3810 0.4920 0.4320 0.3810 0.4040
Cañar 0.3975 0.3181 0.3576 0.2941 0.3475 0.4170 0.3516 0.4069 0.4210 0.4787
Carchi 0.4066 0.3490 0.3675 0.4211 0.1903 0.5018 0.3818 0.4317 0.3458 0.4494
Cotopaxi 0.4854 0.4137 0.4262 0.4180 0.1889 0.4935 0.4443 0.4559 0.3961 0.4698
Chimborazo 0.5248 0.4077 0.4611 0.5988 0.1884 0.6426 0.5474 0.4981 0.3375 0.4241
El Oro 0.3322 0.3286 0.3855 0.1391 0.3197 0.2787 0.2176 0.4155 0.4215 0.4598
Esmeraldas 0.3588 0.3940 0.3821 0.3079 0.5456 0.3589 0.3170 0.3271 0.3974 0.3570
Guayas 0.3838 0.4012 0.3992 0.2434 0.4505 0.2847 0.4098 0.4356 0.4865 0.4682
Imbabura 0.4784 0.3617 0.4047 0.3961 0.2241 0.5918 0.4100 0.4481 0.4151 0.4822
Loja 0.5122 0.3671 0.4676 0.5455 0.5195 0.5645 0.4867 0.4093 0.4228 0.4773
Los Ríos 0.3500 0.2972 0.3153 0.2808 0.5009 0.2973 0.3299 0.3110 0.4181 0.3897
Manabí 0.4294 0.3168 0.3936 0.3903 0.5204 0.3295 0.3700 0.3642 0.4517 0.4194
Morona
Santiago 0.2509 0.3843 0.4169 0.5012 0.5613 0.3040 0.4430 0.4593 0.2290 0.2568
Napo 0.3319 0.3535 0.3891 0.4107 0.5581 0.4382 0.2757 0.3254 0.4455 0.4551
Pastaza 0.2957 0.3373 0.3850 0.3260 0.4830 0.3256 0.4119 0.4219 0.2947 0.3381
Pichincha 0.4441 0.3746 0.4271 0.1298 0.1985 0.5013 0.2787 0.4783 0.3586 0.3819
Tungurahua 0.4798 0.4112 0.4218 0.4586 0.1093 0.5704 0.4172 0.4423 0.3308 0.4013
Zamora
Chinchipe 0.3411 0.3312 0.3633 0.4216 0.5772 0.4170 0.3557 0.3294 0.3535 0.3400
Galápagos 0.3479 0.1209 0.3608 0.1106 0.2193 0.4282 0.0689 0.2973 0.3963 0.4485
Sucumbíos 0.2733 0.2928 0.3079 0.3840 0.6103 0.5308 0.3066 0.2305 0.3883 0.3727
Orellana 0.2971 0.2675 0.3510 0.3491 0.5475 0.4543 0.2798 0.2773 0.4046 0.3939
Santo
Domingo de
los Tsáchilas
0.2949 0.2588 0.3224 0.2736 0.4975 0.3854 0.2697 0.2864 0.3690 0.3755
Santa Elena 0.3140 0.3716 0.3941 0.0832 0.3085 0.2664 0.1858 0.4495 0.4421 0.5077
Source: Authors based on Data from the Population and Housing Census (2010)
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is paved, cobbled or concrete. In the characteristics related to wall (V04) and
floor (V06) conditions, Morona Santiago presents the lowest values at prov-
ince level: 22.89% and 25.67% respectively. The highest values are in Guayas
(48.74%) and Santa Elena (50.77%). A similar analysis can be performed of
the results of the second component.
Quantification analysis
The CATPCA algorithm applied for each province with the selected variables
(See Table 5) makes it possible to obtain the optimal quantifications of the
categories of variables (See table 8). Using these results, the outcomes can be
analyzed. The variables describing the materials of the walls (V03) and floor
(V05) of the house, along with those that describe their condition (V04, V06
respectively) present the lowest value quantifications for the first categories
when compared to the quantification of the first categories for the rest of
the variables.
We can also see that the quantifications obtained are similar (not equal) for
the different provinces, with the exception of the number of light bulbs vari-
able (FO), which in each province takes values that are quite different from
each other. For example, in Pichincha the category of the number of light-
bulbs variable take values in the range of -1.104 to 1.959, while in Orellana
it ranges between -0.501 to 7.230. This effect is due to the difference in fre-
quency of the categories of this variable in each province.
Another exception is seen in the adobe or clay category in the wall material
variable (V03), since in the provinces of Los Ríos, Manabí, Morona Santiago,
Napo, Pastaza, Sucumbíos, Orellana, Santo Domingo de los Tsáchilas and Santa
Elena the quantifications are positive, while in the rest of the provinces they
are negative, thanks to the low frequencies these provinces present for this
category. Finally, the categories with null frequency have a null quantization.
This characteristic is presented in the second category of the variable, main
entrance path to housing (VAP), with alternatives such as river, sea or lake, since
some provinces might not display housing with this characteristic due to their
geographical location. The variable appears mostly for households belonging
to the provinces of the Coast or the Amazon Regions, such as: El Oro, Esmer-
aldas, Guayas, Los Ríos, Manabí, Morona Santiago, Napo, Pastaza, Zamora
Chinchipe, Sucumbíos, and Orellana.
