Mathematical statistical models and qualitative theories for economic and social sciences

Studies in Systems, Decision and Control 104

Šárka Hošková-Mayerová
Fabrizio Maturo
Janusz Kacprzyk Editors

MathematicalStatistical Models
and Qualitative
Theories for
Economic and
Social Sciences


Studies in Systems, Decision and Control
Volume 104

Series editor
Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland
e-mail:


About this Series
The series “Studies in Systems, Decision and Control” (SSDC) covers both new
developments and advances, as well as the state of the art, in the various areas of
broadly perceived systems, decision making and control- quickly, up to date and
with a high quality. The intent is to cover the theory, applications, and perspectives
on the state of the art and future developments relevant to systems, decision
making, control, complex processes and related areas, as embedded in the fields of
engineering, computer science, physics, economics, social and life sciences, as well
as the paradigms and methodologies behind them. The series contains monographs,
textbooks, lecture notes and edited volumes in systems, decision making and

control spanning the areas of Cyber-Physical Systems, Autonomous Systems,
Sensor Networks, Control Systems, Energy Systems, Automotive Systems, Biological Systems, Vehicular Networking and Connected Vehicles, Aerospace Systems, Automation, Manufacturing, Smart Grids, Nonlinear Systems, Power
Systems, Robotics, Social Systems, Economic Systems and other. Of particular
value to both the contributors and the readership are the short publication timeframe
and the world-wide distribution and exposure which enable both a wide and rapid
dissemination of research output.

More information about this series at />

Šárka Hošková-Mayerová
Fabrizio Maturo ⋅ Janusz Kacprzyk
Editors

Mathematical-Statistical
Models and Qualitative
Theories for Economic
and Social Sciences

123


Editors
Šárka Hošková-Mayerová
Department of Mathematics and Physics,
Faculty of Military Technology
University of Defence
Brno
Czech Republic

Janusz Kacprzyk

Systems Research Institute
Polish Academy of Sciences
Warsaw
Poland

Fabrizio Maturo
Department of Business Administration
University “G. d’Annunzio” of
Chieti-Pescara
Pescara
Italy

All chapters were reviewed.
ISSN 2198-4182
ISSN 2198-4190 (electronic)
Studies in Systems, Decision and Control
ISBN 978-3-319-54818-0
ISBN 978-3-319-54819-7 (eBook)
DOI 10.1007/978-3-319-54819-7
Library of Congress Control Number: 2017934466
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Preface

The book “Mathematical-Statistical Models and Qualitative Theories for Economic
and Social Sciences” is part of the important series “Studies in Systems, Decision
and Control” published by Springer. This is the result of a scientific collaboration,
in the field of economic and social systems, among experts from “University of
Defence” in Brno (Czech Republic), “G. d’Annunzio” University of Chieti-Pescara
(Italy), “Pablo de Olavide” University of Sevilla (Spain), and “Ovidius University”
in Constanţa, (Romania).
The variety of the contributions developed in this volume reflects the heterogeneity and complexity of economic and social phenomena; thus, in this book, there
is a convergence of many research fields, such as statistics, decision making,
mathematics, complexity, psychology, sociology, and economics. The different
studies included in this book, selected using a peer-review process, present also
empirical interesting researches conducted in various countries. Each chapter was
peer-reviewed by two independent referees (e.g., J. Beránek, J. Čermák, D. Řezáč,
and V. Voženílek, (CZ); M. Grega, S. Filip, and J. Klučka (SK); A. Porrovecchio
(FR); N. Bortoletto, M. Squillante, and A. Ventre, (IT); E. Barrera Algarín, O.
Vazquez-Aguado, and C.M. Vicente (ES)). The volume is divided into two parts:
The first one is “Recent Trends in Mathematical and Statistical Models for Economic and Social Sciences,” whereas the second one is “Recent Trends in Qualitative Theories for Economic and Social Sciences.”
Part I collects research of scholars and experts on quantitative matters, who

propose mathematical and statistical models for social sciences, economics, finance,
and business administration.
The book opens with the contribution of Veronika Mitašová, Ján Havko, and
Tomáš Pavlenko. They propose a study titled “Correlational Research of Expenditure Spend on Slovak Armed Forces Participation in Peace Support Operations
Led by NATO” in which a multifactor single-equation econometric model is created and tested.
Salvador Cruz Rambaud, Fabrizio Maturo, and Ana María Sánchez Pérez aim to
develop three approaches for obtaining the value of an n-payment annuity, with
payments of one unit each, when the interest rate is random. To calculate the value
v


