=Paper= {{Paper |id=Vol-2927/paper11 |storemode=property |title=Classification Models in the Monitoring Systems of the Population Life Quality |pdfUrl=https://ceur-ws.org/Vol-2927/paper11.pdf |volume=Vol-2927 |authors=Svitlana Prokopovych,Liubov Chagovets,Vitalii Gvozdytskyi,Tamara Klebanova,Tatyana Zavodenko }} ==Classification Models in the Monitoring Systems of the Population Life Quality== https://ceur-ws.org/Vol-2927/paper11.pdf

137

Classification models in the monitoring systems
of the population life quality

Svitlana Prokopovych1[0000-0002-6333-2139], Liubov Chagovets2[0000-0003-4064-9712]
Vitalii Gvozdytskyi3[0000-0003-4686-267X], Tamara Klebanova4[0000-0002-0284-9839]
and Tatyana Zavodenko5
1,2,3,4Simon Kuznets Kharkiv University of Economics, 9a Nauki av., Kharkiv, 61144, Ukraine
5Parimatch Tech, 28 Geroiv Pratsi st., Kharkiv, 61000, Ukraine

prokopovichsv@gmail.com
chahovets.liubov@hneu.net
gvozdikramm@gmail.com
t_kleb@ukr.net
tanyazavodenko188@gmail.com

Abstract. The paper is devoted to the assessment of living standards of popula-
tion. Countries with emerging markets are characterized by significant transfor-
mations of the public sector in the context of European integration processes,
which requires the adaptation of models for assessing the living standards of the
population, allowing to analyze the effectiveness of public administration and
ongoing reforms. The complex of models for assessing the living standards of the
population as an assessment of the effectiveness of public administration is also
interesting for countries with developed markets. The advantages and disad-
vantages of existing methods of predictive analytics for the study of standards of
living are shown. It should be noted that the universal method of analysis and
assessment of living standards contains the set of intangible components. There-
fore, it is advisable to make a proposal on the need to improve a complex of
models for assessing and analyzing living standards. The data set is built using
of such key indicators that objectively reflect the real situation in EU and
Ukraine. The proposed complex of models for assessing the living rating of the
country has been provided by combination of multivariate exploratory analysis
methods and predictive analysis methods (cluster and discriminant methods, the
method of canonical correlations). The adaptation of models for assessing the
quality of life of the population involves solving the problem of assessing the
informativeness of indicators, the formation of a system of diagnostic indicators,
the construction of an integral assessment and its scaling. The clustering and clas-
sification methods can be effectively used to solve these problems, which is
shown in the paper. The provided complex of models can be used to make opti-
mal decisions in developing of social and economic development strategy, trans-
forming the public sector of government, smoothing the asymmetry of territorial
development.

Keywords: System, Standards of Living, Index of Living Standards, Model,
Estimation, Predictive Analytic, Modeling.

Copyright © 2021 for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0).
138

1 Introduction

In the context of the implemented processes of globalization and European integration
of Ukraine, the assessment of the living standards of the population acquires special
significance. It is classified as a key concept in defining the policy of socio-economic
development of the country. Overcoming Ukraine's lag behind the European Union dic-
tates the need for consistent implementation of the principles of a social market econ-
omy, characterized by developed market relations, high economic development, polit-
ical democracy, guaranteed access to education and health care, and a well-developed
social protection system.
The current economic situation in Ukraine confirms that the measures the govern-
ment takes to improve the lives of its citizens (increase of minimum wage, living wage,
etc.) are insufficient. To ensure a significant increase in the efficiency of all sectors of
the economy, the reform of all spheres of public life in accordance with European stand-
ards should be completed. The standard of living of the population of Ukraine during
the market reforms and by the influence of external and internal destabilizing factors
has decreased, and it does not meet international standards. The most important direc-
tion of socio-economic transformations should be the achievement of sustainable posi-
tive dynamics of welfare of the population on the basis of increasing effective demand,
in particular, increasing the wages of the working population.
The relevance of this work lies in the need to substantiate and improve models for
assessing and analyzing the living standards of the population of Ukraine in terms of
mathematical modelling and methods of predictive analytics. The need for this is due
to the development of crisis phenomena and the decline of socio-economic develop-
ment of Ukraine in the context of European integration processes, the existence of sig-
nificant drawbacks in approaches to assessing the level of social development and anal-
ysis of living standards. This need to improve the existing tools and statistical pro-
cessing of information to determine the living standards of the population of Ukraine is
realized through the creation of a set of economic and mathematical models that can
position the country on international indices of living standards and predict living stand-
ards for the future.