Katherine Morales, Miguel Flores and Yasmín Salazar Méndez 61
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Table 8. Quantifications by province
Abbrev. Lev. Azuay Bolívar Cañar Carchi Cotopaxi Chimborazo El Oro Esmeraldas
P23 1 -1.517 -1.054 -1.216 -1.275 -1.152 -1.174 -1.113 -0.901
P23 2 -1.189 -1.054 -.791 -1.275 -1.003 -1.174 -1.113 -0.901
P23 3 -.591 -.354 -.340 -.603 -0.368 -0.351 -0.702 -0.644
P23 4 -.591 -.354 -.340 -.540 -0.368 -0.351 -0.702 -0.644
P23 5 .623 .621 .783 .845 0.757 0.715 0.195 0.405
P23 6 1.231 1.420 1.587 1.554 1.490 1.306 1.148 1.152
P23 7 1.603 2.102 2.210 2.167 2.177 1.762 2.037 2.264
P23 8 2.120 3.259 3.309 2.926 2.999 2.328 3.249 3.142
H07 1 -.826 -0.534 -0.640 -.779 -0.599 -0.627 -0.537 -0.540
H07 2 1.211 1.871 1.561 1.284 1.668 1.595 1.861 1.851
H10 1 -.742 -.362 -0.483 -.502 -0.456 -0.507 -0.540 -0.406
H10 2 1.347 2.761 2.071 1.992 2.193 1.974 1.852 2.466
URH 1 -1.100 -.673 -0.83 -1.038 -0.682 -0.825 -1.841 -1.019
URH 2 .909 1.485 1.204 .963 1.466 1.212 0.543 0.981
V03 1 -2.379 -2.763 -2.712 -2.450 -3.324 -2.852 -2.970 -1.340
V03 2 -2.379 -2.385 -2.111 -2.450 -2.836 -2.852 -2.462 -1.340
V03 3 -2.233 -1.780 -1.725 -2.450 -2.712 -2.760 -2.012 -1.242
V03 4 -1.630 -1.122 -1.725 -1.382 -2.109 -2.128 -1.981 -1.242
V03 5 -1.529 -1.068 -1.725 -1.382 -2.109 -2.128 -1.981 -0.132
V03 6 .589 .712 .501 .641 0.354 0.352 0.118 0.590
V03 7 1.059 2.126 1.176 1.718 1.878 1.797 1.566 1.629
V05 1 -2.507 -1.505 -2.230 -1.693 -1.385 -1.258 -3.137 -0.826
V05 2 -2.507 -1.505 -2.230 -1.693 -1.385 -1.258 -3.137 -0.826
V05 3 -2.001 -1.505 -2.230 -1.693 -1.156 -0.893 -2.871 -0.826
V05 4 -.455 0.182 -.025 -.561 -0.355 -0.279 -0.218 -0.826
V05 5 .297 0.182 .514 .857 0.749 0.759 0.758 -0.826
V05 6 .297 0.182 .514 .857 0.749 0.759 0.758 1.210
V05 7 .895 2.465 .922 1.261 2.128 1.602 1.162 1.210
VAP 1 -1.569 -1.047 -1.322 -1.398 -1.109 -1.135 -2.053 -1.750
VAP 2 -2.053 -1.750
VAP 3 -1.569 -1.047 -1.322 -1.398 -1.109 -1.135 -2.053 -1.488
VAP 4 -.610 -.583 -.389 -.850 -0.526 -0.668 -0.826 -0.348
VAP 5 -.187 .092 .072 -.850 -0.035 0.174 -0.538 -0.116
(Continued)
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Table 8. Quantifications by province
Abbrev. Lev. Azuay Bolívar Cañar Carchi Cotopaxi Chimborazo El Oro Esmeraldas
VAP 6 .975 1.339 1.339 1.009 1.351 1.146 1.063 1.315
FO 1 -1.009 -.556 -.804 -.728 -0.634 -0.688 -0.654 -0.537
FO 2 .291 1.348 .639 .961 1.073 1.101 1.097 1.512
FO 3 1.238 2.806 1.729 2.189 2.329 1.991 2.312 2.680
FO 4 1.594 3.280 2.240 2.386 2.799 2.298 2.817 3.267
FO 5 1.796 3.500 2.692 2.599 3.087 2.451 3.121 3.547
FO 6 2.020 3.500 2.964 2.599 3.087 2.451 3.233 3.547
FO 7 2.217 3.500 3.135 3.089 3.087 2.451 3.341 3.585
FO 8 2.251 3.500 3.135 3.089 3.499 2.476 3.580 4.076
FO 9 2.251 4.042 3.185 3.089 3.894 2.476 3.580 4.076
V04 1 -2.216 -1.549 -2.001 -1.907 -1.982 -2.021 -1.937 -1.662
V04 2 -.580 -0.31 -.342 -.406 -0.390 -0.486 -0.564 -0.390
V04 3 .829 1.28 .956 1.133 1.060 1.042 0.974 1.190
V06 1 -2.084 -1.374 -1.856 -1.621 -1.601 -1.684 -1.776 -1.631
V06 2 -0.517 -.229 -.274 -.391 -0.312 -0.393 -0.479 -0.377
P23 1 -0.943 -1.471 -1.230 -0.847 -1.059 -1.330 -0.991 -1.258
P23 2 -0.943 -1.471 -1.230 -0.813 -1.059 -0.867 -0.916 -1.258
P23 3 -0.821 -0.527 -0.641 -0.553 -0.534 -0.462 -0.618 -0.943
P23 4 -0.762 -0.463 -0.641 -0.553 -0.534 -0.462 -0.618 -0.717
P23 5 -0.014 0.671 0.513 0.363 0.452 0.186 0.081 0.183
P23 6 0.803 1.020 0.934 1.380 1.467 0.676 0.806 0.709
P23 7 1.824 1.748 1.669 2.484 2.047 2.306 2.162 1.728
P23 8 3.167 2.289 2.282 4.045 3.249 3.381 3.327 2.976
H07 1 -0.675 -0.781 -0.621 -0.385 -0.421 -0.636 -0.542 -0.643
