sustainability
Article
Analysis of Time Use Surveys Using CO-STATIS: A Multiway
Data Analysis of Gender Inequalities in Time Use in Colombia
Edith Johana Medina-Hernández 1,2,*, María José Fernández-Gómez 2,3 and Inmaculada Barrera-Mellado 2
1 Faculty of Basic Sciences, Universidad Tecnológica de Bolívar (UTB), Cartagena 131001, Colombia
2 Statistics Department, University of Salamanca (USAL), 37007 Salamanca, Spain; mjfg@usal.es (M.J.F.-G.);
imb@usal.es (I.B.-M.)
3 Institute for Biomedical Research (IBSAL), 37007 Salamanca, Spain
* Correspondence: emedina@utb.edu.co or edith.medina@usal.es
Abstract: The aim of this article was to study 23 time use activities measured in the two latest
Colombian National Time Use Surveys, taken in 2013 (with 119,899 participants over the age of 10)
and in 2017 (with a sample of 122,620 participants), to identify similarities and differences between
the years of the survey by gender, age group, and socioeconomic level. The study’s results were
obtained using the CO-STATIS multiway multivariate data analysis technique, which is comprised of
two X-STATIS analyses and co-inertia analysis. The results confirm the existence of gender issues
related to time use in Colombia, which are associated with gender stereotypes that link women to
unpaid work and home care, especially in low socioeconomic levels, where women face limitations
in terms of the time available to earn their own income. Additionally, differences were found by





 socioeconomic level, where Colombians of high socioeconomic status in all age groups are able to
Citation: Medina-Hernández, E.J.; devote more time to leisure and recreational activities.
Fernández-Gómez, M.J.;
Barrera-Mellado, I. Analysis of Time Keywords: time use; gender inequality; multivariate analysis; CO-STATIS; X-STATIS; co-inertia
Use Surveys Using CO-STATIS: A
Multiway Data Analysis of Gender
Inequalities in Time Use in Colombia.
Sustainability 2021, 13, 13073. https:// 1. Introduction
doi.org/10.3390/su132313073 Historically, time use has been studied for a variety of reasons, such as for economic
studies aimed at making specific estimates on the contribution of unpaid work to a nation’s
Academic Editors: Stefano Boca and economy, to calculate the ratio of household work over total time worked, or to establish
Ambra Gentile the association between monetary poverty, income and time distribution, and assignment
of men and women. Household work is recognized by those who see the economy as a
Received: 31 October 2021
way of satisfying human needs in a broader context, as well as by researchers who study
Accepted: 22 November 2021
Published: 25 November 2021 non-monetary or informal processes [1] (p. 188), and time use is included in the latter.
In social science and public policy studies, time use is analyzed to determine the
types of activities people engage in on a regular basis in order to identify ways to satisfy
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in their needs and improve their life quality. Making effective use of time can help achieve a
published maps and institutional affil- better life balance between work, family, studying, and daily activities. In the public health
iations. area, studies are made on how different time use patterns determine the development or
worsening of illnesses and their effects on mental health [2–6]. Therefore, the study of time
use is an interdisciplinary field with contributions from sociology, psychology, gender and
sexuality studies, economics, and other social sciences [7] (p. 20).
The above points to the relevance of discussing the importance of the various ap-
Copyright: © 2021 by the authors.
proaches and purposes of time use studies, in order to contextualize the problem analyzed
Licensee MDPI, Basel, Switzerland.
This article is an open access article in this paper, the multidimensional analysis method used, the results obtained, and its
distributed under the terms and practical implications.
conditions of the Creative Commons
1.1. Time Use Analysis in Gender Studies
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/ Time use is considered one of the key social and economic determinants of gender
4.0/). inequality. As in the case of the study of other gender issues, such as workforce partici-
Sustainability 2021, 13, 13073. https://doi.org/10.3390/su132313073 https://www.mdpi.com/journal/sustainability
Sustainability 2021, 13, 13073 2 of 20
pation by females, the feminization of poverty, or women’s participation in senior level
government or private company positions, the study of time use has gained prominence in
recent years because it enables understanding existing gender differences and similarities
in the context of the care economy and the economic empowerment of women.
The care economy is studied in order to quantify the unpaid work carried out at
home in household maintenance activities and the amount of time devoted to caring
for the family. Rubiano-Matulevich and Viollaz [8] argue that even though substantial
progress toward gender equality has been made in the past decades, the inequalities linked
to gender norms, stereotypes, and the unequal distribution of housework and childcare
responsibilities persist. This implies the existence of inequalities in the use of time between
women and men.
Ferrant [9] also emphasizes the importance of recognizing unpaid care work by
measuring and valuing it, because it helps to redistribute unpaid care tasks more equally
between men and women by transforming gender stereotypes. This author argues that this
is necessary in order to support the achievement of the Sustainable Development Goals
in the different countries of the world, because when women have control over their time
and are free to weigh the challenges they face at home against those they face in their
professional careers, they become empowered and are able to make positive contributions
to a nation’s economy.
For this reason, it is important for gender studies to assess the different factors that
determine the way men and women use their time, differentiating between home care,
work, and free time activities, because studies of this type are conducive to the search for
gender equality and female empowerment.
1.2. Time Use Studies by Socioeconomic Status
A specific aspect that is often studied is how socioeconomic level also determines
and conditions the way people distribute and use their time. Aguiar [10] claims that
there are differences in the way people from different socioeconomic levels and lifestyles
organize their remunerated and leisure time. Moreover, Neubert [11], in comparing
the assignment of work in different occupational categories, socioeconomic levels, and
educational attainment levels, found that people with higher education have advantages
in terms of time use, not only in connection with the time devoted to work, but also in the
organization of their leisure and everyday activities.
Specifically on the use of time by women, Kolpashnikova [12] studied the time devoted
to housework in Japan, Canada, and the United States by gender, marital status, age,
socioeconomic level (SEL), and the presence of children at home. She found that women
with greater purchasing power and higher educational attainment are able to hire assistance
to carry out domestic work, enabling them to remain more committed to remunerated
work activities.
In terms of studies in the Latin American context, Candia [13] carried out a study
disaggregated by socioeconomic variables (gender, age, income, and geographic location
of their home) on the use of time by Chilean workers. She found that women have a
greater overall workload than men because of unpaid work. This author also found that
individuals of higher socioeconomic status devote more time to leisure and free time
activities than to unpaid housework.
1.3. Time Use Studies with a Life Cycle Approach
Time use is studied not only with a gender approach, but also in public health studies,
with the purpose of analyzing variables of this type that determine differences in the quality
of life of people, especially taking into consideration their life cycle stage or age.
For example, in recent literature we can cite the work of Chong et al. [4], Samonova
et al. [14], and Blaurock et al. [15] in connection with time use studies with children. These
authors support the idea that in this age group, the patterns of time use are associated with
a family’s resources (i.e., level of education) and the age of the children. On the other hand,
Sustainability 2021, 13, 13073 3 of 20
Vernon [16] and Kim et al. [17] are among the authors that assess time use by adolescents
and youth. These authors argue that in this life stage, it is important to consider the
patterns of time use, including traditional activities (i.e., paid work, homework, television,
physical activity, leisure activities, sleeping, etc.) and technological activities (gaming,
social networking, Internet).
In the specific case of older adults, some studies that argue why it is important to
study time use in this age group are Powers et al. [2], Foong et al. [3], Ko [5], Chai et al. [18],
and Steptoe and Fancourt [19].
Specifically, the latter, in reviewing survey data from over 7000 men and women in the
United Kingdom in the age range of 50 or older, found similarities and differences in their
“worthwhile life ratings” by age, sex, educational attainment, and socioeconomic status.
The authors claim that the differences in the life quality of older adults depend on social
and economic variables, health conditions and time spent with friends, watching television,
being alone, engaging in volunteer activities, and devoting time to exercising or walking.
Due to the above, time use studies are also important for comparisons between age
groups, because at different life stages, daily activities are distributed differently, which
implies that age can be understood as a determinant of life quality and personal satisfaction.
1.4. Time Use Studies by Means of Modeling Techniques
Time use studies tend to be of a socio-political type and do not always involve
modeling techniques to identify multiple associations or patterns that are not obvious
from the data at first sight. Studies of this type typically assess the data using descriptive
techniques with one or two variables or through econometric estimation methods, where
the time use variables are usually analyzed separately or descriptively. However, it is
viable to conduct multivariate analysis on data of this type to arrive at results of interest for
gender studies. There is no good reason to be limited to simple analyses that are usually
solely for confirmation purposes. The possibility of combining the variables opens the door
to obtaining results that are sometimes unexpected and beyond the obvious [20] (p. 14).