vi

Preface

of these annuities, the authors assume that only some non-central moments of the
capitalization factor are known. The first technique consists in using a tetra parametric function which depends on the arctangent function. The second expression is
derived from the so-called quadratic discounting, whereas the third approach is
based on the approximation of the mathematical expectation of the ratio of two
random variables by Mood et al. (1974). A comparison of these methodologies
through an application, using the R statistical software, shows that all of them lead
to different results.
Josef Navrátil and Veronika Sadovská concentrate on the health risk assessment
of selected pollutants derived from residential fire simulated in fire container. The
key interest of their study is dedicated to polycyclic aromatic hydrocarbons (PAHs)
and their toxicity and harmful effects on the health of firefighters, whose protection
by breathing apparatus is insufficient.
Qualitative and quantitative comparison of the results of the entrance draft tests
and the entrance tests of mathematics is illustrated by Radovan Potůček. His
contribution focuses on the applicants for the bachelor and master study at the

Faculty of Military Technology of the University of Defence in Brno. He refers to
tests organized by the Department of Mathematics and Physics and presents the
results of the applicants (from the military secondary school and civilian secondary
schools), comparing and evaluating them from the qualitative and quantitative point
of view.
Recent trends in digital ethnography are presented by Vanessa Russo. She shows
theories, models, and case studies with the aim of defining the boundaries of digital
ethnography. Finally, with the help of the comparison between empirical cases, she
tries to understand critical points, limits, and research prospects for digital
ethnographers.
Lenka Hrbková, Jozef Zagrapan, and Roman Chytilek analyze the demand side
of negativity and privatization in news with an experimental study of news consumer habits. They remark that negativity in media and emphasis on personal side
of politics are often cited as a common journalist practice, which is harmful to
democratic processes. Journalists and media houses are often held accountable for
these phenomena because they prioritize profit over the quality of content. Then,
they offer an analysis focused on demand side of both negativity and privatization
of political news. Using the Dynamic Process Tracing Environment (DPTE), they
test the assumption that both of these features of political media coverage may be
driven by audience demand for negative and personal news.
Martin Hubacek and Vladimir Vrab propose a constructive simulation for cost
assessment of training. They highlight that constructive simulation, which is used as
a tool for training of commanders and staffs of military units, has important benefits
for a higher quality of training. Furthermore, constructive simulation gradually
penetrates into other spheres such as the training of emergency staff. However,
relevant studies about the economical benefits of the use of constructive simulation
for training are relatively rare. The presented cost comparison of the exercises is
based on the authors’ experience gained during the implementation of various types


Preface

vii

of exercise, at the Center of Simulation and Training Technologies of Brno, with
the use of constructive simulation OneSAF.
Social problems and decision making for teaching approaches and relationship
management in an elementary school are the topics of interest of Luciana Delli
Rocili and Antonio Maturo. Their chapter illustrates teaching experiences in the
primary school and applications of theories regarding the choice of teaching
methods in this particular context. In order to decide the most appropriate intervention strategies, both in terms of teaching and for an efficient management of
relationships within the class and with the students’ families, they consider that the
first step is to discover the students’ social and environmental background. The
experience described herein is at the basis of the final proposal on how to concretely
implement some decisional procedures at school, as for instance those linked to the
limited rationality and the analytic hierarchy process theorized by Saaty.
Ferdinando Casolaro and Alessandra Rotunno propose a chapter titled “From the
pictorial art to the linear transformations.” In particular, the authors suggest a path
for the teaching of geometry in Italy that reflects the development, which took place
over the past two centuries. Moreover, they highlight the social aspects of a
teaching based on the graphical visualization as required by the projective
geometry.
Bekesiene, Hošková-Mayerová, and Diliunas focus on the identification of
effective leadership indicators in army forces of Lithuania. They remark that
leadership is of overriding importance in the military sphere because the foundation
for leading a unit consists in influence, motivation, and soldiers’ inspiration by the
leader’s personal example. The Lithuanian Army seeks to develop a military
leadership identity as a way to promote mission success. This study is sought to
identify the effective leadership style, which is appreciated by soldiers in the
Lithuanian Armed Forces. The authors adopt the Leader Behavior Description
Questionnaire (LBDQ) for measuring the behavior of leaders. The data collected