H07 2 1.480 1.280 1.610 2.598 2.375 1.572 1.846 1.556
H10 1 -0.545 -0.634 -0.597 -0.344 -0.421 -0.490 -0.511 -0.600
H10 2 1.835 1.578 1.676 2.904 2.378 2.042 1.956 1.666
URH 1 -2.334 -1.114 -1.124 -1.070 -1.144 -0.800 -0.834 -0.990
URH 2 0.428 0.897 0.890 0.935 0.874 1.250 1.199 1.010
V03 1 -2.360 -3.616 -1.863 -1.760 -1.380 -2.148 -1.082 -4.293
V03 2 -2.360 -3.616 -1.863 -1.760 -1.380 -2.148 -1.082 -3.753
V03 3 -1.884 -3.616 -1.721 -1.542 -1.263 -2.093 -1.082 -3.148
V03 4 -1.884 -1.572 -1.132 -1.394 -1.263 -0.368 -1.007 -0.243
(Continued)
Katherine Morales, Miguel Flores and Yasmín Salazar Méndez 63
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Table 8. Quantifications by province
Abbrev. Lev. Azuay Bolívar Cañar Carchi Cotopaxi Chimborazo El Oro Esmeraldas
V03 5 0.055 -1.572 -1.132 0.547 0.442 0.289 0.530 -0.059
V03 6 0.406 0.511 0.731 0.547 0.629 1.060 0.912 0.569
V03 7 0.745 1.599 1.473 1.305 1.554 1.273 1.268 0.679
V05 1 -0.445 -1.754 -1.587 -0.590 -0.752 -2.597 -0.908 -3.780
V05 2 -0.445 -1.754 -1.587 -0.590 -0.752 -2.597 -0.908 -3.780
V05 3 -0.445 -1.649 -1.587 -0.590 -0.752 -2.484 -0.908 -3.273
V05 4 -0.445 -0.473 -0.156 -0.590 -0.752 0.233 -0.908 0.217
V05 5 -0.445 0.911 0.626 -0.590 -0.752 0.233 -0.908 0.217
V05 6 2.247 0.911 0.626 1.696 1.329 0.233 1.102 0.217
V05 7 2.247 1.297 1.378 1.696 1.329 1.530 1.102 0.554
VAP 1 -2.165 -1.547 -1.389 -1.604 -1.672 -1.945 -2.116 -3.745
VAP 2 -2.165 -1.604 -1.672 -1.945 -2.116 -3.745
VAP 3 -2.165 -1.547 -1.389 -1.604 -1.672 -1.495 -1.899 -1.571
VAP 4 -1.041 -0.980 -0.532 -0.704 -0.439 0.022 -0.288 0.155
VAP 5 -0.487 -0.200 0.187 -0.171 0.160 0.322 0.317 0.445
VAP 6 0.876 1.074 1.117 1.294 1.105 1.167 1.094 0.659
FO 1 -0.633 -0.827 -0.754 -0.439 -0.588 -0.645 -0.601 -0.709
FO 2 0.987 0.764 0.704 1.807 1.156 1.209 1.137 1.002
FO 3 2.183 1.728 1.915 3.633 2.714 2.063 2.451 2.037
FO 4 2.762 2.054 2.257 4.304 3.309 2.410 2.906 2.388
FO 5 2.973 2.192 2.484 4.608 3.393 2.589 3.444 2.527
FO 6 3.336 2.192 2.484 4.903 3.666 2.717 3.444 2.527
FO 7 3.336 2.192 2.601 5.159 3.995 2.717 3.444 2.527
FO 8 3.633 2.255 2.725 5.159 3.995 2.874 3.444 2.633
FO 9 3.668 2.255 2.725 5.159 3.995 3.081 3.444 2.739
V04 1 -1.999 -2.118 -1.702 -1.887 -1.263 -1.598 -1.510 -1.692
V04 2 -0.674 -0.548 -0.469 -0.150 -0.472 -0.536 -0.450 -0.593
V04 3 0.952 0.925 1.038 1.063 1.336 1.122 1.248 1.061
V06 1 -1.667 -1.896 -1.537 -1.807 -1.247 -1.603 -1.429 -1.636
V06 2 -0.681 -0.551 -0.325 -0.197 -0.453 -0.574 -0.464 -0.683
V06 3 1.036 0.948 1.109 1.138 1.375 1.095 1.279 1.017
(Continued)
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Table 8. Quantifications by province
Abbrev. Lev. Pichincha Tungurahua Zamora Ch Galápagos Sucumbíos Orellana Sto D S.Elena
P23 1 -1.676 -1.463 -1.154 -1.381 -0.962 -1.014 -1.170 -0.870
P23 2 -1.626 -1.463 -0.684 -1.381 -0.837 -0.872 -1.170 -0.870
P23 3 -1.030 -0.836 -0.597 -1.135 -0.589 -0.831 -0.618 -0.705
P23 4 -0.990 -0.535 -0.597 -1.135 -0.589 -0.647 -0.618 -0.661
P23 5 -0.003 0.603 0.428 -0.032 0.378 0.546 0.403 0.455
P23 6 0.657 1.178 1.131 0.834 1.309 1.571 1.324 1.352
P23 7 1.248 1.768 2.177 1.443 2.657 2.364 2.231 2.343
P23 8 1.877 2.304 2.926 1.858 3.621 3.859 3.360 3.795
H07 1 -1.216 -0.733 -0.637 -1.483 -0.478 -0.387 -0.661 -0.447
H07 2 0.822 1.365 1.569 0.675 2.091 2.581 1.512 2.235
H10 1 -0.968 -0.594 -0.490 -0.927 -0.444 -0.447 -0.523 -0.393
H10 2 1.033 1.682 2.041 1.079 2.253 2.236 1.912 2.542
URH 1 -1.541 -0.847 -0.850 -2.351 -0.952 -0.958 -1.698 -1.120
URH 2 0.649 1.181 1.177 0.425 1.050 1.044 0.589 0.893
V03 1 -3.953 -3.982 -1.205 -4.128 -1.163 -0.836 -2.575 -2.083
V03 2 -3.953 -3.982 -1.205 -4.128 -1.163 -0.836 -2.575 -2.083