2 Literature Review

The conducted analysis of modern scientific literature has shown that many approaches
to determining the living standards of the population exist in world practice. A part of
scientific works [5, 7, 11 – 13, 15 – 19, 22, 26, 28] is devoted to the analysis of the
standard of living, identification of the factors influencing it in individual countries. For
example, in the paper [15], the influence of the shadow labor market in Ukraine living
standards through a mathematical model of balance based on modeling of a small group
using the graph theory is investigated. In the paper [16] the author explores the interre-
gional β- and σ-convergence of the living standards of the population in Ukraine. In the
article [11] the relationship between sustainability and quality of life was evaluated.
The indicators were presented as an example used in the quality of urban life study for
139

the Istanbul Metropolitan Area. Author [22] proposes the model is built to identify the
factors that influence income inequality in Vietnam based on the application of the
Generalized Method of Moments (GMM).
A large of modern research [2, 4, 9, 23, 25, 27, 33] is devoted to the development of
models by multivariate exploratory technics and regression analysis. In the paper [23]
authors found a positive effect of GDP growth and average gross earnings at employ-
ment growth in the EU based on panel data and cluster analysis. In the paper [25] au-
thors describe a model to integrate data between two surveys (Eurostat EU-SILC and
Lifestyles survey) through a statistical matching method (hot deck distance) and cluster
analysis. In [9] the authors investigate the influence of the information and communi-
cation technologies development on the social and political activities of modern society
based on the application of correlation-regression analysis and cluster analysis. In [3],
the authors, based on the use of correlation analysis, studied the correlation of the rate
of economic growth (according to the forecast of the IMF) and the indicators of qualify
of life, calculated by Numbeo, and the index of economy digitization, calculated by the
IMD. And based on the analytic hierarchy process (AHP), they investigated the impact
of social development on economic growth. Authors of the research [33] propose a
model of the impact of technology on the standard of living based on fuzzy linear re-
gression. The Human Development Index (HDI) was chosen as a dependent variable as
an indicator of the health and well-being of the population. The explanatory variables
are the Network Readiness Index (NRI), which measures the impact of information and
communication technologies on society and the development of the nation, and the
Global Innovation Index (GII), which measures the driving forces of economic growth.
The study was conducted for four groups of countries with different levels of GDP per
capita.
Alhambra-Borrás, T., Doñate-Martínez, A. [1] studies of The Living Standards Ca-
pabilities for Elders scale (LSCAPE), its application for assessing living standards ca-
pabilities among older adults based on the use of self-reported measures of quality of
life and income. Other researchers [20] conduct a comparative assessment of the con-
cepts of “comfort” and “well-being” on the example of the EU countries and Ukraine.
In this work, the authors paid the main attention to identifying the main economic and
non-economic factors affecting the external migration of the population (the result of
the discomfort of living in their country). In the paper [26] authors are focusing on
determining the degree of influence of macroeconomic indicators characterizing certain
areas of life (health, education, living conditions, safety, income, etc.) in living stand-
ards.
Thus, the methods described above do not allow creating a unified assessment sys-
tem.
But, achieving a high standard of living, similar to the level in European countries is
possible for Ukraine, subject to the study and adaptation of European social standards
in their practice.
In international practice, the index of social (human) development was proposed by
the UN Research Institute for Social Development. It indicate the level of the country's
achievements in the most important socio-economic spheres and accumulates the fol-
lowing indicators: life expectancy; literacy and learning coverage; GDP per capita at
140