from military personnel, holding different ranks and doing their professional military service of all the units of the Lithuanian Armed Forces, were analyzed using
structural equation models (SEM).
“Why We Need Mathematics in Cartography and Geoinformatics” is the title
of the chapter of Václav Talhofer. He highlights that mathematics is necessary for
understanding of many procedures that are connected to modeling of the Earth as a
celestial body, to ways of its projection into a plane, to methods and procedures of
modeling of landscape and phenomena in society, and to visualization of these
models in the form of electronic as well as classic paper maps. Not only general
mathematics, but also its extension of differential geometry of curves and surfaces,
ways of approximation of lines and surfaces of functional surfaces, mathematical
statistics, and multicriteria analyses seem to be suitable and needful. Moreover, he
suggests that the underestimation of the significance of mathematical education in
cartography and geoinformatics is inappropriate and lowers competences of cartographers and geoinformaticians to solve problems.
Hana Svatoňová and Radovan Šikl investigate the cognitive aspects of interpretation of image data. Interpretation of image data is a complex of complicated


viii

Preface

intellectual operations, which is based on visual. The theoretical part of their study
summarizes the scientific knowledge of processes of visual perception applied in
the process of visual interpretation of satellite, aircraft, and map image data. Author
presents partial phases of image data interpreting process: from the initial recording
of the image to detection, identification, and objects classification. The complexity
of the cognitive process with regard to biological and psychological characteristics
of the individual is highlighted. The research section presents the results of image
data interpretation research according to gender of individuals/research
respondents.
Engin Baysen, Šárka Hošková-Mayerová, Nermin Çakmak, and Fatma Baysen

study the misconception regarding providing citations. Their research aims at
finding out citation understandings of Czech and Turkish secondary and high
school students. Except for few students, secondary and high school students have
misconceptions concerning providing citations. Students are unintentionally vulnerable to plagiarize while reporting. The study shows that only secondary and high
school education is not enough for implementing honesty regarding citation.
Therefore, the authors remark the importance of educating and informing students
about honesty in research and plagiarism.
Subjective preconditions and objective evaluation of interpretation of image data
are analyzed in the chapter of Hana Svatoňová and Šárka Mayerová-Hošková. In
learning and teaching, there is an ongoing teaching relationship with specific and
bidirectional relations between the teacher and student. Teacher can have either a
strongly positive or, on the contrary, a strongly negative impact via his communication and interactions with students. From the wide idea of attitudes and values
that constitute the relationship between the teacher and the student, their article is
focused on a part of subjective assumptions about the success of students in a
specific task: in this case, interpretation of aerial and satellite images and maps. The
respondents of the researcher were elementary school teachers and students aged
between 11 and 15. The subjective assumptions of teachers were compared with
assumptions of students, and subsequently, all subjective assumptions were compared with objective data.
Fabrizio Maturo, Stefania Migliori, and Francesco Paolone analyze the influence
of institutional and foreign shareholders on national board diversity of companies.
Investigating the external antecedents of board diversity, they suggest the use of
functional data analysis for diversity assessment in corporate governance studies.
Focusing on a sample of 1230 Italian medium–large firms, their results show that
institutional shareholders do not influence national board diversity, while foreign
shareholders strongly affect it, especially when they hold more than 50% of shares.
Thus, the authors address the research gap on the determinants of national board
diversity and enrich comparative European research on this topic.
Francesco Paolone and Matteo Pozzoli investigate the effect of financial crisis of
Earnings Manipulation by adopting the Beneish model. Specifically, empirical
evidence from the “Top World Enterprises,” ranked by “Sales Revenues” in the

fiscal year 2013, is presented. Their results show that there has been a greater
propensity for manipulating earnings in the first year of the global crisis:


Preface

ix

Companies have had a tendency to increase creation of social wealth, in terms of
generating higher profits. This would mean that the crisis has had a positive effect
on handling of income by the largest companies in the world because the crisis itself
has restricted the earnings manipulation policies.
Reasoning and decision making in practicing counseling are considered by
Antonio Maturo and Antonella Sciarra. The counseling procedure is considered as a
dynamical decision-making problem, where the awareness of alternatives and
objectives and their evaluations are maieutically induced by the counselor. After
presenting some relevant practices of counseling and related decision-making
procedures, this study shows the use of the mathematical theory of decisions for a
formalization of the counseling methods, in order to model, clarify, and make
rigorous procedures of decision. Finally, it is shown that fuzzy reasoning can give a
useful formal help to the task of the counselor because of its flexibility.
Ana Vallejo Andrada, Šárka Hošková-Mayerová, José Luis Sarasola
Sanchez-Serrano, and Josef Krahulec deal with how society views the current wave
of migration, specifically in Andalusia (Spain) and Czech Republic. The problem is
described in a pre-case study, which covers results concerning citizens’ approach to
an urgent social topic, i.e., migration and immigration and risks related to these
questions. First, the research presents a summary about the history of migrations in
both regions; then, the current situation in those regions is characterized; after that,
the questionnaire was prepared with the idea of how people feel this phenomenon,
and survey was made. Finally, based on the results, possible risks are presented and