V03 3 -3.953 -3.982 -1.205 -4.026 -1.163 -0.836 -2.575 -1.653
V03 4 -3.953 -3.592 -1.205 -4.026 -1.085 -0.769 -2.575 -0.775
V03 5 -2.621 -3.592 -0.755 -1.769 0.273 0.060 0.044 0.456
V03 6 0.006 0.124 0.787 -0.040 0.875 1.211 0.351 0.456
V03 7 1.577 1.482 1.118 1.401 1.181 1.736 0.687 1.259
V05 1 -2.631 -1.678 -0.999 -2.947 -0.873 -1.205 -0.384 -2.081
V05 2 -2.631 -1.678 -0.999 -2.947 -0.873 -1.205 -0.384 -2.081
V05 3 -2.631 -1.678 -0.999 -0.873 -1.205 -0.384 -2.081
V05 4 -1.258 -0.697 -0.999 -1.002 -0.873 -1.205 -0.384 0.481
V05 5 0.105 0.371 -0.999 0.896 -0.873 -1.205 -0.384 0.481
V05 6 0.105 0.371 1.001 0.896 1.145 0.830 2.606 0.481
V05 7 1.117 1.421 1.001 0.896 1.145 0.830 2.606 0.481
VAP 1 -1.906 -1.268 -1.645 -1.667 -2.179 -1.743 -3.307 -1.437
VAP 2 -1.645 -2.179 -1.743
VAP 3 -1.906 -1.268 -1.645 -1.667 -1.932 -1.743 -3.307 -1.437
VAP 4 -1.638 -0.913 -0.162 -1.667 -0.602 -0.337 -0.414 -0.704
VAP 5 -1.541 -0.430 0.083 -0.262 0.260 0.284 0.190 0.038
(Continued)
Katherine Morales, Miguel Flores and Yasmín Salazar Méndez 65
desarro. soc. 88, bogotá, segundo cuatrimestre de 2021, pp. 43-82, issn 0120-3584, e-issn 1900-7760, doi: 10.13043/dys.88.2
Table 8. Quantifications by province
Abbrev. Lev. Pichincha Tungurahua Zamora Ch Galápagos Sucumbíos Orellana Sto D S.Elena
VAP 6 0.605 1.082 1.277 0.671 1.071 1.247 0.805 1.604
FO 1 -1.104 -0.796 -0.625 -0.869 -0.514 -0.501 -0.693 -0.523
FO 2 0.390 0.737 1.207 0.783 1.496 1.495 0.919 1.352
FO 3 1.183 1.799 2.391 1.574 2.985 2.940 2.292 3.007
FO 4 1.521 2.323 2.581 1.832 3.512 3.920 2.930 3.649
FO 5 1.708 2.491 3.117 2.351 4.396 3.920 3.256 3.802
FO 6 1.818 2.529 3.117 2.414 4.412 4.668 3.256 3.802
FO 7 1.916 2.729 3.117 2.747 4.412 4.668 3.256 3.889
FO 8 1.916 2.773 3.343 2.747 4.412 4.805 3.256 3.889
FO 9 1.959 2.885 3.519 2.747 4.412 7.230 3.583 3.889
V04 1 -2.583 -2.479 -1.524 -3.371 -1.630 -1.374 -1.901 -1.583
V04 2 -1.278 -0.626 -0.485 -1.486 -0.351 -0.482 -0.619 -0.386
V04 3 0.672 0.860 1.196 0.582 1.292 1.336 1.057 1.383
V06 1 -2.400 -2.016 -1.449 -3.161 -1.506 -1.301 -1.719 -1.461
V06 2 -1.299 -0.546 -0.422 -1.411 -0.424 -0.543 -0.682 -0.183
V06 3 0.664 0.935 1.260 0.596 1.326 1.325 1.059 1.447
Source: Authors based on Data from the Population and Housing Census (2010)
Stability analysis (Bootstrap)
A stability analysis is shown below to complement the results obtained in the
previous sections and to identify whether the quantifications are stable. In
other words, the analysis must be robust to changes in the selection of data
and given that the quantification process is considered an integral part of the
analysis, the algorithm is applied for each bootstrap sample. If the quantifi-
cations are substantially different from the quantifications of the principal
sample in the analysis of the bootstrap samples, the quantifications will be
unstable. If the quantifications have small confidence intervals, this means that
they are stable. Table 9 presents the quantifications (Quantification) obtained
from the CATPCA algorithm, along with the lower (Lower) and upper (Upper)
limits of each category obtained using the bootstrap method. Specifically, the
stability analysis of the results obtained for the province of Guayas is shown.
The study considers a total number of bootstrap samples within each province,
with a 95% confidence level and the solutions are obtained in two dimen-
sions. Considering the aforementioned criteria, it can be concluded that the
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quantifications obtained in the province of Guayas are stable, since the con-
fidence intervals are small.