currency parities, the ratio of prices to the "consumer basket", consisting of several
hundred goods and services. In 2010, the method of calculating the HDI was signifi-
cantly adjusted: the indicators of education and income were modified, the procedure
for their aggregation changed [14]. They allow a more balanced assessment of the coun-
try's progress than GDP per capita.
The standard of living is also determined by gross national product (GNP), using
indicators of purchasing power parity (PPS) per capita. There is also The Social Pro-
gress Index, a combined measure of the international research project “The Social Pro-
gress Imperative”, which measures the achievements of countries around the world in
terms of social well-being and social progress. Developed in 2013 under the direction
of Michael E. Porter [31] the index does not include indicators of economic develop-
ment of the world (such as GDP and GNI). The index evaluates achievements in the
social sphere separately from economic indicators, which allows a deeper study of the
relationship between economic and social development.
The Global Innovation Index is a global study and the accompanying ranking of the
world's countries in terms of the level of innovation development [10]. It consists of 82
different variables that characterize in detail the innovative development of the world
at different levels of economic development. The authors of the methodology believe
that the success of the economy is associated with both the availability of innovation
potential and conditions for its implementation.
The World Happiness Report is an international research project by The Earth Insti-
tute, which measures the happiness of the world's population as part of the UN Sustain-
able Development Solutions Network in order to show the achievements of countries
and individual regions in terms of their ability to provide their residents with a happy
life [8].
Among the attempts to comprehensively assess and analyze the level and quality of
life of the population the index of physical quality of life developed by D. Morris can
be named [6]. It is based on life expectancy after the age of 1, infant mortality and
literacy. For each indicator, countries are ranked on a 100-point scale, where 1 is the
worst result and 100 is the best. The results of the research showed a slight correlation
between the value of the quality life index and GDP per capita. That is, some countries
with high GDPs had low estimates of the Morris index.
Quite common is the calculation of a generalized indicator in the form of a weighted
average of partial indicators of living standards (groups of indicators). The weights are
expert estimates, and the sum of the weights is 1. An example of such an indicator is
the conjugation indicator. Its components are the degree of supply of consumer goods,
the level of crime, the degree of dissatisfaction of the population with a set of unre-
solved social and political, and economic environmental problems.
Another way to reduce partial living standards to a single scale is to rank countries
for each indicator. However, this method also has disadvantages: firstly, it is assumed
that the comparison of objects on all indicators is in relation to a sample; secondly, that
all indicators appear to be equivalent. Generalizations of the most famous techniques,
their advantages and disadvantages are presented in table 1.
141

Table 1. International methods of assessing living standards

Name Indicators Main advantage Main disadvantage
1 2 3 4
Gives the opportunity to
Domestic na-
measure the personal in- The method takes into
tional product,
come of society mem- account only the eco-
gross domestic
System of Na- bers, to link together the nomic aspects of life,
product, net na-
tional Accounts formation of income which determine the
tional income,
(SNA) [21] and expenditure, to standard of living,
personal and
identify trends in re- which is only one of the
personal availa-
gional economic devel- criteria of quality of life
ble income
opment
Physical Quality of Social indicators are not
The quality of life indi-
Life Index (PQLI ) Life expectancy taken into account. The
ces obtained using this
and its modification after the age of question of what mean-
technique are simple,
(PSLI) developed one year, infant ing is attached to the
accessible, but focused
by the American mortality, adult concept of "physical
on a low degree of satis-
Council on Foreign literacy quality of life" remains
faction of natural needs
Development [6] open.
Subjective indicators of
The method makes it
Human Potential quality of life are not
possible to conduct a
Development In- taken into account, the
comparative analysis of
dex (HDI) and its social aspect is repre-
Life expectancy, socio-economic devel-
modification sented only by the level
education, liv- opment by country and
which considers of education, there are
ing standards in- region, allows tracking
the gender factor no such sections as the
dex the dynamics, compar-
(IRGF) developed degree of development
ing achievements. The
by UN experts of science, social ten-
technique is simple and
[14] sion, the state of the en-
accessible
vironment, etc.
The level of de- By means of this tech-
The need to collect a
velopment of nique both the level of
large set of indicators,
Triangular wel- the economic development of the
as well as the fact that
fare index of the sphere, social specified spheres of vi-
the political and spir-
nation [29] environment, in- tal activity of a society
itual spheres are not
formation infra- and their balance are es-
taken into account
structure timated.

Analysis of foreign methods of assessing living standards in relation to the structure
and indicators of living standards, found that this issue remains controversial. The fol-
lowing conclusions can be drawn:
foreign scientists are actively working in the development of methods for assessing
the level and quality of life; the world community pays more and more attention to the
living standards of the population every year;
achieving and maintaining its high quality is the goal of all developed countries;
existing methods differ significantly in the number and composition of indicators
(the number of indicators varies from three to several dozen, and the composition in-
cludes indicators of economic, social and physiological components of quality of life);
142

most of the considered methods evaluate only objective indicators of quality of life
and do not take into account subjective ones; all the considered methods allow to esti-
mate only separate components of quality of life of the population and cannot claim
universality. There is no universal method of analysis and assessment of living stand-
ards.
In our opinion, it is necessary to improve the assessment models, which include such
assessment indicators that will more objectively reflect the living standards of the pop-
ulation.

3 Problem Formulation, Methods

The purpose of the study is to develop a set of models for assessing and analyzing the
living standards of the population of Ukraine based on the use of tools of economic and
mathematical modelling: canonical correlation analysis, cluster and discriminant anal-
ysis. This allows to assess Ukraine's position in the European space and to forecast the
living standards of the population in the future. For a qualitative analysis of the living
standards of the population of Ukraine and its assessment in the European space, as
well as to solve these problems, the following conceptual scheme of modelling the liv-
ing standards of the population is proposed (Fig. 1).