some strategies on how to deal with inconvenient situations, which might arise, are
suggested.
Domenico Di Spalatro, Fabrizio Maturo, and Lorella Sicuro face the issue of
inequalities in the provinces of Abruzzo making a comparative study through the
indices of deprivation and principal component analysis. The indices of deprivation
are a valuable tool to measure the socioeconomic disadvantage in certain geographical areas of interest. This study aims to compare inequalities between the
provinces of Abruzzo over the last two decades suggesting some indices of
deprivation to capture the key aspects of the great wealth of information relating to
population census. Specifically, they propose three indices of deprivation to measure the material and social disadvantage. Moreover, a principal component analysis is performed using the most known indicators of deprivation. Using these
methods, their results show an increase in the proportion of disadvantaged areas in
the Abruzzo region from 1991 to 2011 in its four provinces.
Part II “Recent Trends in Qualitative Theories for Economic and Social Sciences” collects research of scholars and experts on qualitative matters, who propose
and discuss on social, economic, and teaching issues.
Part II opens with the chapter of Grazia Angeloni which highlights the reasons
why educational institutions should be considered complex systemic organizations.
Specifically, she suggests a multidisciplinary approach tending to make use, on the
one hand, of different lenses, in order to appreciate the organizational phenomenon
taken into consideration, and on the other, it is an effort to join different epistemes
for practical purposes.


x

Preface

Jose Luis Sarasola Sánchez-Serrano, Ana Vallejo Andrada, and Alberto Sarasola
Fernandez in their study “Sociability and Dependence” illustrate the results of a
survey conducted for studying elders sociability in the urban area and its relation
with the dependency degree.
Stefania Fantinelli presents her research titled “Knowledge Creation Processes

Between Open Source Intelligence and Knowledge Management.” She adopts some
interviews on a sample of Italian analysts and experts to reveal what is the common
use of “Open Source Intelligence” methods and how they are linked to the
knowledge creation and knowledge management processes. Furthermore, she
explores this method in a social psychology perspective and in relation to knowledge management in organizations.
Advanced technologies for social communication are proposed by Roberto
Salvatori, who highlights the speed of change and spread of ICT in Education,
which put the entire educational system in the position of continuously redesigning
new methods and teaching models adapted to a globalized and interconnected
society, where knowledge is distributed, easily accessible, and constantly updated.
Valentina Savini deals with the concept of social distance as an interpretation of
a territory. She shows that the physical and spatial aspects of social distance
identified by Simmel disappeared from the theoretical setting when the issue was
analyzed in America. Moreover, the approaches that combine the physical and
relational dimensions, based on Italian and English sociologists of the last few
years, should be preferred.
Gabriele Di Francesco presents a socio-vital areas analysis with a qualitative
approach to sociological analysis of urban spaces and social life. He presents the
theoretical synthesis and the technical and methodological setting of a research,
aimed to analyzing and evaluating the urban places and spaces of social life, where
the human interactions take place and the city come to life.
Cultural and natural heritage challenges are illustrated by Zdena Rosická. The
author remarks that every cultural heritage object and its content has its unique
character and calls for an individual approach considering safety, protection,
security, risk-preparedness, and further viable use. The public usually know about
high-value losses of cultural property caused by burglary, fire of flood when the
mass media report them; however, physical care, including environmental and
conservation control, property transfer and transport, personal access, thefts from
exhibits during the day, and incidents of smash bring about higher-cost internal
losses, which are sometimes not reported at all. In case any disaster strikes, harm to

cultural treasure is sometimes serious and losses irreplaceable unless relevant
measures are taken in time.
Fiorella Paone aims to contribute to reflection about new form of emerging
literacy starting from communicational changes, which characterize new social and
cultural paradigm due to the use of electronic media. The narrative paradigm
thought as linguistic practice of construction of liquid identities is considered as a
possible operative strategy able to promote personal development in a holistic
perspective, enforcing both personal and social self.