Due to the above, in order to contextualize the analysis of this study, it is also important
to cite some authors who in recent studies analyze official time use data by means of
statistical techniques and multivariate analyses to obtain their results.
In the European context, Rogge and Van Nijverseel [21] quantified and reviewed
the quality of life of European Union countries using a multidimensional design. To
this end, they used citizen satisfaction data in eight dimensions, based on which they
developed a composite index, concluding that the correlations between the variables show
a strong relationship between the multidimensional and one-dimensional measurements
of subjective life quality.
Fraire [22] also carried out a comparative analysis between European Union countries.
This author used the STATIS Dual and Multiple Factor Analysis techniques to compare
time use results of surveys made near to 2000 in six European countries: Belgium, Estonia,
Finland, Norway, Slovenia, and the United Kingdom. In this study, after presenting
descriptive statistics by gender, employment status and marital status by age group, and
presence of children in the family, a STATIS Dual analysis was performed to compare the
12 time use activities in each country under each of the considered categories to characterize
the population.
Kızılırmak and Köse [23] studied the determinants of the use of free time in Turkey
by exploring associations between time used in cultural, social, sports, and other leisure
activities compared to socio-demographic variables on gender, age, educational level,
household income level, marital status, employment status, health conditions, and time
used for childcare. To this end, they examined data from the 2014–2015 TurkStat Time Use
Survey and obtained research results by means of a multiple regression model.
Yoon et al. [24] studied time use by Korean citizens over the age of 65 based on surveys
taken by the Korean National Statistics Office in 2004 and 2009. The study’s results were
Sustainability 2021, 13, 13073 4 of 20
obtained using multivariate techniques: correspondence analysis and Biplot analysis, based
on which they search for and describe clusters of individuals.
In the Australian context, Richardson et al. [25] conducted a longitudinal cohort study
with a group of first-year university students to discover time use associations by gender
and age group. The authors found statistically significant differences through hypothesis
testing on comparisons between population groups. Bittman [26] also studied time use in
Australia, based on data from the Australian Bureau of Statistics.
Several studies of reference in the United States of America [27–30] used modeling
techniques to characterize time use in different population groups and also used the records
of the American Time Use Survey (ATUS). This international survey is well known for
periodically publishing annual information with disaggregation levels that enable using
different analytic approaches and facilitate the use of different modeling techniques.
Due to all of the above, in this study, we conducted a multi-dimensional exploration,
with no specific response variable to find and analyze underlying patterns and to compare
the data from the 2013 and 2017 Colombian National Time Use Surveys (ENUT, by its
acronym in Spanish: Encuesta Nacional de Uso del Tiempo) from a gender perspective.
The results were obtained from data analysis using the CO-STATIS method [31]. In this
technique, the co-inertia analysis [32] is used to relate two compromises obtained from two
partial triadic analysis (PTA). The PTA was proposed by Jaffrenou [33] to analyze k-table
data, which is also called X-STATIS according to Abdi et al. [34]. Thus, CO-STATIS seeks
the relationships between two stable structures.
In this study, we were particularly interested not only in determining whether both
survey years are similar, but also in identifying the variables that display gender differences
and in determining associations by age group and socioeconomic status. Even though
most time use studies focus on how men and women spend their time differently, few
conclusions are presented on whether such differences persist in different age groups, or if
there are differences by socioeconomic status, a characteristic that, in Colombia, determines
the daily routines of the population.
2. Materials and Methods
2.1. Data in Analysis
The data of interest for this study were the responses given by Colombians over
the age of 10 in the ENUT DANE surveys taken in 2013 and 2017 [35,36]. In Colombia,
these surveys are taken by means of electronic forms filled out by interviewers during
face-to-face visits to the households selected to participate in the statistical study. In the
first national survey, there were 146,190 participants, for whom the 696 variables were
recorded, and the second survey had 146,190 records and 743 variables. Currently, a new
survey is in progress, which will enable studying the effects produced by the COVID-19
pandemic on the use of time by Colombians.
Given the level of detail of the ENUT surveys and the substantial amount of infor-
mation gathered, for this study, it was necessary to process the databases of both years to
summarize in 23 fields the different types of time use to be subject to multidimensional
analysis, which are displayed in Table 1. The sociodemographic characteristics of the popu-
lation that were selected for the study were gender, age group, and socioeconomic status.
In Colombia, the latter is defined according to a Socioeconomic Stratification system, which
is based on the classification of residential properties in accordance with the Colombian
Public Utilities Regime (Law 142/1994), according to which higher income households pay
more for public utilities and cross-subsidize the bills of lower income households [37].
Sustainability 2021, 13, 13073 5 of 20
Table 1. Activities and times in analysis.
Notation Activities
AGR Agricultural activities
BAC Basic activities (eating, sleeping, and taking a shower)
BAR Going to bars
CUA Attend cultural events or activities
DHA Domestic and household activities (preparing food, cleaning the home, etc.)
FHC Family and home care activities (caring for children and other household members)
FRI Visit to friends
HAI Time at the hairdresser
INT Internet and chats
LJO Looking for a job and establishing your own business
LMU Listening to music
MJO Movements and journeys (for studying, working, or household care)
MUS Music and art (practice a musical instrument, paint, etc.)
PHO Speaking on the phone
REA Reading
REL Religious acts (to attend or organize religious activities)
RES Time to rest
SPE Going to sport events
SPO Practicing sports
STU Study time
VOL Voluntary activities
VTV Watching videos and TV (media consumption)
WOR Work time
For this study, the data were processed as follows: for each variable, the total hours
and minutes reported by the survey respondents were added, to then find the average use
of time in the different population groups by sociodemographic characteristics.
The data were structured as follows. For each of the four age groups, adolescents
and youths (between the ages of 10 and 17), young adults (between the ages of 18 and 34),
adults (ages from 35 to 59), and older adults (60 or older), a data table was developed
(matrix) formed by 23 columns representing the 23 time use activities described above, and
by 6 rows that represent the gender combinations (W and M) and socioeconomic status
(summarized as 3 levels, where levels 1 and 2 of the DANE classification are designated as
L (low socioeconomic status—L SES), levels 3 and 4 as medium level (M SES) and levels 5
and 6 as H (high socioeconomic status—H SES). As mentioned, the elements of each matrix
are the time use measurements of each activity by the different sociodemographic levels.
Consequently, for each survey year (2013 and 2017), there is one multidimensional
data table, structured as a data cube, because they have the same characteristics (the time
use variables) measured over the same objects (combination of gender and socioeconomic
status) in the different age groups. Figure 1 summarizes the structure of the information
described above for each year of the study. Table 2 summarizes the total records of the
study by the demographic variables of interest, with the totals reported by Colombians in
the two ENUT surveys.
Below, we present the main methodological references used for this study, which
is proposed as a descriptive and exploratory study, and a summary of the conceptual
foundations of the modeling techniques used to obtain and present the results.
SSuustsatianinabaiblitliyty2 022012,11, 31,31, 3x0 F7O3 R PEER REVIEW 6 ooff2 021 
 
 
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  ENENUUTT CCoololommbbiiaa ((22001133)) EENNUUTT CCoolloommbbiaia( 2(021071)7) 
WWoommeenn//MMeenn 101–01–177 1818––3344 3355––5599 6600++ TToottaall 1100––1177 1188––3344 3355––5599 6600++ TTootatal l 
Low SES 8112 15,005 15,769 5885 44,771 7402 15,186 17,309 7293 47,190 
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LLooww SSEESS 81851353 131,30,05577 1133,3,35577 55006677 3399,,663344 77664444 1133,,779933 1144,,770077 66118844 4422,3,32288 
MMiiddddllee SSEESS 21251050 46466666 55332244 22331177 1144,,445577 11775533 44113366 55005511 22662277 1133,5,56677 
HHiiggh SES 141545 337700 556655 333399 114419 132 351 5177 334477 11334477 
TToottaall Meenn 101,04,44488 181,80,09933 1199,2,24466 77772233 5555,,551100 99552299 1188,,228800 2200,,227755 99115588 5577,2,24422 
Below, we present the main methodological references used for this study, which is 
2p.2r.oCpOos-eSdT AasT IaS dAenscarlyipsitsive and exploratory study, and a summary of the conceptual foun-
datioTnhse oCfO th-SeT mAoTdISelminegt hteocdhwniaqsupesr oupsoesde dtob oybTtahinio aunlodu psere[s3e1n]ta tshae prerosuceltsss. to summarize
the three-way data analysis when two X-STATIS analyses and one co-inertia analysis are
c2o.n2.s eCcOu-tSivTeAlyTIuSs eAdn,aalyssiisn this study. This technique has been popular for the study of
ecological and environmental information [38,39], and has recently used in the context of
Sustainability 2021, 13, x FOR PEER REVIEWT he CO-STATIS method was proposed by Thioulouse [31] as a process to summ7 aofr i2z1e  
 stohcei ot-herceoen-womayic daantaa laynsiasly[4si0s, 4w1]h.eFni gtwuroe X2-pSrTeAseTnItSs athnealsycsheesm anedo fotnhee csot-eipnserttoiab aenfaollyloswis eadre 
wcoitnhstehciustmiveetlhyo uds,ewd,h aisc hini sththise smtuadiny. tTechhisn tieqcuhenuiqseude ihnasth biesesntu pdoyp. ular for the study of eco-
logical and environmental information [38,39], and has recently used in the context of so-
cio-economic analysis [40,41]. Figure 2 presents the scheme of the steps to be followed 
with this method, which is the main technique used in this study. 