Methods of analysis and synthesis
Stage 1. Forming of the data set Analysis of the categorical basis
Analysis of modern approaches to
assessing living standards
Stage 2. Development of a model
for assessing the interrelationship of Methods of canonical analysis
indicators for assessing living
standards

Stage 3. Development of a model Hierarchical cluster analysis
for classifying countries by standard Iterative methods of cluster analysis
of living

Stage 4. Development of a model
for forecasting the living standards Methods of discriminant analysis
of the country's population

Fig. 1. Conceptual scheme of modelling the living standards of the population

Let's consider in more detail the main stages of the constructed model, the methods
applied at the corresponding stage and the selected indicators on the basis of which
calculation was carried out. The first stage of the study is to form arrays of source data.
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The main method for information processing is the method of synthesis and analysis of
information, based on the analysis of the categorical basis and analysis of modern ap-
proaches to assessing living standards.
The array of initial data was formed from such international indices as the ranking
of countries in the world by happiness, the global index of innovation, the index of
social progress, the index of human development, the global charity index, the index of
global competitiveness. All the above indices define the standard of living as a complex
set of characteristics, which includes indicators: a person's ability to work and live in
normal conditions, to have a decent level of education, to receive high quality health
care, to have access to cultural values, to live in a safe society.
The next stage of the study reveals the process of building models of living standards
analysis based on methods of predictive analytics and data science. Therefore, in the
second stage, to determine the significant groups of indicators that have an impact on
the quality of life, a model of assessing the relationship between sets of groups of indi-
cators of economic development and a group of international indices of socio-moral
direction. The method of canonical analysis is used for this purpose.
The concept of methods of canonical analysis is based on the nature of multiple cor-
relation, which, according to V. Hotteling, is the maximum correlation between the
chosen random result change and the linear function of the set of explanatory variables
[2]. Since individual indicators do not fully characterize the group to which they belong,
in the process of canonical analysis of the characteristic indicator of groups, two linear
combinations of indicators of another group are established; the pair of linear combi-
nations found by this way forms the first pair of canonical functions (roots), which
describes certain properties of both groups of primary indicators. Performing a canon-
ical correlation analysis of data, namely the construction of a scatter chart of canonical
values provided the basis for further more detailed analysis of the cluster of EU member
states according to international indices of living standards.
At the 3rd stage of the research, models of formation of homogeneous groups of
countries are built according to the formed groups of indicators of living standards as-
sessment. For this purpose, agglomerative and iterative methods of cluster analysis are
used [4, 9, 24]. This allows to assess the quality of grouping, to form the optimal num-
ber of clusters, to determine the distribution of the country in clusters. Clustering algo-
rithms are usually built as a specific way to search the number of clusters and to deter-
mine its optimal value in the search process and include 5 basic steps (Fig. 2).
To eliminate the problem of heterogeneity of observation groups, z-transformation
(standardization) of variable values was performed. Standardization reduces the values
of all converted variables to a single range of values, namely the average of each is
reduced to 0, and the mean deviation – to 1. Then all observations vary in the range of
standard deviation from - 3 to +3.
At the 4th stage of the research a model of identification and forecasting of the living
standard of the population of the European Union member states is built by methods of
discriminant analysis, which allowed to determine the situation of our country and
144

Assessment of the degree of similarity between observations

Hierarchical clustering and formation of the distribution hypothesis

Iterative clustering of group observations

Assessment of statistical significance of grouping

The final grouping of countries by quality of life

Fig. 2. Algorithm for constructing cluster analysis

further way of approaching one of the groups. Schematically, the algorithm for con-
structing the model is presented in Fig. 3.

Formation of the specification of the discriminant function

Assessment of the quality and statistical significance of the discriminant
model

Positioning of observation classes in the space of discriminant roots and
assessment of the country's forecast cluster for the quality of life of the
population

Fig. 3. Algorithm for using discriminant analysis

In the case of one variable, the F-criterion is used as the final criterion of significance
of whether the variable separates the two sets or not. When using discriminant analysis
for multidimensional variables, the procedure is identical to the procedure of multiple
analysis of variance. At each step, all variables are viewed and the one that contributes
most to the difference between the populations is located. This variable must be in-
cluded in the model in the current step, and there is a transition to the next step.
Thus, the proposed set of models of assessment and analysis of living standards
based on methods of predictive analysis and analysis of multidimensional objects al-
lows to comprehensively analyze the impact of key indicators on the quality of life, to
assess the country's membership in one of the clusters and to find the forecast distribu-
tion and membership of certain clusters.
145

4 Findings

In accordance with the considered concept of the study, let’s consider the implementa-
tion of models. According to stage 1 of the study, living standards were analyzed, which
can be divided into two sets: indices of the social and moral component (left set): Social
Progress Index (SPI) [31]; World Giving Index (WGI) [32]; and the indices of the eco-
nomic component (right set): Ranking of countries in the world by level of happiness
(WHR, World Happiness Report) [8]; Global Innovation Index (GII) [10]; Human De-
velopment Index (HDI) [14]; Global Competitiveness Index (GCI) [30].
Estimation of mean (median) and scattering (quartiles and scope) for variables al-
lowed to establish the symmetry of variable distribution. The results of building a model
for assessing the relationship of two sets of indicators by canonical analysis are pre-
sented in Fig. 4.