Table 9. Guayas - Quantifications and confidence intervals
Abbreviation Category Level Quantification Lower Higher
P23 None 1 -0.94 -0.99 -0.89
P23 Literacy center 2 -0.94 -0.99 -0.89
P23 Pre-school 3 -0.82 -0.97 -0.75
P23 Primary 4 -0.76 -0.78 -0.74
P23 Secondary 5 -0.01 -0.04 0.01
P23 Higher (non-university) 6 0.80 0.65 0.97
P23 Higher (university) 7 1.82 1.79 1.86
P23 Postgraduate 8 3.17 3.04 3.30
H07 No 1 -0.68 -0.68 -0.67
H07 Yes 2 1.48 1.46 1.50
H10 No 1 -0.54 -0.55 -0.54
H10 Yes 2 1.84 1.81 1.86
URH Rural area 1 -2.33 -2.37 -2.30
URH Urban area 2 0.43 0.42 0.43
V03 Other materials 1 -2.36 -2.41 -2.31
V03 Uncoated cane 2 -2.36 -2.41 -2.31
V03 Coated cane 3 -1.88 -1.95 -1.84
V03 Wood 4 -1.88 -1.93 -1.78
V03 Adobe or clay 5 0.06 -0.16 0.27
V03 Brick or block 6 0.41 0.40 0.42
V03 Concrete 7 0.75 0.71 0.78
V05 Other materials 1 -0.44 -0.45 -0.44
V05 Dirt 2 -0.44 -0.45 -0.44
V05 Cane 3 -0.44 -0.45 -0.44
V05 Brick or concrete 4 -0.44 -0.45 -0.44
V05 Ceramic. tile. vinyl or marble 5 -0.44 -0.45 -0.44
V05 Untreated plank 6 2.25 2.22 2.28
V05 Boarding, parquet or floating floor 7 2.25 2.22 2.28
VAP Other 1 -2.16 -2.25 -2.07
VAP River / sea / lake 2 -2.16 -2.25 -2.07
(Continued)
Katherine Morales, Miguel Flores and Yasmín Salazar Méndez 67
desarro. soc. 88, bogotá, segundo cuatrimestre de 2021, pp. 43-82, issn 0120-3584, e-issn 1900-7760, doi: 10.13043/dys.88.2
Table 9. Guayas - Quantifications and confidence intervals
Abbreviation Category Level Quantification Lower Higher
VAP Road, path, chaquiñán (trail) 3 -2.16 -2.25 -2.07
VAP Dirt road 4 -1.04 -1.08 -1.00
VAP Paved stone 5 -0.49 -0.54 -0.44
VAP Cobbled. p c 6 0.88 0.86 0.89
FO 5 or less 1 -0.63 -0.64 -0.62
FO From 6 to 10 2 0.99 0.96 1.02
FO From 11 to 15 3 2.18 2.11 2.25
FO from 16 to 20 4 2.76 2.66 2.87
FO From 21 to 25 5 2.97 2.81 3.14
FO From 26 to 30 6 3.34 3.18 3.49
FO From 31 to 35 7 3.34 3.18 3.50
FO From 36 to 40 8 3.63 3.41 3.78
FO More than 41 9 3.67 3.51 3.87
V04 Poor 1 -2.00 -2.07 -1.93
V04 Regular 2 -0.67 -0.70 -0.64
V04 Good 3 0.95 0.94 0.97
V06 Poor 1 -1.67 -1.73 -1.61
V06 Regular 2 -0.68 -0.70 -0.66
V06 Good 3 1.04 1.02 1.05
Source: Authors based on Data from the Population and Housing Census (2010)
4.2. Discussion
4.2.1 Analysis of national behavior
The indicators for each province are constructed based on the quantifications of
the categories of variables in Table 5. Figure 2 displays the distributions of the
indicators for Ecuador’s different provinces. The indicator values fall within
the range of [0; 1] due to the rescaling performed; however, it is important to
note that this does not mean that the indicators are comparable, as the quan-
tifications of categories obtained for each province and with which the indi-
cator is constructed with are different. To exemplify, for the variable head of
the household’s education level (P23), the quantification of the first category
—no education— in Pichincha is equal to -1.73, while in Sucumbíos it is equal
Analysis of Nonlinear Components for Socioeconomic Stratication Index
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Figure 1. Guayas - Bootstrap
(a) Initial Scale - Optimal Quantification
(Quantifications, Upper and lower limits)
(b) Component 1 - Component 2
(Quantification - Confidence Ellipse)
Katherine Morales, Miguel Flores and Yasmín Salazar Méndez 69
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to -0.96. The quantification of the last category, postgraduate, in Pichincha is
equal to 1.88 and in Sucumbíos, it is equal to 3.63.
Figure 2. Indicator for the national level
Once the socioeconomic indicators of each province have been constructed,
a descriptive statistics analysis for each of these indicators is carried out. See
Table 10. For the reasons stated above, the analysis to follow is not performed
in a comparative context, but a descriptive context within each province. The
average value for the socioeconomic indicator of households in the provinces
of: Azuay, Pichincha, Pastaza and Galápagos shows high figures, whereas the
lowest values appear for the provinces of: Orellana, Bolívar, Los Ríos and Manabí.