 
Figure 2.. Data analysis scheme for the CO-STATTIISSt teecchhnniiqquuee.. 
2.3. Step 1: Triadic Partial Analysis or X-STATIS 
This technique was first proposed by Jaffrenou in 1978 [33]. It was initially called 
Triadic Analysis by Thioulouse et al. [42], was later called Partial Triadic Analysis by 
Kroonenberg [43], and was recently named X-STATIS by Abdi et al. [34]. It has been cited 
in papers such as [44–49]. This analytical method applies to sets of matrices with three 
inputs made up by the same individuals (rows) and the same variables (columns), under 
several conditions or points in time. The intent of X-STATIS is to simultaneously study 
the sub-matrices of quantitative data in order to detect common patterns. The method is 
developed in three stages, the first of which is the interstructure analysis, the purpose of 
which is to study the overall similarities between the tables. 
The second stage is the analysis of the compromise, the purpose of which is to sum-
marize the information from the initial matrices to provide an image of the structures that 
are common to all the tables. Lastly, the intrastructure analysis is performed, which con-
sists in analyzing the reproducibility of the compromise. In this stage, the positions or 
trajectories are presented for each individual and/or variable included in the original ta-
bles, and their relative positions are analyzed in terms of their positions with each other 
and with the position of the compromise. 
To understand how X-STATIS works, Figure 3 below summarizes the scheme of the 
analysis and provides a description of its general aspects, based on references from 
[42,50,51]. The chart in Figure 3 shows that the first step is the interstructure analysis, to 
which end a Z matrix is constructed as a composition of the original data; i.e., starting out 
with T data matrices (XT), which are comprised of the same I rows (same individuals) and 
J columns (same variables), in such a manner that each column vector of the Z matrix 
matches one of the T matrices in an extended way. Consequently, the Z matrix contains 
as many columns as matrices for the study and can be viewed as a two-dimensional table. 
The Z matrix is analyzed by means of a principal component analysis. The first ei-
genvector is used to construct the compromise matrix as a weighted average of the origi-
nal tables, using the elements of this first eigenvector as weights. Furthermore, this de-
composition of Z allows to represent each matrix as a vector over the first two principal 
components obtained from the analysis, which enables assessing the relationships be-
tween the original matrices. 
Sustainability 2021, 13, 13073 7 of 20
2.3. Step 1: Triadic Partial Analysis or X-STATIS
This technique was first proposed by Jaffrenou in 1978 [33]. It was initially called
Triadic Analysis by Thioulouse et al. [42], was later called Partial Triadic Analysis by
Kroonenberg [43], and was recently named X-STATIS by Abdi et al. [34]. It has been cited
in papers such as [44–49]. This analytical method applies to sets of matrices with three
inputs made up by the same individuals (rows) and the same variables (columns), under
several conditions or points in time. The intent of X-STATIS is to simultaneously study
the sub-matrices of quantitative data in order to detect common patterns. The method is
developed in three stages, the first of which is the interstructure analysis, the purpose of
which is to study the overall similarities between the tables.
The second stage is the analysis of the compromise, the purpose of which is to summa-
rize the information from the initial matrices to provide an image of the structures that are
common to all the tables. Lastly, the intrastructure analysis is performed, which consists in
analyzing the reproducibility of the compromise. In this stage, the positions or trajectories
are presented for each individual and/or variable included in the original tables, and their
relative positions are analyzed in terms of their positions with each other and with the
position of the compromise.
To understand how X-STATIS works, Figure 3 below summarizes the scheme of the
analysis and provides a description of its general aspects, based on references from [42,50,51].
The chart in Figure 3 shows that the first step is the interstructure analysis, to which end a
Z matrix is constructed as a composition of the original data; i.e., starting out with T data
matrices (XT), which are comprised of the same I rows (same individuals) and J columns
(same variables), in such a manner that each column vector of the Z matrix matches one of
Sustainability 2021, 13, x FOR PEER RtE h
VeIETWm atrices in an extended way. Consequently, the Z matrix contains as many col8u mof n2s1 
as matrices for the study and can be viewed as a two-dimensional table.
 
Figure 3.. Data analysis scheme for the X-STATTIISS.. 
TThhee nZexmt asttraigxei sofa tnhael yazneadlybsiys mis etoan csonosftraupctr itnhcei pcaolmcpormompoisnee nmtaatrniaxl yasnids. toT ahneafilyrzste 
ethigee cnovmecptroormisisue ssetdrutcotucroen. sTthrue cptuthrpeocsoem ofp rthoims issteagme aitsr itxo asusmamwaeriigzhet ethde aivneforarmgeatoiof nth oef 
othrieg iinniatliatla Tbl emsa, tursicinesg (tXhTe) einle ma seinntgsleo fmthaitsrifixr. sTtheiisg menavtericxt oprraosviwdeesig ahnt so. vFeurratlhl esrummomrea,rtyh oisf 
dalelc tohme pinofsoitrimonatoiofnZ caollnotwribsutoterde pbrye sthenet oeraigchinmala mtraixtraicseas,v aelcotnogr  othvee rt tchoenfidritsitotnwso. principal
compTohnee ncotsmopbrtaoimneisde fmroamtritxh emaanxailmysizise,sw thheic mh eeanna bolfe tshaes cseosrsrienlagtitohnesr ebleattwioenesnh iiptss vbaertiwabeleens 
tahnedo trhige ivnaarlimabaltersi coefs e. ach Xt matrix. It can be said that the compromise provides an image 
of theT hsteruncetxutrsetsa tgheaot fatrhe ecoamnamlyosnis tios atoll cthoen sttarbulcets.t he compromise matrix and to analyze
the coLmasptlryo,m thisee fsintraul csttuerpe .oTf htheep aunraploysseiso ifs tthhies sintatgraesitsrutoctusurem amnaarlyizseist, hwehinicfho rcmonastiiostns oinf  
tthhee ianniatilaylsTis mofa tthreic reesp(rXoTd)uicnibailsiitnyg olef tmhea tcroixm. pTrhoims misea.t rIti xenparobvleisd reesparnesoevnetrinagll tshuem pmosairtiyoonfs 
aolnl  tthhee icnofmorpmroatmioinsec (oonrt rtribaujetcetdorbieyst)h oef oeraicghin ianldmivaidtruicaels a, nadlo/nogr vthaeritabcolen tdhiatito cnosm. prises the 
various tables, and their relative positions in relation to the position on the compromise. 
The compromise positions of the elements are their mean positions. A trajectory is defined 
as the change in the position of a variable (or individual) over time or in different condi-
tions. Consequently, a trajectory with low variation (wraps around) indicates that this 
variable (or individual) is stable over time. 
If the trajectory is eccentric, it means that this variable (or individual) is not stable 
over time or across conditions. In the first type, colored in blue in Figure 3, the individuals 
follow a medium evolution; i.e., the difference in the value for each individual at each 
point in time and that of an average individual remains regular over time. On the other 
hand, the eccentric trajectories, also known as large amplitude trajectories, reflect changes 
in the structure of the individuals over time. 
The use of X-STATIS in this study is justified for the effects of determining whether 
there are similarities between age groups in terms of how Colombians make use of time. 
This technique also enables observing any differences by sex and socioeconomic level in 
the trajectories by age groups, in order to make a descriptive comparison between the 
observations in the two years in which ENUT surveys were made in Colombia. 
2.4.Step 2: Co-Inertia Analysis 
Co-inertia analysis, proposed by Doléc and Chessel [52], enables finding common 
structures between two set of variables; i.e., to simultaneously analyze two data matrices 
that contain the same individuals (rows) and different or similar variables (columns), to 
describe their co-structure by maximizing the covariance between the coordinates of the 
rows of the two tables. This method belongs to the family of techniques that study matri-
ces in pairs, such as canonical analysis and canonical correspondence analysis (CCA), but 
unlike these, this technique does not maximize the correlations between the coordinates, 
but instead maximizes the covariance between them. 