Fig. 4. The window of the results of canonical analysis

Since the number of canonical roots is equal to the number of variables in the smaller
set (2), both canonical roots explain 100% of the variance (variability) from the left set
and 87.81% from the right. From Fig. 4 it follows that the canonical correlation
R = 0.9039, that is the correlation between the first weighted sums corresponding to the
first pair of canonical variables (root 1), is strong. Its value indicates a strong relation-
ship between the indices of the social and moral component (left set) and the indices of
the economic component (right set). This means that the growth of indices of countries
by social and moral components leads to an increase in the rating of the country by
indicators of economic development, and vice versa - the growth of the rating of the
country by indicators of economic development causes the growth of indices of coun-
tries with social and moral orientation. High value SPI = 40,3476 and level of signifi-
cance𝑝 = 0,00, which is much less than 0,05, demonstrate the significance of R. The
second row of the table shows the percentage of explained variances from the left and
right sets of variables.
The value of the total redundancy of 69.25% means that the variables of the right set
explain on average 69.25% of the variability of the variables of the left set. changes in
the left set explain an average of 68.99% of the variability of variables in the right set.
Thus, the left set is more redundant for a given right than the right for a given left set.
146

Indicators of redundancy additionally confirm the strong relationship between indica-
tors of social and moral orientation and economic orientation, while indicators of eco-
nomic orientation are more informative than indicators of social and moral orientation.
The canonical value of R corresponds only to the first root - the most significant
correlation. The obtained results according to chi-square statistics for canonical roots
showed that only the first root is statistically significant and should be investigated in
more detail in Fig. 5.

Chi-Square Tests with Successive Roots Removed
Root
Canonical Canonical Chi- Lambda
Removed df p
R R-sqr. Square Prime
0 0.903861 0.816965 40.34756 8 0.000003 0.179619
1 0.136610 0.018662 0.44271 3 0.931284 0.981338

Fig. 5. Checking the significance of canonical roots

All correlations between the right variables are quite high, the highest correlation is
observed between GCI (Global Competitiveness Index) and GII (Global Innovation In-
dex), the lowest - between HDI (Human Development Index) and GCI (Global Com-
petitiveness Index). The correlation between the variables of the left set is also positive,
quite high, greater than 0.5 (Fig. 6).

N=28 WHR GII HDI GCI
N=28 SPI WGI WHR 1.0 0.82364 0.83901 0.84403
SPI 1.0 0.69603 GII 0.82364 1.0 0.84516 0.89920
WGI 0.69603 1.0 HDI 0.83901 0.84516 1.0 0.79918
GCI 0.84403 0.89920 0.79918 1.0

Fig. 6. Correlations between set variables

The analysis of the relationship between the variables of the left and right sets is of
particular interest, as it explains the structure of the relationship between the interna-
tional indices of the level of development of the countries under analysis. The strong
correlation between social and moral indices and economic development indices is ex-
plained by the strong correlations between such indicators of economic development
countries as: GII (Global Innovation Index), HDI (Human Development Index) and SPI
(Social Progress Index) of a moral aspect of the development level of the countries. The
WGI (World Charity Index) also has close to strong correlations with economic devel-
opment indices, but these relationships are less pronounced than the relationship be-
tween SPI and economic development indices. It should be noted that the GCI (Global
Competitiveness Index) has the least impact on the ranking of countries (Fig. 7).

N=28 WHR GII HDI GCI
SPI 0.76163 0.83421 0.805667 0.75557
WGI 0.73346 0.779934 0.730343 0.68746

Fig. 7. Correlations between variables of the left and right sets
147

The largest factor loads (correlations) of the left and right sets have with the canon-
ical variables that correspond to the Root 1 (Fig. 8). This fact underlines once again the
strong correlation between the indicators of social and moral indices and indices taking
into account the economic development of the country.