At national level, the average values are in the range of 0.3350 to 0.673. On
the other hand, the dispersion of the socioeconomic indicators of the provinces
of Azuay, Chimborazo and Loja are high; while in Santo Domingo and Los Ríos
the dispersion is low. The degree of dispersion for all provinces varies between
0.146 and 0.251 and, in general, it is high in all provinces. Moreover, Pastaza,
Galápagos, Pichincha, Azuay and Imbabura have a negative asymmetry value;
that is, the values of the household indicator tend to be located more on the
right side of the average. In the rest of the provinces (See Figure 2), this coef-
ficient is positive, so their distribution is concentrated on the left. This frame
demonstrates that within each province a large percentage of households are
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below average. The result reflects the country’s unequal living conditions in
the country and also suggests that there is a minority group of households
with good socioeconomic conditions.
Table 10. Summary of indicators
Province Average Standard
Deviation
Coefficient of
asymmetry Kurtosis Coefficient
of variation
Azuay 0.572 0.230 -0.355 2,260 40,243
Bolívar 0.337 0.200 0.764 2,840 59,348
Cañar 0.481 0.204 0.016 2,560 42,370
Carchi 0.458 0.216 0.235 2,260 47,131
Cotopaxi 0.395 0.210 0.547 2,570 53,048
Chimborazo 0.427 0.246 0.363 2,200 57,618
El Oro 0.484 0.181 0.219 2,620 37,317
Esmeraldas 0.376 0.182 0.617 2,820 48,418
Guayas 0.450 0.182 0.225 2,440 40,452
Imbabura 0.523 0.223 -0.034 2,130 42,653
Loja 0.460 0.251 0.125 1,920 54,565
Los Ríos 0.351 0.158 0.487 3,370 44,994
Manabí 0.352 0.187 0.596 2,730 53,050
Morona Santiago 0.464 0.209 0.263 2,360 45,014
Napo 0.386 0.194 0.613 2,640 50,299
Pastaza 0.627 0.178 -0.706 3,880 28,323
Pichincha 0.628 0.202 -0.418 2,440 32,206
Tungurahua 0.493 0.218 0.146 2,190 44,302
Zamora Chinchipe 0.420 0.200 0.393 2,420 47,702
Galápagos 0.673 0.163 -0.484 2,860 24,159
Sucumbíos 0.391 0.167 0.556 2,920 42,780
Orellana 0.335 0.164 0.693 3,670 48,922
Santo Domingo de
los Tsáchilas 0.473 0.146 0.098 2,850 30,945
Santa Elena 0.377 0.185 0.597 3,120 49,160
Source: Authors based on Data from the Population and Housing Census (2010)
The kurtosis coefficient for Los Ríos, Orellana and Pastaza is greater than 3, which
implies that the distributions of the indicator are leptokurtic; that is, households
are concentrated in the average. In the rest of the provinces this coefficient takes
values of less than 3, indicating that there is a small concentration of households
Katherine Morales, Miguel Flores and Yasmín Salazar Méndez 71
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around the average. As the coefficient of variation makes it possible to com-
pare the relative dispersion of the socioeconomic indicators of provinces, the
greatest dispersion of the socioeconomic indicator is observed in the provinces
of Bolívar, Chimborazo, Cotopaxi, Loja and Manabí. This reflects that house-
holds within these provinces present greater variability than in the rest of the
provinces. Finally, in Pichincha, Pastaza, Galápagos and Santo Domingo de los
Tsáchilas there is less variability among households.
Thus, the households within each province are grouped over quintiles, where
the first quintile represents the households in worse conditions in terms of
goods and services, while the fifth quintile represents the households in better
conditions. In the Figure 3 and 4, the cut-off point of the quintiles is observed
for each of the country’s provinces.
Figure 3. Indicator - Quintiles by provinces
Azuay
Carchi Cotopaxi Chimborazo
Indicator
Households
0
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
5000
10000
15000
0
1000
2000
3000
4000
5000
6000
Households
Households
Households
Households
Households
Indicator
Indicator
Indicator
Indicator
Indicator
Bolívar Cañar
0
0.0 0.2 0.4 0.6 0.8 1.0
1000
2000
3000
4000
0
0.0 0.2 0.4 0.6 0.8 1.0
4000
6000
2000
8000
10000
0
0.0 0.2 0.4 0.6 0.8 1.0
4000
6000
2000
8000
10000
12000
0.0 0.2 0.4 0.6 0.8 1.0
0
1000
2000
3000
4000
5000
6000
(a) Azuay, Bolívar, Cañar, Carchi, Cotopaxi, Chimborazo
El Oro
Imbabura Loja Los Ríos
Indicator
Households
0
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
5000
10000
15000
20000
Households
Households
Households
Households
Households
Indicator
Indicator
Indicator
Indicator
Indicator
Esmeraldas Guayas
0
5000
10000
15000
0
0.0 0.2 0.4 0.6 0.8 1.0
2000
4000
6000
8000
0
0.0 0.2 0.4 0.6 0.8 1.0
4000
6000
2000
0
0.0 0.2 0.4 0.6 0.8 1.0
5000
25000
15000
0.0 0.2 0.4 0.6 0.8 1.0
0e+00
2e+04
4e+04
6e+04
8e+04
1e+05
(b) El Oro, Esmeraldas, Guayas, Imbabura, Loja, Los Ríos
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Figure 4. Indicator - Quintiles by provinces
Manabi
Pastaza Pichincha
Indicator
Tungurahua
Households
0
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
10000
20000
30000
40000
Households
Households
Households
Households
Households
Indicator
Indicator
Indicator
Indicator
Indicator
Morona Santiago Napo
0
500
1000
1500
2000
2500
3000
3500
0
500
1000
1500
2000
2500
3000
0
0.0 0.2 0.4 0.6 0.8 1.0
500
1000
1500
2000
2500
0.0 0.2 0.4 0.6 0.8 1.0
0
0.0 0.2 0.4 0.6 0.8 1.0
2000
4000
6000
8000
10000
0
10000
30000
50000
70000
0.0 0.2 0.4 0.6 0.8 1.0
(a) Manabí, M. Santiago, Napo, Pastaza, Pichincha, Tungurahua
Zamora Chinchipe
Orellana Santo Domingo de los Tsáchilas Santa Elena
Indicator
Households
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
Households
Households
Households
Households
Households
Indicator
Indicator
Indicator
Indicator
Indicator
Galápagos Sucumbios
0
200
400
600
800
500
1000
1500
2000
0
1000
2000
3000
4000
5000
0
0.0 0.2 0.4 0.6 0.8 1.0
1000
2000
3000
4000
0.0 0.2 0.4 0.6 0.8 1.0
0
0.0 0.2 0.4 0.6 0.8 1.0
2000
4000
6000
8000
10000
0
2000
6000
10000
14000
0.0 0.2 0.4 0.6 0.8 1.0
0
(b) Z. Chinchipe, Galápagos, Sucumbíos, Orellana, S. Domingo , S. Elena
It is important to mention that the province of Galápagos is a nature reserve
that is isolated to a certain extent thanks to its geographical position. Also,
its main economic activity is tourism, which indirectly affects all sectors of
the island’s local economy (Taylor et al., 2007). The above, together with the
fact that it presents the lowest percentage of variance explained by the com-
ponents (See Table 6), the general results for Galápagos are different from the
rest of the country’s provinces.