Sustainability 2021, 13, 13073 8 of 20
The compromise matrix maximizes the mean of the correlations between its variables
and the variables of each Xt matrix. It can be said that the compromise provides an image
of the structures that are common to all the tables.
Lastly, the final step of the analysis is the intrastructure analysis, which consists in the
analysis of the reproducibility of the compromise. It enables representing the positions
on the compromise (or trajectories) of each individual and/or variable that comprises the
various tables, and their relative positions in relation to the position on the compromise.
The compromise positions of the elements are their mean positions. A trajectory is defined
as the change in the position of a variable (or individual) over time or in different conditions.
Consequently, a trajectory with low variation (wraps around) indicates that this variable
(or individual) is stable over time.
If the trajectory is eccentric, it means that this variable (or individual) is not stable
over time or across conditions. In the first type, colored in blue in Figure 3, the individuals
follow a medium evolution; i.e., the difference in the value for each individual at each point
in time and that of an average individual remains regular over time. On the other hand,
the eccentric trajectories, also known as large amplitude trajectories, reflect changes in the
structure of the individuals over time.
The use of X-STATIS in this study is justified for the effects of determining whether
there are similarities between age groups in terms of how Colombians make use of time.
This technique also enables observing any differences by sex and socioeconomic level in
the trajectories by age groups, in order to make a descriptive comparison between the
observations in the two years in which ENUT surveys were made in Colombia.
2.4. Step 2: Co-Inertia Analysis
Co-inertia analysis, proposed by Doléc and Chessel [52], enables finding common
structures between two set of variables; i.e., to simultaneously analyze two data matrices
that contain the same individuals (rows) and different or similar variables (columns), to
describe their co-structure by maximizing the covariance between the coordinates of the
Sustainability 2021, 13, x FOR PEER RroEVwIEsWof the two tables. This method belongs to the family of techniques that study mat9r iocfe s21 
 in pairs, such as canonical analysis and canonical correspondence analysis (CCA), but
unlike these, this technique does not maximize the correlations between the coordinates,
but instead maximizes the covariance between them.
TThhisism meeththooddi sisa ag geenneerraalilzizaatitoionno offt htheec caannoonnicicaallc coorrrreelalatitoionna annaalylyssisis( C(CAANNCCOORR))a anndd 
tthhee rreedduunnddaannccee aannaallyyssiiss ((RRDA)),, whhiicchh pprreesseenntt moorree rreessttrriiccttiioonnss ththaann ccoo-i-nineertritaia aannalaylysi-s 
s[i5s3[]5.3 I]n.  Ionrodredr etrot odedsecsrcirbieb eththe emmaainin oobbjejecctitvivee ooff ccoo--iinneerrttiiaa aannaallyyssiiss,, FFiigguurree 44 pprreesseennttssa a 
sscchheemmeet hthaatts suummmmaarrizizeesst htheem maaininf ofouunnddaatitoionnsso offt htheem meeththoodd. . 
 
FFigiguurree4 4. .C Coo--inineerrtitaiaa annaalylyssisiss scchheemmee. . 
For the matrices X and Y, which have the same number of individuals i and the same 
variables j*, as in this study, or different variables, j* and j**, respectively, the starting point 
is to analyze the behavior of each data table separately, by means of general principal 
component analysis. Based on this first analysis, we obtain the cross-sectional matrix of 
the weights of the individuals or observations in rows Di and the correspondent metrics 
Dj* and Dj**. 
Co-inertia analysis consists in the eigenvalue analysis of the matrix: 
XTDiYDj** YTDiXDj*, where XT and YT are the transpositions of the original matrices. 
If the columns of the matrix are centered, then the total inertia of each table would be the 
sum of its variances, i.e., in each case: 
InertiaX = trace (XDj*XTDi) and InertiaY = trace (YDj**YTDi), and the co-inertia of X 
and Y is: CoInertiaXY = trace(XDj*XTDiYDJ**YTDi), which maximizes the covariance be-
tween the row scores of the two matrices. In this regard, Thioulouse [31] indicates that the 
fact of maximizing covariance assures that the scores do not have small variances, and 
consequently the result assures a good percentage of explained variance in each space. 
The results of this multivariate technique are interpreted as follows: when the two 
studied structures (matrices X and Y) vary simultaneously, either directly or inversely, the 
XY co-inertia is high, and when the structures vary independently or do not vary, co-
inertia is low or none. The degree of co-structure is measured using the RV coefficient [54], 
which can take values between 0 and 1, where a higher value indicates greater similarity 
between the patterns of the two matrices, indicating that matrix Y provides similar infor-
mation to that provided by matrix X, and vice-versa, in terms of characterizing the studied 
individuals. 
The RV is called the vector correlation coefficient and is a multivariant extension of 
the Pearson correlation coefficient, with the key difference that it measures the existing 
correlation between data tables rather than between variables. For the effects of analysis, 
in addition to interpreting the RV coefficient, graphic representations of the results can be 
made, showing the individuals as dots and the variables of each matrix as vectors. The co-
structure between both set of variables can be inspected graphically representing both sets 
of individuals onto the same graph using an arrow to connect the same pair of individuals. 
The shorter these arrows, the greater the co-structure between the matrices. It is also 
Sustainability 2021, 13, 13073 9 of 20
For the matrices X and Y, which have the same number of individuals i and the same
variables j*, as in this study, or different variables, j* and j**, respectively, the starting point
is to analyze the behavior of each data table separately, by means of general principal
component analysis. Based on this first analysis, we obtain the cross-sectional matrix of
the weights of the individuals or observations in rows Di and the correspondent metrics
Dj* and Dj**.
Co-inertia analysis consists in the eigenvalue analysis of the matrix:
XTD T T TiYDj** Y DiXDj*, where X and Y are the transpositions of the original matrices.
If the columns of the matrix are centered, then the total inertia of each table would be the
sum of its variances, i.e., in each case:
InertiaX = trace (XD *XTj Di) and InertiaY = trace (YDj**YTDi), and the co-inertia of
X and Y is: CoInertiaXY = trace (XDj*XTDiYD TJ**Y Di), which maximizes the covariance
between the row scores of the two matrices. In this regard, Thioulouse [31] indicates that
the fact of maximizing covariance assures that the scores do not have small variances, and
consequently the result assures a good percentage of explained variance in each space.
The results of this multivariate technique are interpreted as follows: when the two
studied structures (matrices X and Y) vary simultaneously, either directly or inversely,
the XY co-inertia is high, and when the structures vary independently or do not vary,
co-inertia is low or none. The degree of co-structure is measured using the RV coeffi-
cient [54], which can take values between 0 and 1, where a higher value indicates greater
similarity between the patterns of the two matrices, indicating that matrix Y provides
similar information to that provided by matrix X, and vice-versa, in terms of characterizing
the studied individuals.
The RV is called the vector correlation coefficient and is a multivariant extension of
the Pearson correlation coefficient, with the key difference that it measures the existing
correlation between data tables rather than between variables. For the effects of analysis,
in addition to interpreting the RV coefficient, graphic representations of the results can
be made, showing the individuals as dots and the variables of each matrix as vectors.
The co-structure between both set of variables can be inspected graphically representing
both sets of individuals onto the same graph using an arrow to connect the same pair of
individuals. The shorter these arrows, the greater the co-structure between the matrices. It
is also possible to plot the inertia axes over the co-inertia axes to inspect in which extent
each co-inertia axis will approach a direction of maximum inertia.
3. Results
First, we present the results obtained from application of X-STATIS in each year in
order to find underlying data patterns for the characteristics of gender, age group, and
socioeconomic status of Colombians in each year of the ENUT survey. Afterwards, we
present the results obtained from the comparative analysis of the two years of the study by
means of co-inertia analysis of the compromises of the series of tables from each year. The
graphic representations and tables presented below were obtained using the R statistical
package and the ade4 function.
3.1. Results Using X-STATIS
3.1.1. Interstructure Analysis
The first step of the X-STATIS is the interstructure analysis to compare the overall
structures of the matrices that summarize the age groups, in order to observe which age
groups are similar to each other. The information provided by the vector correlation
matrices (RV) shown in Table 3 and the representations in Figure 5 indicate that in both
years the greatest vector correlations are perceived in the older adult groups, whereas the
lowest correlations are found between the latter and minors. Moreover, in ENUT 2017, all
vector correlations were lower than those found in 2013.
Sustainability 2021, 13, x FOR PEER REVIEW 10 of 21 
 
possible to plot the inertia axes over the co-inertia axes to inspect in which extent each co-
inertia axis will approach a direction of maximum inertia. 