Factor structure, right set
Factor structure, left set Variable Root 1 Root 2
Variable Root 1 Root 2 WHR -0.898585 0.182226
SPI -0.94754 -0.31963 GII -0.972681 -0.026579
WGI -0.88902 0.45787 HDI -0.928119 -0.246937
GCI -0.871654 -0.207150

Fig. 8. Factor structure of sets

Analysis of canonical roots showed the following. Canonical Root 1 explains on
average about 84% of the variance from the indicators of the economic component of
the level of development and about 84% of the variance from the indicators of the socio-
moral component of the level of development, that is it explains 84% of the variability
of the rating of countries considering socio-moral aspect. In turn, the canonical Root 2
explains, respectively, about 15% and about 3% of the variability of the economic
component of the level of development and the socio-moral component of the level of
development (Fig. 9).

Variance Extracted (Proportions), Variance Extracted (Proportions),
left set Factor right set
Factor Variance Extracted Redundancy Variance Extracted Redundancy
Root 1 0.844095 0.689596 Root 1 0.843687 0.689263
Root 2 0.155905 0.002910 Root 2 0.034450 0.000643

Fig. 9. Table of fractions of explanatory variance

According to the values of the first canonical root, the indicators of the right set -
indices of the economic aspect, explain about 69% of the variability in the indicators of
the left set - the indices of the socio-moral aspect; the indicators of the left set also
explain about 84% of the variability in the indicators of the right set. Thus, the
indicators of both sets are almost identical in informativeness to predict each other.
Next, the coefficients of regression equations were calculated, in which the re-
sponses are canonical variables that correspond to both canonical roots, and the predi-
cates are the indicators of the left and right sets, respectively (Fig. 10).

Canonical weights, right set
Canonical weights, left set Variable Root 1 Root 2
Variable Root 1 Root 2 WHR -0.246226 1.81287
SPI -0.637697 -1.23817 GII -0.720910 1.19173
WGI -0.445160 1.31968 HDI -0.276181 -1.46789
GCI 0.205126 -1.63576

Fig. 10. Table of canonical weight coefficients of sets
148

Let us write the regression equations of the canonical variables of the left and right
sets that correspond to the root 1:

root 1right = − 0,25𝑊𝐻𝑅 – 0,72𝐺𝐼𝐼 – 0,28𝐻𝐷𝐼 + 0,21𝐺𝐶𝐼

root 1left = −0,64𝑆𝑃𝐼 – 0,45𝑊𝐺𝐼

Let us write the regression equations of the canonical variables of the left and right
sets that correspond to the root 2:

root 2right = 1,81𝑊𝐻𝑅 + 1,19𝐺𝐼𝐼 – 1,46𝐻𝐷𝐼 − 1,64𝐺𝐶𝐼

root 2left = − 1,24𝑆𝑃𝐼 + 1,32𝑊𝐺𝐼

In terms of the value and sign of the coefficients (canonical weights) for variables in
the regression equations, for the ranking of countries by social aspect, the largest
contribution to Root 1left corresponds to SPI, slightly less than WGI. For the ranking
of countries by economic aspect, the largest contribution to Root 1right corresponds to
the GII, the smallest – GCI. Regression equations for each root represent the weighted
sum. To calculate the canonical values (values of canonical variables) for each country,
it is necessary to substitute standardized (normalized) values of the country's indicators
in the linear regression models corresponding to each set.
The analysis of the scattering cloud of observations in the space of canonical roots
has a shape characteristic of linear dependence. The correlation between the values of
the canonical variables of the left (indicators of socio-moral orientation) and the right
set (economic orientation) is equal to 0.9038. The horizontal axis (abscissa)
corresponds to the indicators of the indices of the socio-moral aspect, and the vertical
axis (ordinate) - to the indicators of the indices of the economic aspect (Fig. 11).

Canonical Variables: Var. 1 (left set) by 1 (right set)
2,0

1,5

1,0

0,5
Right set

0,0

-0,5

-1,0

-1,5

-2,0
-2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0 2,5
Left set

Fig. 11. Scattering diagram of canonical variables

The scattering diagram of the values of the canonical variables corresponding to the
Root 2 has a cloud shape that is less characteristic of the linear relationship. This is due
to the fact that the correlation between the values of the canonical variables of the left
and right sets takes a small value equal to 0.1366.
149

Thus, the analysis of the model of the relationship between the sets of indicators for
assessing the quality of life of the population revealed the presence of strong relation-
ships between all components of the sets. The results of the modelling, namely the con-
struction of a scattering diagram of canonical values, gave the opportunity for further
detailed analysis - the development of a model for the formation of clusters of EU mem-
ber states according to international indices of living standards.
Hierarchical (tree-like) methods of cluster analysis were used to determine the cur-
rent standard of living of the population of Ukraine in comparison with the EU coun-
tries. In the work to determine the number of clusters of regions of the EU countries a
dendrogram of classification was constructed according to the method of Ward, de-
pending on the values of international indices of living standards (Fig. 12).
Tree Diagram for 28 Cases
Ward`s method
Euclidean distances
35