4.2.2 Distribution analysis of the indicator over quintiles
Given the importance of having a detailed description of the different quintiles
within each province, their characteristics are presented for the particular case
of the province of Pichincha.
Katherine Morales, Miguel Flores and Yasmín Salazar Méndez 73
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Pichincha
The province of Pichincha contains about 19.14% of the country’s households
distributed in 8 cantons. Figure 5(a) shows that the Rumiñahui canton has the
highest average indicator value (0,66), followed by Quito (0,65). This implies that,
in general, the households of these cantons have better living conditions. This
could be explained by the fact that Quito, the capital of Ecuador, and Rumiñahui
are strongly interconnected by geographical location, labor interests and economic
activity between these two cities. On the other hand, Pedro Moncayo has the
lowest average value (0.39). The households in this canton have the worst living
conditions in the province of Pichincha. When analyzing Figure 5(b), the largest
indicator dispersion is in the Cayambe canton (0.22), while the smallest disper-
sion occurs in Pedro Vicente Maldonado and San Miguel de los Bancos (0.16).
Figure 6 displays an analysis of the quintiles of the households belonging to
Pichincha cantons. 64.66% of Pedro Vicente Maldonado’s households belong
to the first quintile, which makes it the canton with the highest percentage of
households belonging to this quintile, followed by San Miguel de los Bancos
and Pedro Moncayo with 63.39% and 63.09% respectively. The main activities
in these cantons are agriculture and tourism. At the other extreme, Quito and
Rumiñahui have the lowest percentage of households within the quintile, with
16.65% and 15.57% respectively and the dispersion in each canton ranges
between 0.08 and 0.12. Some 26.35% of Mejía households are in the second
quintile, followed by Pedro Vicente Maldonado with 21.64%. The cantons with
the lowest percentage of households in this quintile are Quito and Rumiñahui
with 19.74% and 19,.5%, respectively. The analysis of the following quintiles
is similar, since as of the third quintile, Quito and Rumiñahui have a higher
percentage of households. Pedro Moncayo and Pedro Vicente Maldonado have
the lowest percentage of households within these quintiles. The dispersion of
Pichincha households within each quintile is low, except for the one belong-
ing to the first quintile that has dispersions of up to 0.12. In the other quin-
tiles, the dispersion fluctuates between 0.03 and 0.04.
Table 11 presents the profile of the households belonging to each quintile. The
characteristics of the first quintile consist of rented, lent or ceded housing or
type of rooms in tenement house —which constitutes the majority— and those
located in the rural area. The housing materials are tile, wood, adobe, and brick
with poor conditions. They do not have basic services such as electric power,
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Figure 5. Pichincha - Indicator
(a) Average
(b) Standard deviation
Fuente: Elaboración propia
Katherine Morales, Miguel Flores and Yasmín Salazar Méndez 75
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WC, garbage collection, landline telephone, internet, computer, cell phone and
cable television. The head of household has a low level of schooling, none of the
household members has private insurance, and they study in state-run educa-
tional centers. The households belonging to the second quintile are character-
ized by being in the rural area, with their own housing but inherited or ceded,
the materials of the roof, walls and floor are zinc, adobe and brick or cement,
respectively. These tend not to be in very good condition. They don’t have the
Figure 6. Pichincha - Quintiles
(a) Quintile 1 (b) Quintile 2
(c) Quintile 3 (d) Quintile 4
(e) Quintile 5
Fuente: Elaboración propia
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basic services; the shower and WC is shared with other households and the level
of education of the head of household is primary. The members of the house-
holds of this quintile conduct their studies in public educational centers and no
one has private insurance. In the third, fourth and fifth quintiles, the households
have a WC and shower for private use, as well as the basic services mentioned
above. The housing of these households in these quintiles are their own, and tend
to be apartments or houses that are in good condition, built with brick, block,
concrete, ceramic tile or parquet materials. The main entrance road is paved or
concrete. Household members of the third quintile study in public centers and
do not have private insurance. Those in the fourth and fifth quintiles study in
private centers and some or all members of the household have private insurance.