3. Results 
First, we present the results obtained from application of X-STATIS in each year in 
order to find underlying data patterns for the characteristics of gender, age group, and 
socioeconomic status of Colombians in each year of the ENUT survey. Afterwards, we 
present the results obtained from the comparative analysis of the two years of the study 
by means of co-inertia analysis of the compromises of the series of tables from each year. 
The graphic representations and tables presented below were obtained using the R statis-
tical package and the ade4 function. 
3.1. Results Using X-STATIS 
3.1.1. Interstructure Analysis 
The first step of the X-STATIS is the interstructure analysis to compare the overall 
structures of the matrices that summarize the age groups, in order to observe which age 
groups are similar to each other. The information provided by the vector correlation ma-
trices (RV) shown in Table 3 and the representations in Figure 5 indicate that in both years 
the greatest vector correlations are perceived in the older adult groups, whereas the low-
est correlations are found between the latter and minors. Moreover, in ENUT 2017, all 
vector correlations were lower than those found in 2013. 
Table 3. Vector correlation matrices. 
ENUT 2013 ENUT 2017 
  10–17 18–34 35–59 60 or older   10–17 18–34 35–59 60 or older 
10–17 1.00 0.48 0.45 0.22 10–17 1.00 0.24 0.35 0.18 
Sust1ai8n–ab3i4lit y 2021, 103,.41830 73 1.00 0.57 0.43 18–34 0.24 1.00 0.28 0.3103 of 20
35–59 0.45 0.57 1.00 0.67 35–59 0.35 0.28 1.00 0.48 
60 or older 0.22 0.43 0.67 1.00 60 or older 0.18 0.33 0.48 1.00 
Figure 5 Tsahbolwe 3s. tVheactt oirnc obrortehla tyioenarms atthreic eins.terstructure is almost similar showing that 
ENUTth2e0 1l3argest angle is formed between the vector thatE rNeUprTe2se01n7ts pre-teens and over-60 
group. Therefore, these are the less similar groups. From this pattern it can be interpreted 
10–17 18–t3h4at the3re5– i5s9 a muc6h0  ocrleoaldreerr common pattern be1t0w–1e7en adu18lt–s3 4and ol3d5e–r5 9adults6 0ino trhoeld merost 
10–17 1.00 0.4r8ecent EN0.4U5T survey 0th.2a2n in the firs1t0,– i1n7 terms of1 h.0o0w Colo0m.2b4ians use0 .t3h5eir time a0c.c1o8rding 
18–34 0.48 1.0t0o their s0o.5c7ioeconom0ic.4 s3tatus (SES)1. 8I–n3 24013, the 0o.2rd4er of th1e.0 v0ectors i0s. 2m8 ore evide0n.3t3, start-
35–59 0.45 0.57 1.00 0.67 35–59 0.35 0.28 1.00
60 or older 0.22 0.4i3ng with0 .t6h7e younge1s.t0 0group (a6t 0thore otlodper of the0 .g1r8aph), to0 .3th3e over-06.458 age grou
0
1p
.4
.0 
8
0(at the 
bottom). 
 
(a) ENUT 2013 (b) ENUT 2017 
FFiiggurree 55.. IIntteerrssttrrucctturree ggrraaphiiccss.. 
Figure 5 shows that in both years the interstructure is almost similar showing that the
largest angle is formed between the vector that represents pre-teens and over-60 group.
Therefore, these are the less similar groups. From this pattern it can be interpreted that
there is a much clearer common pattern between adults and older adults in the most recent
ENUT survey than in the first, in terms of how Colombians use their time according to
their socioeconomic status (SES). In 2013, the order of the vectors is more evident, starting
with the youngest group (at the top of the graph), to the over-65 age group (at the bottom).
Before interpreting the graphic results of the compromise table, it should be noted
that based on the eigenvalues obtained, which are shown in Table 4, in the 2013 ENUT, the
first two axes account for 45.6% of the variability of the information, whereas in the second
survey this percentage decreases to 35.9%.
Table 4. Compromise eigenvalues (accumulated inertia).
Dim1 Dim2 Dim3 Dim4 Dim5
ENUT 2013 25.19 20.42 4.84 4.22 1.32
ENUT 2017 24.27 11.67 5.72 2.21 0.83
3.1.2. Compromise Analysis
Figure 6 displays the covariance structure of the time variables for the first 2 dimen-
sions of the axes of the principal components of the compromise, and also presents the
positions of the gender–SES (socioeconomic status) combinations in that compromise. By
observing the first two axes of the compromise, we can interpret three characteristics
that the two years have in common: the behavior of the gender–SES combinations, the
associations between the variables and the interpretation that can be given in combination
to the positions of gender by socioeconomic status in the compromise space.
Sustainability 2021, 13, x FOR PEER REVIEW 11 of 21 
 
Before interpreting the graphic results of the compromise table, it should be noted 
that based on the eigenvalues obtained, which are shown in Table 4, in the 2013 ENUT, 
the first two axes account for 45.6% of the variability of the information, whereas in the 
second survey this percentage decreases to 35.9%. 
Table 4. Compromise eigenvalues (accumulated inertia). 
  Dim1 Dim2 Dim3 Dim4 Dim5 
ENUT 2013 25.19 20.42 4.84 4.22 1.32 
ENUT 2017 24.27 11.67 5.72 2.21 0.83 
3.1.2. Compromise Analysis 
Figure 6 displays the covariance structure of the time variables for the first 2 dimen-
sions of the axes of the principal components of the compromise, and also presents the 
positions of the gender–SES (socioeconomic status) combinations in that compromise. By 
observing the first two axes of the compromise, we can interpret three characteristics that 
Sustainability 2021, 13, 13073 the two years have in common: the behavior of the gender–SES combinations, the a1s1soofc2i0-
ations between the variables and the interpretation that can be given in combination to 
the positions of gender by socioeconomic status in the compromise space. 
 
(a) ENUT 2013 (b) ENUT 2017 
FFiiggurree 66.. Grraaphhss ooff tthhee ccoomprroomiissee vvaarriiaabblleess aannd tthhee sseexx––SSESS ((ssoocciiooeeccoonnoomiicc ssttaattuuss)) ccoombbiinnaattiioonnss.. 
The fifirrsstti nintetererestsitninggp aptatettrenrnw we cea ncaonb soebrsveervine Finig uFrigeu6ries 6th ies sthaer pshdairffpe rdeinfcferbeentcwe ebeen-
gtwenedener gaennddseor caionedc osoncoimoeicosntaotmusic.  Isntabtoutsh. Iyne abrost,hth yeefiars,t athxeis foirfsth aexciso mofp trhoem ciosemmpraokmesisiet  
pmoasksiebsl eit tpoodsisfifbelre ntoti adtieffbeyregnetinadte rb(yw goemndenero (nwtohme leenf toonf the glerfat pohf tahned gmraepnho anntdh emreignh ot)n, 
wthhei lreigthte),s wechoinled tahxei serceoflnedct saxthise roerfdleecrtisn tghbe yorsdoeciroinegco bnyo msoicciol evceoln. omic level. 
The sharrp diifffferrences by genderr diispllayed by botth comprromiises arre basiicalllly ex--
pllaaiineed by tthee vaarriiaablleess WOR,, IINT,, aand SSPO ((ttiimee ddeevotteed tto woorrk,, tthee IInntteerrneett,, aand 
sspoorrttss)).. IItt ccaann bbee sseeeenn hhoow tthhee vveeccttoorrss tthhaatt rreeprreesseenntt tthheessee vvaarriiaabblleess cchhaarraacctteerriizzee tthhee rriigghhtt 
eenndd ooff aaxxiiss 11,, aanndd ccoonnsseeqquueennttllyy iitt iiss tthhee meenn ((eessppeecciiaallllyy iinn 22001133,, aanndd wiitthh ggrreeaatteerr iinntteennssiittyy 
iinn tthhee lloow SSEESS)) whhoo ssppeenndd moorree ttiimee iinn tthheessee aaccttiivviittiieess ccoomppaarreedd ttoo woomeenn ((llooccaatteedd oonn 
tthhee lleefftt ssiizzee ooff tthhee aaxxiiss)).. 
AAnn aannaallooggoouuss iinntteerrpprreettaattiioonn,, bbuutt iinn tthhee ooppppoossiittee ddiirreeccttiioonn,, iiss tthhaatt wwoommeenn ((eessppeecciiaallllyy 
iinn lloowwa annddm medediuimums oscoiocieoceocnoonmoimc ilce vleelvse)lds)e vdoetveomteu mchumcho rme toirme etitmhaen tmhaenn tmoeDnH tAo ,DBHAAC,, 
HBAACI,,a HndAIF,H anCd( dFHomCe (sdtiocmanesdtihco aunsde hhooludsaechtoivldit iaecst,ibvaitsiiecsa, bctaivsiicti aecst,ihvaitiiredsr,e hsasiinrdgr, easnsdinfga,m ainlyd 
and home care), because the vectors that display such activities are on the negative portion
of axis 1, which displays the points that represent women.