25
Linkage Distance

0
C_22 C_26 C_15 C_6 C_5 C_21 C_16 C_4 C_3 C_9 C_14 C_11 C_10 C_18
C_19 C_25 C_8 C_12 C_24 C_17 C_13 C_23 C_27 C_28 C_20 C_7 C_2 C_1

Fig. 12. Dendrogram of the classification of EU countries by living standards according to the
Ward method

Dendrogram analysis allows to recognize three groups (clusters) of homogeneous
states in the observed data set. Based on the data of the dendrogram, the hypothesis of
the existence of three clusters, which are divided into EU countries depending on the
values of international indices of living standards is accepted in advance. An iterative
method of clustering of k-means was used to divide the regions of the country into three
clusters depending on the value of the components of the living standards of the popu-
lation. The graph of average values for clusters of countries is given in Fig.13.
Plot of Means for Each Cluster
2,0

1,5
Cluster 1

1,0 Cluster2
0,5
Cluster3
0,0

-0,5

-1,0

-1,5

-2,0
WHR 2016 GII 2016 GCI 2016-2017 Cluster 1
SPI 2016 HDI 2016 WGI 2017
Cluster 2
WHR SPI GIIVariablesHDI GCI WGI Cluster 3

Fig. 13. Graph the means of each cluster
150

As can be seen from Fig. 13, clusters differ in all respects and you can see clearly
defined boundaries between groups of objects. This corresponds to the initial assump-
tion of the division of countries by living standards into three groups: countries with
very high living standards; countries with a high standard of living; countries with an
average standard of living. Thus, with the help of the obtained results of the classifica-
tion model the countries are distributed by clusters (Table 3).

Table 3 Distribution of countries by clusters

1st cluster 2nd cluster 3rd cluster
Austria Czech Republic Bulgaria
Belgium Estonia Croatia
Denmark Italy Greece
Finland Malta Hungary
France Portugal Latvia
Germany Slovenia Lithuania
Ireland Spain Poland
Luxembourg Romania
Netherlands Slovakia
Sweden Cyprus
United Kingdom

The results of analysis of variance: evaluation of the F-criterion, the values of inter-
group and intragroup variances, showed the statistical significance of all selected indi-
cators for clustering at 99 % (Fig. 14).

Analysis of variance
Between Within
Variable Significant
Group df Group df F
p-value
Variation Variation
WHR 19.50747 2 7.492533 25 32.54485 0.000000
SPI 21.08796 2 5.912037 25 44.58693 0.000000
GII 23.44965 2 3.550346 25 82.56115 0.000000
HDI 20.10858 2 6.891420 25 36.47394 0.000000
GCI 23.15670 2 3.843300 25 75.31516 0.000000
WGI 17.43817 2 9.561831 25 22.79659 0.000002
Fig. 14. Table of analysis of variance

Thus, the cluster No. 1 includes 11 countries with the highest ratings according to
international indices of living standards compared to other countries. Therefore, it can
be described as a cluster with countries with a very high level of development. Coun-
tries with a high level of development belong to the cluster № 2, namely 8 countries
have average values of indicators of the level of development of regions in all studied
areas. Paying attention to the fact that according to the Index of Social Progress, coun-
tries are closer to the countries of the first cluster, and according to the Index of Global
Competitiveness - on the contrary, they fall to the indicators of the countries of the third
151

cluster. The member states of the European Union - Bulgaria, Croatia, Greece, Hun-
gary, Latvia, Lithuania, Poland, Romania, Slovakia were included in the cluster No. 3.
These are the countries with an average level of development, which have the lowest
level of population development among the countries of the European Union. Particular
attention should be paid to the rather low indicators of the Social Progress Index and
the Global Innovation Index, which indicate significant problems in the social and ed-
ucational aspects.
We consider the next stage of modelling the living standards of the population - the
implementation of the model of identification and forecasting the living standards of
the population. The task is to use the International Indices for Assessing the Living
Standards of the European Union (the Social Progress Index, the Global Innovation
Index, the Human Development Index, the Global Happiness Report Index, the Global
Competitiveness Index and the World Charitable Index) for classifying Ukraine into
one of the three clusters identified by cluster analysis. The main characteristics of the
model of recognizing the living standards of the population of the EU countries are
shown in Fig. 15.