Preface

xi

Vincenzo Corsi takes into account the sociological methods and construction of
local welfare in Italy. He describes the importance of the study of the social care
needs of the population for the construction of the local welfare system. Then, he
shows some aspects of the local welfare system in Italy.
Daniel Flaut and Enache Tuşa analyze some aspects of social life in Romanian
villages in the interwar period. At the same time, they describe the standard of
living in rural areas, which varied depending on the ethnicity of the residents, using
examples taken from the Dobrudja region.
A large spectrum of problems related to statistics, mathematics, teaching, social
science, and economics has been presented in this volume. Therefore, a broad range
of tools and techniques that may be used to solve problems on these topics has been
presented in detail in this book, which is an ideal reference work for all those
researchers interested in recent quantitative and qualitative tools. Due to the wide
range of topics of the research results collected in this book, it is addressed, in equal
measure, to mathematicians, statisticians, sociologists, philosophers, and specialists
in the fields of communication, social, and political sciences.

Brno, Czech Republic
Pescara, Italy
Warsaw, Poland
July, 2017

Šárka Hošková-Mayerová
Fabrizio Maturo
Janusz Kacprzyk


Contents

Part I
1

2

3

Recent Trends in Mathematical and Statistical
Models for Economic and Social Sciences

Correlational Research of Expenditure Spend on Slovak
Armed Forces Participation in Peace Support Operations
Led by NATO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Veronika Mitašová, Ján Havko and Tomáš Pavlenko
Health Risk Assessment of Combustion Products from Simulated
Residential Fire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Josef Navrátil, Veronika Sadovská and Irena Švarcová

15

Qualitative and Quantitative Comparison of the Entrance
Draft Tests and the Entrance Tests Results in Mathematics . . . . . .
Radovan Potůček

25

4

Digital Ethnography Theories, Models and Case Studies . . . . . . . .
Vanessa Russo

5

The Demand Side of Negativity and Privatization in News:
Experimental Study of News Consumer Habits . . . . . . . . . . . . . . . .
Lenka Hrbková, Jozef Zagrapan and Roman Chytilek

6

Cost Assessment of Training Using Constructive Simulation . . . . .
Martin Hubacek and Vladimir Vrab

7

Social Problems and Decision Making for Teaching Approaches
and Relationship Management in an Elementary School . . . . . . . . .
Luciana Delli Rocili and Antonio Maturo

8

3

From the Pictorial Art to the Linear Transformations . . . . . . . . . .
Ferdinando Casolaro and Alessandra Rotunno

41

55
71

81
95

xiii


xiv

9

Contents

Identification of Effective Leadership Indicators
in the Lithuania Army Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S. Bekesiene, S. Hoskova-Mayerova and P. Diliunas

107

10 Why We Need Mathematics in Cartography
and Geoinformatics? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Václav Talhofer

123

11 Cognitive Aspects of Interpretation of Image Data . . . . . . . . . . . . .
Hana Svatoňová and Radovan Šikl
12 Misconceptions Regarding Providing Citations: To Neglect
Means to Take Risk for Future Scientific Research . . . . . . . . . . . . .
Engin Baysen, Sarka Hoskova-Mayerova, Nermin Çakmak
and Fatma Baysen
13 Social Aspects of Teaching: Subjective Preconditions
and Objective Evaluation of Interpretation of Image Data . . . . . . .
Hana Svatoňová and Šárka Hošková-Mayerová
14 Do Institutional or Foreign Shareholders Influence National
Board Diversity? Assessing Board Diversity Through
Functional Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
F. Maturo, S. Migliori and F. Paolone
15 Inequalities in the Provinces of Abruzzo: A Comparative
Study Through the Indices of Deprivation and Principal
Component Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Domenico Di Spalatro, Fabrizio Maturo and Lorella Sicuro
16 Expected Present and Final Value of an Annuity when some
Non-Central Moments of the Capitalization Factor
are Unknown: Theory and an Application using R . . . . . . . . . . . . .
Salvador Cruz Rambaud, Fabrizio Maturo
and Ana María Sánchez Pérez
17 Assessing the Effect of Financial Crisis of Earnings
Manipulation. Empirical Evidence from the Top 1,000

World Listed Companies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Francesco Paolone and Matteo Pozzoli
18 Reasoning and Decision Making in Practicing Counseling . . . . . . .
Antonio Maturo and Antonella Sciarra
19 Risks Associated with Reality: How Society Views the Current
Wave of Migration; One Common Problem—Two Different
Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ana Vallejo Andrada, Sarka Hoskova-Mayerova, Josef Krahulec
and José Luis Sarasola Sanchez-Serrano