Regarding the differences in time use by socioeconomic status, the graph shows that
higher socioeconomic levels spend more time in leisure activities than lower levels. See
how in 2013, resting or listening to music (vectors RES and LMU located in the direction of
the second axis) characterize men and women from higher levels, whereas in 2017, they
display more time in the direction of activities such as reading, speaking on the phone and
visiting friends (vectors REA, PHO, and FRI).
According to the above, regarding the structure of variance and covariance of the
variables in the compromise space, we can summarize by saying that in both years, we
can see four sets of variables that are differentiated from each other. The first involves
household activities, home care, going to the hairdresser, and, to a lesser extent, basic
activities, and which characterize the women who are located towards the left of the
representations of Figure 6 (the vectors DHA, FHC, HAI, and BAC). On the opposite side of
this group of variables are paid work, practicing sports, and agricultural activities, which
are associated with men (the vectors WOR, SPO, and AGR).
On the second axis, which sets the differences in terms of socioeconomic status, two
other groups of variables stand out, which are: reading, speaking on the phone, and visiting
friends, and to a lesser extent commuting time and studying (vectors REA, PHO, FRI, RES,
and STU), all of which are on the opposite side of watching television or attending sports
Sustainability 2021, 13, 13073 12 of 20
events (vectors VTV and EVE). This latter group of variables displays differences between
the years: in 2013, the vectors that represent just resting and listening to music (RES and
LMU) are also directly correlated with the variables VTV and SPE (small angle between
the vectors).
3.1.3. Intrastructure Analysis
Intrastructure analysis enables projecting all the variables from each studied matrix
over the compromise, i.e., to analyze each age group matrix to assess the degree of similarity
or difference between the covariance structures of the various age groups, between the
groups and compared to the compromise of time use activities. This is represented in
Figure 7, which specifically presents the results of the latest ENUT. The graphics from 2013
Sustainability 2021, 13, x FOR PEER RaErVeI n
EWot included because, in terms of interpretation, the conclusions that can be obt1a3i noef d21 
from that year are, in general, similar to those described below.
 
FFiigguurree7 7. .C Coompprroommisiseep prroojejecctitoionnsso offg geennddeerr––SSEESSa anndda aggeeg grorouuppi nint htheey yeeaarr2 2001177. . 
IInn Fthigeu craes7e, oifn atghee grreopurepsse onft athtieo necsoonnomthiecalellfyt asicdtiev,ef opropalullaagtieong,r oa ucplesa,rt hdeiffdeirsetnacnec eis 
boebtwseervenedm ienn taenrmdsw oofm thene iascltaivrgiteie, sa ncdartrhieedy oaruet obryd emreedn bfyrosmoc hioiegcho nsoocmioieccsotantoums;ici. el.e,vtehles. 
dYifofuernegn acedsuilnt mtimene supseenbde mtwoereen tiCmoel obmeibniga nwmithe nfraiennddws, ogmoienng atore bfaorus,n sdtuthdryoiungg,h aonudt  elivseterny-
aigneg gorfo umpu.sSipc e(cFiRfiIc,a BllAy Rfo,r SmTeUn,, athned dLisMtaUn)c,e ws bheetrweaese nmloenw iann tdhme e3d5 ituom 59so acgioee gcoronuomp iscpleenvd-  
emlsoarree tailmwea ywsosrmkianllge,r rceoamdipnagr,e dspteoatkhiengh iognh etrhseo pcihooencoen, oanmdic wleivthe lf.rTiehnedgsr e(vaatersiat bdlieffse Wrencebetween age groups is in the structure of variance and covariance of the vectors, becauOsRe , 
dRifEfeAr,e nPtHvOar,i aabnldes FfRorIm). Rsuebggarroduinpgs owfogmreeante irna saslol caigaeti ognrodueppse,n idt ocannt hbees opbecsiefircveadg ethgarot uthpe.  
vectoArcsc tohradti nregptroesFeignut trhee7 v, aamriaobnlgesp oref theoeunsseahnodldte aennds ,htohme seu cbagrreo aucptivoiftvieasr (iaFbHleCs arnelda tDedHtAo) 
satured ayliwnga,ylsi sltoecnaitnegd toonm tuhesi cle,frte oafd tinhge ,garnadphc.o Tmhmisu mtineagntsim theast( iSnT CUo, lLoMmUbi,aR, EinAd,eapnedndMenJOtl)y 
ifsrdomiff ethreenirt iaagteed, wfroommetnh reeoptohret rthvaatr itahbelye sdaevnodteth ae ygraeraet aasmsoocuinatte odf ttoimaeg troe autnepraeixdt eancttiwviittihes 
wreolmateend aton dhomuesnehforoldm chhoigrhese ransodc icoaercinogn ofomr itchlee vfaemlsi.lIyn. contrast, in the older adult group,
the variables with the closest associations with each other (with less correlation compared
t3o.2o.t Rheesruvltesc otof trhse) Caroe-Ilnoeortkiian Agnfaolrysaisj ob or creating an own business, activities related to
Below we present the results of the simultaneous comparative analysis of the com-
promises from the X-STATIS analyses of the two ENUT Colombia surveys, to inspect ob-
jectively the obtained patterns. Co-inertia analysis was performed to describe patterns 
that are not visible at first sight by means of indirect comparisons made in explaining the 
partial triadic analyses between years (the results displayed previously in Tables 3 and 4 
and Figures 6 and 7). 
Figure 8 presents a table that summarizes the explained variability of each co-inertia 
axis and their eigenvalues, along with the correlations between them and the axes of the 
principal component analysis of the individual compromises for each ENUT survey. In 
this figure, we can see that the first two co-inertia axes summarize 81.2% of the variability 
of information, and for this reason, in the eigenvalue graph, only two axes are highlighted 
as necessary to explain the data’s behavior. This is also confirmed by observing that the 
high correlations (greater than 0.91 in absolute value) between the PCAs of each 
Sustainability 2021, 13, 13073 13 of 20
agriculture, listening to music, and resting (vectors LJO, AGR, LMU, and RES). Such
activities are more characteristic among older men from medium and low socioeconomic
levels, who are therefore the ones who devote most time to these activities in this age group.
In the case of age groups of the economically active population, a clear difference
is observed in terms of the activities carried out by men from high socioeconomic levels.
Young adult men spend more time being with friends, going to bars, studying, and listening
of music (FRI, BAR, STU, and LMU), whereas men in the 35 to 59 age group spend more
time working, reading, speaking on the phone, and with friends (variables WOR, REA,
PHO, and FRI). Regarding women in all age groups, it can be observed that the vectors that
represent the variables of household and home care activities (FHC and DHA) are always
located on the left of the graph. This means that in Colombia, independently from their
age, women report that they devote a great amount of time to unpaid activities related to
household chores and caring for the family.
3.2. Results of the Co-Inertia Analysis
Below we present the results of the simultaneous comparative analysis of the com-
promises from the X-STATIS analyses of the two ENUT Colombia surveys, to inspect
objectively the obtained patterns. Co-inertia analysis was performed to describe patterns
that are not visible at first sight by means of indirect comparisons made in explaining the
partial triadic analyses between years (the results displayed previously in Tables 3 and 4
and Figures 6 and 7).
Figure 8 presents a table that summarizes the explained variability of each co-inertia
axis and their eigenvalues, along with the correlations between them and the axes of the
principal component analysis of the individual compromises for each ENUT survey. In this
figure, we can see that the first two co-inertia axes summarize 81.2% of the variability of
Sustainability 2021, 13, x FOR PEER R
 in
EVfoIErmW ation, and for this reason, in the eigenvalue graph, only two axes are highligh1t4e dofa 2s1 
necessary to explain the data’s behavior. This is also confirmed by observing that the high
correlations (greater than 0.91 in absolute value) between the PCAs of each compromise
tcaobmleparnodmtihsee tcaob-lien aenrtdia thaex ecso-ainriesretiian atxhees fiarrisstet iwn othdei mfiresnt stwioon sdi(mtheensesioanres h(tihgehsleig ahrete hdigahs-
ilmigphotretda nats iinmbproorwtann)t. in brown). 
 
FFiigguurree8 8. .C Coo--iinneerrttiiaaa axxeessa annddc coorrrreelalatitoionnssw witihtha axxeesso offt htheep prrininccipipaallc coommppoonneenntta annaalylyssisis. . 