Table 11. Analysis of Pichincha Individuals
Variable Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5
Education of
the head of
household
Literacy
center
None
Preschool
Preschool
Primary Secondary Higher
(non-university)
Higher
(university)
Postgraduate
Type of WC None Shared Exclusive use Exclusive use Exclusive use
Shower None Shared Exclusive use Exclusive use Exclusive use
Telephone land-
Line No No Ye s Yes Yes
Cell phone No No Ye s Yes Ye s
Internet No No No Yes Yes
Computer No No No Yes Yes
Cable TV No No No Yes Ye s
Possession of
housing
Rented, lent,
or ceded (not
paid)
Own (gifted,
donated,
inherited or
in possession)
For service Own and
being-Paid
Own and
totally
Area A. Rural A. Rural A. Urban A. Urban A. Urban
Ceiling material Tile or shingle Zinc sheet Asbestos Concrete Concrete
Wall material Wood
Adobe or clay Adobe or clay Brick or block Concrete Concrete
(Continued)
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Table 11. Analysis of Pichincha Individuals
Variable Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5
Floor covering
material
Dirt
Brick or
concrete
Brick or
concrete
Ceramic,
ceramic
tile, vinyl or
marble
Ceramic,
ceramic tile,
vinyl or marble
Boarding,
parquet,
Plank
Boarding,
parquet, plank
floating floor
Water pro-water
From river,
slope, canal
from well
By public
network
By public
network
By public
network
By public
network
How do they the
water
Does not
receive water
pipeline
By pipeline
outside
By pipeline
outside
The housing,
inside the
Building
By pipeline
inside the
housing
By pipeline
inside the
housing
By pipeline
inside the
housing
WC
None
Connected to
septic tank or
cesspit
Connected to
public Sewage
Network
Connected to
public sewage
network
Connected to
public Sewage
Network
Connected to
public sewage
network
Garbage the
disposal
Other
They burn it
Throwing into
river, ditch or
channel
By garbage
collection
vehicle
By garbage
collection
vehicle
By garbage
collection
vehicle
By garbage
collection
vehicle
Main entrance
Path
Other
Road, path,
chaquiñan
Ballast or dirt
Paved stone
Ballast or dirt
Cobbled,
paved,
concrete
Cobbled,
paved,
concrete
Cobbled,
paved,
concrete
Electric energy
service
None
Electric
company
network
Electric
company
network for
public service
Electric
company
network for
public service
Electric
company
network
Network for
public service
Electric
company
network
network for
public service
Electric meter None Shared Exclusive use Exclusive use Exclusive use
Type of housing
Room(s) in
tenement
House
Apartment
in house or
building
Apartment
in house or
building
House/Villa House/Villa
Ceiling
condition Poor Regular Good Good Good
Wall condition Poor Regular Good Good Good
Condition of the
floor covering Poor Regular Good Good Good
(Continued)
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Table 11. Analysis of Pichincha Individuals
Variable Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5
Number of light
bulbs 5 or less From 6 to 10 From 6 to 10 From 6 to 10 More than 10
Last payment of
electricity 5 or less From 5 to 9 From 10 to 14 From 10 to 20 More than 20
Type of
education Mostly Mostly Mostly Mostly Mostly
center State-run State-run State-run Private private
Private
insurance Nobody Nobody Nobody Some people All
5. Conclusions
This article built socioeconomic stratification indicators for provinces in Ecua-
dor. The results of this analysis constitute a tool for the fields of economics,
political science, demography, sociology and marketing. In economics, for
example, the information on social strata is essential for designing and imple-
menting public policies. We constructed indicators of socio-economic strati-
fication at the provincial level, which reduce the variability of the indicators
obtained with respect to those obtained in similar studies, also conducted in
Ecuador. Another contribution of this article is the application of the nonlinear
PCA that allows the incorporation of quantitative and qualitative variables.
Our results were subjected to a sensitivity analysis using the bootstrap method
and in general, showed that they are robust. However, some categories pre-
sented a low frequency which ultimately lead to large confidence intervals.
This issue could be solved by appropriately clustering these low frequency cat-
egories. Another alternative is to modify the scaling of the abovementioned
categories by using different scale levels, such as ordinal spline. On the other
hand, the main advantage of using nonlinear PCA, compared to other similar
techniques, is that the optimal quantifications obtained from ordinal variables
retain their ordinal property, which allows for a socio-economic stratification
interpretation of indicators.
Regarding the socio-economic conditions, it can be concluded that the house-
holds located in the urban area display better conditions and greater access to
Katherine Morales, Miguel Flores and Yasmín Salazar Méndez 79
desarro. soc. 88, bogotá, segundo cuatrimestre de 2021, pp. 43-82, issn 0120-3584, e-issn 1900-7760, doi: 10.13043/dys.88.2
basic services. Likewise, the education level of the head of household is a key
factor when characterizing household quintiles and the results suggest that,
in general, education positively affects social and economic conditions of both
individuals and the households. The results also suggest high inequality among
the provinces. In Guayas, for example, there is huge inequality between Sam-
borondón and Colimes. A similar situation is observed in Pichincha with can-
tons like Quito and Pedro Vicente Maldonado. In light of these results, public
policy should be focused on the education, both in quantity and quality, of
the school-age inhabitants of the cantons in worse social and economic con-
ditions. Likewise, public investment in the provision of basic services such
as drinking water, sewerage, electricity, access roads and garbage collection
should focus on the cantons that, as explained by their conditions, have been
the most neglected.
Acknowledgements
The authors did not receive funding from any institution to carry out this
research. The authors would like to thank the anonymous reviewers for their
suggestions and comments to the original version of this paper.
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