Discriminant Function Analysis Summary
Step 4, N of vars in model: 4; Grouping: Claster (3grps)
N=28 Wilks’ Lambda: 0.04509 approx. F (8,44)=20.401 p<0.0000
Wilks’ Partial F-remove p-value Toler. 1-Toler.
Lambda Lambda (2,22) (R-Sqr.)
GII 0.053644 0.840575 2.086278 0.148027 0.731639 0.268361
GCI 0.081887 0.550653 8.976275 0.001411 0.738063 0.261937
SPI 0.064797 0.695889 4.807120 0.018533 0.948881 0.051119
WGI 0.052473 0.859328 1.811704 0.188689 0.931293 0.068707
Fig. 15. Assessment of the adequacy of the model of discriminant analysis of EU countries by
living standards

The value of Wilk's Lambda is close to zero (Wilk's Lambda = 0.045), which char-
acterizes the excellent quality of discrimination. According to the analysis, it is seen
that the GCI and SPI indices give the most significant contribution to the discriminant
function, which was also noted when using the hierarchical method of clustering of k-
means. The coefficients of discriminant functions for each of the indices of living stand-
ards assessment are calculated. Discriminant functions have the form:

𝐶𝑙𝑢𝑠𝑡𝑒𝑟1 = 3,44 ∙ 𝐺𝐼𝐼 + 5,70 ∙ 𝐺𝐶𝐼 + 2,23 ∙ 𝑆𝑃𝐼 + 2,47 ∙ 𝑊𝐺𝐼– 7,97;

𝐶𝑙𝑢𝑠𝑡𝑒𝑟2 = 0,59 ∙ 𝐺𝐼𝐼 − 4,12 ∙ 𝐺𝐶𝐼 + 1,2 ∙ 𝑆𝑃𝐼 − 0,71 ∙ 𝑊𝐺𝐼– 2,42;

𝐶𝑙𝑢𝑠𝑡𝑒𝑟3 = −4,73 ∙ 𝐺𝐼𝐼 − 3,31 ∙ 𝐺𝐶𝐼 − 3,78 ∙ 𝑆𝑃𝐼 − 2,39 ∙ 𝑊𝐺𝐼– 8,68,

Estimated values of classification functions for Ukraine: Cluster1 = −30,4757,
Cluster2 = −0,56229, Cluster3 = 17,15047. Thus, Ukraine in terms of develop-
ment of living standards of population can be attributed to cluster 3, namely the coun-
tries with average living standards, as the classification value for this function is maxi-
mum. The graph of the scattering of countries in the space of discriminant roots shows
152

that the objects in the three classes are grouped quite densely, and the distances between
the classes are large enough (Fig. 16). This will allow us to prove with greater certainty
that the recognition of countries by the three levels of life of the population has been
done correctly.

Root 1 vs. Root 2
4

1
Root 2

-1

-2

-3

-4 G_1:1
-6 -4 -2 0 2 4 6 8
G_2:2
Root 1 G_3:3

Fig. 16. Scattering of countries in the space of discriminatory roots

The case, namely Ukraine, belongs to a group to which the distance of Mahalanobis
is at least 16,458 – this is a group of countries with an average standard of living. The
recognition of living standard of the population on the basis of the international indices
and forecasting of its level both for the investigated period and for the future is carried
out by the constructed discriminant functions. Given the results, we can once again
make a statement that Ukraine in terms of living standards falls into the cluster № 3 -
countries with average living standards.

5 Discussion and Conclusion

According to the research results it can be concluded that the analysis of modern ap-
proaches to the assessment of living standards shows that this issue remains controver-
sial. It needs refinement and improvement due to a number of related problems, such
as the lack of a universal method of analysis and assessment of the level, the difficulty
of determining the optimal categorical basis, the measurement of which with objective
indicators is almost impossible. Therefore, it is fair to make a proposal on the need to
create a new system of analysis and assessment of living standards, which will include
indicators that more objectively reflect the real situation not only in Ukraine, but it will
be suitable for assessing living standards in Europe. The paper develops an adapted
methodological approach to the rating of the European Union and Ukraine, which, in
contrast to existing ones, is based on a combination of multidimensional analysis meth-
ods, namely the method of canonical correlations, cluster and discriminant methods,
which allows to classify EU countries by living standards taking into account the dif-
ferentiation of international indices of living standards for such groups of countries
(with a very high level, high, average) and to refer our country to the third cluster of
153

countries. This allows to ensure the objectification of the evaluation results and to form
a system of recommendations for further development of the country.
Prospects for further research include the possibility of developing separate strate-
gies and trajectories of social development of the country and of a significant increase
in living standards on the basis of the proposed set of models. The set of models can be
expanded with additional modules for assessing the asymmetry of living standards by
regions of the country and individual territories. This will build a decision-making sys-
tem to equalize social asymmetry in general.

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