TThheeR RVVc cooeeffiffcicieienntto obbtatainineeddf rfroommt htheec coo-i-nineerrtitaiaa annaalylyssisisw waass0 0.7.7333344, ,w whhicichhi ninddicicaatetess 
tthhat the two switaht hthigeh twcoo- s
ttrruuccttuurreesso offt htheec coommprinertia. This, in terms opfr
oommisiseessof ENUT 2interpre otaft iEoNn,UimT 2
00113 and 20plie3s  tahnadt  t2h0
1177vary se ti mvaersyr s
imult
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os
ly
thly 
swuritvhe yhsigahre ccoo-ninseisrtteian.t Twhiitsh, einac theromthse ro;fh ionwteervperer,tasotimone, bimehpalvieiosr tshiant stpheec itfiimc evsa rrieapbolersteadn din 
gbrootuhp ssuorfvseoycsi oardee cmoongsrisatpehnitc wchitahr eaactcehr iostthicesr;a hreowweovrtehr,m soemnteio bneihnagvbioarsse dino snpethciefiicn vtearrpiarebtlae-s 
taionnd ogfrFouigpusr oef9 s,owcihoidchemporegsreanpthsitch cehparroacjetectriiostnicosf atrhee wfiorsrttht wmoencoti-oinneinrtgi abaasxeeds, obno tthheo ifnttheer-
pretation of Figure 9, which presents the projection of the first two co-inertia axes, both of 
the new sets of standardized coordinates of the sex, socioeconomic status, and age groups, 
and of the canonical weights of the variables of each compromise table. 
The co-structure graph on the top of Figure 9 projects the new standardized coordi-
nates of the sociodemographic characteristics on the Co-inertia axes of the two datasets. 
Each pair of points are linked by an arrow. The origin of each arrow indicates the position 
according to the ordering of the first compromise matrix (from the ENUT 2013 survey), 
and the arrow indicates the position according to the ordering of the second matrix (of 
ENUT 2017). 
It can be observed that most combinations of gender, SES, and age display short ar-
rows, which means that the times reported in both ENUT surveys were similar and con-
sistent. The exceptions are for the older adult groups, independently from gender, in the 
medium socioeconomic level (MM60+ and WM60+), and for teens of medium and high 
status (MH10-17, WH10-17, MM10-17, and WM10-17), whose vectors are longer. 
Regarding this finding, specifically for older adults of medium SES, it can be said that 
the direction of the vectors indicates a shift in the reported times from watching videos 
and television and simply resting (vectors VTV and RES in ENUT 2013), toward studying 
(direction of the STU vector in ENUT 2017). This behavior is because in the first ENUT 
survey this group did not report time related to studying, but in the second survey, both 
men and women over the age of 60 reported that they spent on average over two hours 
studying, and they reported a slight decrease in the time they use to watch TV or simply 
rest. 
Sustainability 2021, 13, 13073 14 of 20
Sustainability 2021, 13, x FOR PEER REnVeIE w
Ws ets of standardized coordinates of the sex, socioeconomic status, and age grou1p5 so, fa n21d 
of the canonical weights of the variables of each compromise table.
 
FFigiguurree 99. .CCoo-s-tsrturucctuturere ggrraapphhss oof fththee ccoo-i-nineerrtitaia bbeetwtweeeenn EENNUUTT 22001177 aanndd 22001133. .
The co-structure graph on the top of Figure 9 projects the new standardized coordi-
nateOs no fththee ostohceiro hdaenmdo, gthrea pghraicpchhsa irna Fctiegruirseti c9s sohnowth tehCe ow-ienigehrttisa oafx tehseo vfatrhiaebtlweso fdroamta sthetes .
cEoa-icnherptaiair aonfaplyosinist.s Hareereli nwkee dcabny saene adrirfofewr.enTchees oinri gthine osfizeea cohf athrreo vwecintodrisc aatneds  tchheapnogseist iionn 
thaceciro rddirinecgtitoont,h tehaotr idse, rcihnagnogfesth ien fithrest sctroumctpurroem oifs ecom-vaatrriiaxti(ofrno imn ethaechE yNeUarT. F2o0r1 3exsaumrvpelye,) ,
thane dvethcteoarsr rtohwat irnedpirceasteenstt hreelipgoiosuitsio anctaivccitoierds ianngdt oretahdeinogrd (eRrEinLg aonfdt hReEsAe)c,o wndhimcha atrriex l(oo-f
cEatNedU Tin2 q0u17a)d.rant I of the representations in both years, are longer in ENUT 2013, which 
reflectIst ac agnrebaeteor bvsaerrivaebdilittyh aint  mthoes itncfoormmbaitnioatni oonf sthoaft gyeenadr ecro,mSpEaSr,eadn tdo a2g0e17d. isplay short
arroIwn sc,ownthriacsht, mtheea vnesctthoar tththate ctaimn ebse rseepenor ttoe dchiannbgoet dhirEeNctUioTn sbuertwveeyesn w20e1re3 asinmdi l2a0r17a nisd 
CcUonAs,i swtehnict.hT rheepreexsceenpttsi othnes caureltuforralt heeveonldtse rora dacutlitvgitrioeus.p Tsh, iisn dcheapnegned einn tClyUfAro pmosgietinodne irm, i-n
ptlhieesm thedati uimt csoovcairoieactoesn opmosicitlievveelyl  (oMr Mne6g0a+tiavnedlyW wMit6h0 +d)i,ffaenrdenfto rvatereianbsloefs mine dthiue mtwaon dyehaigrsh 
csotmatpuasr(eMd,H a1n0d-1 c7h, WaraHc1te0r-i1z7e,sM dMiff1e0r-e1n7t, aagned gWroMu1p0s-.1 I7n) ,twheh ofisrestv EecNtoUrsT aCreolloomngbeira. survey, 
attendRinegga crudlitnugratlh eivsefinntsd iwnags, ospbesecirfivceadl lays fao freoaltduerer oafd yuoltusnogf amdeudltisu, mwhSeErSe,aist icna tnheb elasteasidt 
EtNhaUtTth, iet idsi rinecctluiodnedo finth theev gercotourps oinf dviacraiatebsleas tshhaiftt cihnartahceterreipzeo rotleddert iamdeusltfsr. om watching
videAos qaunaddrtaelnetv cihsiaonngaen wdassi malpsoly orbessetrinvged( vinec LtoJOrs (VloToVkianngd foRrE aS jionbE aNndU Tes2ta0b1l3i)s,htionwg aarnd 
oswtund byuinsgin(edsisr)e, cwtiohnicohf itnh e20S1T7U isv leocctaotreidn iEnN thUeT th2i0r1d7 )q.uTahdirsabneth. aItv dioirreicstblye ccaouvsaeriianteths ewfiitrhst 
FEHNCU, TMsJuOr,v WeyOthRi,s agnrdou PpHdOid (nfaomt rielyp oarntdt imhoemreel actaerde taoctsitvuidtiyeisn, gti,mbue tsipnetnhte inse mcoonvdesmuernvetsy ,
abnodt hjomurenneyasn,d wwoorkm teinmoe,v earndth sepaegaekionfg6 0onr etphoer tpehdotnhea).t Ntheevyesrptheenltesosn, ianv e2r0a1g3e, LoJvOer wtwaso 
lohcoautersd sitnu dthyei nsgec, oand qthueaydrraenpto drtierdecatlysl irgehlattedde ctroe aRsEeLi,n MthUeSt,i manedt hReEyAu (steimtoe wtoa atctthenTdV oorr 
osrigmapnliyzer ersetl.igious activities, time spending in practice a musical instrument, paint, etc., 
and tiOmne thoe reoathde).r hand, the graphs in Figure 9 show the weights of the variables from the
co-inertia analysis. Here we can see differences in the size of the vectors and changes in
4t.h Deiirscduirsesciotino n, that is, changes in the structure of co-variation in each year. For example,
the vBeecltoowrs wthea tdriescpuressse tnhter iemligpiloicuastiaocntisv oitfi etshea nrdesruelatsd ionbgta(RinEeLd ainn dthRisE sAtu),dwyh fircohma raenl oincateter-d
pretive standpoint, with the aim of contrasting the main findings with observations from 
studies by other authors, and to emphasize their potential for the formulation of public 
and socioeconomic policies. 
Sustainability 2021, 13, 13073 15 of 20
in quadrant I of the representations in both years, are longer in ENUT 2013, which reflects
a greater variability in the information of that year compared to 2017.
In contrast, the vector that can be seen to change direction between 2013 and 2017
is CUA, which represents the cultural events or activities. This change in CUA position
implies that it covariates positively or negatively with different variables in the two years
compared, and characterizes different age groups. In the first ENUT Colombia survey,
attending cultural events was observed as a feature of young adults, whereas in the latest
ENUT, it is included in the group of variables that characterize older adults.
A quadrant change was also observed in LJO (looking for a job and establishing an
own business), which in 2017 is located in the third quadrant. It directly covariates with
FHC, MJO, WOR, and PHO (family and home care activities, time spent in movements and
journeys, work time, and speaking on the phone). Nevertheless, in 2013, LJO was located
in the second quadrant directly related to REL, MUS, and REA (time to attend or organize
religious activities, time spending in practice a musical instrument, paint, etc., and time
to read).
4. Discussion
Below we discuss the implications of the results obtained in this study from an
interpretive standpoint, with the aim of contrasting the main findings with observations
from studies by other authors, and to emphasize their potential for the formulation of
public and socioeconomic policies.
4.1. Findings with the X-STATIS Analysis
Regarding the compromise results obtained from the X-STATIS analysis, we can say
that in Colombia there is gender inequality in terms of time use, with greater dedication by
women to unpaid activities related to household maintenance and care, especially in low
socioeconomic levels, which limits the time they devote to income generation activities.
This is concluded based on Figures 6 and 7, through the joint interpretation of the positions
of the dots of females of low SES (represented as WL, to the left of the graphs for both
years) and the positions of the household and family care activities (DHA and FHC), which
are located in the same direction.
Internationally, we can cite at least five authors whose findings are in line with these
results regarding the time use gender gap that stereotypes women in care and unpaid
work activities [55–60]. Other studies in Latin America arrive at the same conclusion, such
as those by Jara-Díaz and Candia [61], which studies the socioeconomic information of
different population segments in the latest Chilean time use survey and conclude that there
are substantial gender differences in terms of workload, where women take on most of the
unpaid work and enjoy less leisure time, whereas men devote more time to paid work.
Consequently, in the region, it is necessary to continue implementing public policies
that promote the positioning of women in different social spheres and in the labor market,
promoting their efforts to obtain decent and egalitarian remunerated work opportunities.
This is necessary in order to promote women’s economic empowerment and for highlight-
ing the idea that the inequalities in time use between men and women reflects deep social
inequality [62] (p. 50).
From the interpretation of the compromise structures of the X-STATIS analysis pre-
sented, conclusions can also be reached in terms of the dependence of free time on the
economic capacity of the population, because unequal time use conditions were found
between people from low socioeconomic levels compared to high levels, and economic
wellbeing depends not only on the consumption of goods and services, but also on the con-
sumption of free time [63] (p. 29). In this study’s results, both the positions that represent
the gender–SES combinations, and the associations found between the variables indicate a
greater predisposition of the population with higher income to engage in more leisure and
free time activities.
Sustainability 2021, 13, 13073 16 of 20
This result is also consistent with what was observed a decade ago by Aguiar [10] (p. 106)
in studying time use in Brazil, where time use is stratified as a function of paid work, care
of the home and family, leisure, and commuting, which characterize highly differentiated
lifestyles in a hybrid or unequally developed society. Consequently, this result, although
it implies inequality in terms of socioeconomic status, could also be interpreted as an
opportunity in terms of possible communications-focused public policies, given that free
time should not only be defined in terms of the consumption of cultural goods or activities
that must be paid for (such as going to a movie theater, attending sport events, or investing
in private parties).
There are numerous free time activities that can be done at no cost and that also
offer rest; consequently, communications campaigns targeted at the population of low
socioeconomic status promoting activities of this type could help low-income Colombians
make better use of their free time without affecting their income. The existing relationship
between time use and socioeconomic status of the population has also been recently studied
by Vagni [64], who holds that time use is both a cause of social inequality and a consequence
of social inequality. However, how social class stratifies time use patterns is seldom studied.
Another important finding that was obtained through the X-STATIS analysis is regard-
ing behaviors of the age groups. It can be said that time use studies should not only focus
on establishing differences by gender, but also by stage of life, because as indicated in the
interstructure and intrastructure analyses, the time use activities mostly depend on the age
group. Cowan was one of the first theorists to point this out, noting that life transitions
such as finding a first job, marriage, and retirement are moments that necessarily involve a
reorganization in the way people use their time [65] (p. 18).
4.2. Findings with the Co-Inertia Analysis
It can be concluded that the time use reported in the two ENUT studies in Colombia is
highly consistent; however, application of this methodology enabled perceiving differences
in the reported times that were not evident through indirect and descriptive comparisons
between the two X-STATIS evaluations. One of the most relevant of these findings is related
to the free time activities of older adults, and specifically regarding the time devoted to
resting, watching television, studying, reading, and attending religious or cultural events.
This finding is important in terms of the demographic transition that Colombia is
currently experiencing, because as the country’s population tends to become older, per-
ceiving by means of modeling techniques the changes in behavior related to the times
reported by older adults in the country, implies considering the importance of designing
and implementing policies for the wellbeing of this population. This is given that their
needs, social interaction experiences, and individual free time activities may be dynamic
with the passing of time.
The activities that may be worthwhile for adult life may be focused on maintaining
harmonious family relationships, fulfilling personal hobbies or rooting for a favorite
football team, being in touch with nature, religious faith or spiritual activities, making
money, intellectual achievements, feeling satisfaction at work, or engaging in stimulating
travel or other experiences [19].
In general, regarding time use by Colombians by age group, we can say that the
findings of this study are consistent with other conclusions in the Latin American context.
Benvin, Rivera, and Tromben [66] point out that the life cycle of individuals is another
important element for the analysis of time use. For example, men and women in the 25 to
45 age group work more time and it is in this age group that the greatest gaps are found
between men and women.
4.3. General Conclusions
From all of the above, the main conclusion of this study is consistent with the idea that
time use is highly stereotyped according to expectations on gender, age, and status [12,67].
These three demographic characteristics display a substantial number of associations that
Sustainability 2021, 13, 13073 17 of 20
explain time use. Specifically, based on the graphics, tables, and results presented in this
paper, we can conclude that the ordering of these factors to condition the way people use
their time is consistent with what these authors propose.
Time use studies, and especially those based on a multidimensional perspective,
should be considered a useful tool to design public policy actions and strategies that not
only help mitigate the inequality between men and women, but that also facilitate planning
of the population’s needs depending on their life cycle stage and purchasing power.
It is in this specific aspect that we can summarize the practical implications of this
study’s results, because the design of social public policy strategies and actions aimed at
mitigating the gender issues reflected in time use patterns should also consider possible
differences by age group and socioeconomic level. Furthermore, in the specific context of
Colombia, strategies of this type should focus on mitigating other conditions not reviewed
in this study, such as belonging to ethnic groups and to vulnerable populations that are
victims of the armed conflict.
From a methodological standpoint, it is fair to say that in the field of social sciences
and politics, time use variables are often analyzed separately and in a descriptive manner;
however, examining them by means of multivariate techniques such as CO-STATIS, X-
STATIS, and/or co-inertia enables finding several relationships that are not evident at
first sight. In this sense, it should be noted that this study, unlike other time use studies
carried out in Colombia [62–68], contributes to the assessment of existing interrelationships
between the numerous factors that determine time use by the population.
Consequently, it is recommended to use multivariate techniques in future time use
studies and in general in the context of sociodemographic studies because these techniques
can make significant contributions for the design of population intervention actions that
help improve the life quality of people (in different dimensions) and promote gender
equality. This recommendation is particularly applicable to time use research in Latin
American countries, where at the regional level there is a need to periodically move
forward in measuring time use to recognize women’s contribution to the economy in both
the productive and reproductive dimensions [69].
Lastly, it is relevant to point out that the main limitation of this study is that even
though it compares the data of the two latest time use surveys in Colombia for the years of
the study (2013 vs. 2017), the findings obtained do not reflect the current situation of time
use in the country and these studies do not yet reflect changes in patterns that may have
been produced in the routines of Colombians due to the COVID-19 pandemic. We will
have to wait for new surveys that cover the pandemic and post-pandemic periods, which
implies that more academic research is now needed to assess the organization of time use
and the mental health effects on family and social life during the health emergency [70,71].
Studies of this type are necessary specifically because women report that they work more in
lock-down than in ordinary conditions with no health emergency. The boundaries between
work and leisure become lost when there are no defined start and end times.
Author Contributions: Conceptualization, M.J.F.-G., E.J.M.-H. and I.B.-M.; methodology, M.J.F.-
G. and E.J.M.-H.; software, E.J.M.-H.; validation, I.B.-M.; formal analysis, M.J.F.-G.; investigation,
E.J.M.-H.; resources, E.J.M.-H.; data curation, E.J.M.-H.; writing—original draft preparation, E.J.M.-H.
and M.J.F.-G.; writing—review and editing, E.J.M.-H., I.B.-M. and M.J.F.-G.; visualization, E.J.M.-H.;
supervision, I.B.-M. and, M.J.F.-G. All authors have read and agreed to the published version of
the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
Sustainability 2021, 13, 13073 18 of 20
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