161

177

187

199

219

233

249
265

283


Contents

Part II

xv

Recent Trends in Qualitative Theories for Economic
and Social Sciences

20 Sociability and Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
José Luis Sarasola Sánchez-Serrano, Ana Vallejo Andrada
and Alberto Sarasola Fernandez

309

21 School Institutions as Complex Systemic Organizations:
A Multidisciplinary Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Grazia Angeloni

325

22 Advanced Technologies for Social Communication: Methods
and Techniques in Online Learning . . . . . . . . . . . . . . . . . . . . . . . . .
Roberto Salvatori

333

23 Social Distance as an Interpretation of a Territory . . . . . . . . . . . . .
Valentina Savini

343

24 Socio-Vital Areas Analysis a Qualitative Approach to Sociological
Analysis of Urban Spaces and Social Life . . . . . . . . . . . . . . . . . . . . .
Gabriele Di Francesco

365

25 Knowledge Creation Processes Between Open Source
Intelligence and Knowledge Management . . . . . . . . . . . . . . . . . . . . .
Stefania Fantinelli

377

26 Cultural and Natural Heritage Challenges . . . . . . . . . . . . . . . . . . . .
Zdena Rosická

389

27 Cultivating Storytelling Practice: “Every Uses of Words
to Everybody” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fiorella Paone

401

28 Sociological Methods and Construction of Local
Welfare in Italy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vincenzo Corsi

413

29 Some Aspects of Social Life in Romanian Villages

in the Interwar Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Daniel Flaut and Enache Tuşa

425


Summary

The book “Mathematical-Statistical Models and Qualitative Theories for Economic
and Social Sciences” is part of the important series “Studies in Systems, Decision
and Control” published by Springer. This is the result of a scientific collaboration,
in the field of economic and social systems, among experts from “University of
Defence” in Brno (Czech Republic), “G. d’Annunzio” University of Chieti-Pescara
(Italy), “Pablo de Olavide” University of Sevilla (Spain), and “Ovidius University”
in Constanţa, (Romania).
The first part of the book deals with “Recent Trends in Mathematical and Statistical Models for Economic and Social Sciences,” whereas the second one concerns “Recent Trends in Qualitative Theories for Economic and Social Sciences.”
The variety of the contributions developed in this book reflects the heterogeneity
and complexity of economic and social phenomena; thus, a large spectrum of
problems related to statistics, mathematics, teaching, social science, and economics
has been presented in this volume. Therefore, a broad range of tools and techniques
that may be used to solve problems on these topics has been presented in detail.
Due to the wide range of topics of the presented research results, this
peer-review book is addressed, in equal measure, to mathematicians, statisticians,
sociologists, philosophers, and specialists in the fields of communication, social,
and political sciences.

xvii


Part I

Recent Trends in Mathematical
and Statistical Models for Economic
and Social Sciences


Chapter 1

Correlational Research of Expenditure
Spend on Slovak Armed Forces
Participation in Peace Support Operations
Led by NATO
Veronika Mitašová, Ján Havko and Tomáš Pavlenko

Abstract The expenditure which Ministry of Defence of the Slovak Republic
spends on Armed Forces members’ participation in peace support operations led by
the North Atlantic Treaty Organisation is dependent on many factors. The main aim
of this chapter is to find out the dependence level of this parameter from two
selected factors, namely the level of defence expenditure and the GDP of the Slovak
Republic. For this purpose the multifactor single-equation econometric model is
created and tested. Based on the tests results, conclusions and proposals for further
examination are formulated.
Keywords Peace support operation
model

1.1

⋅

Expenditure

⋅

Correlation

⋅

Econometric

Introduction

Nowadays, peace support operations are an effective tool for conflict prevention and
conflict resolution in problematic areas of the world. Mentioned type of operation is
under the auspices of the international crisis management organizations. International organization of collective security, the North Atlantic Treaty Organisation
(“NATO”), has undoubtedly a significant place among them.

V. Mitašová (✉) ⋅ J. Havko ⋅ T. Pavlenko
Faculty of Security Engineering, University of Žilina, Univerzitná 1, Žilina Slovak Republic
e-mail:
J. Havko
e-mail:
T. Pavlenko
e-mail:
© Springer International Publishing AG 2017
Š. Hošková-Mayerová et al., Mathematical-Statistical Models and Qualitative Theories
for Economic and Social Sciences, Studies in Systems, Decision and Control 104,
DOI 10.1007/978-3-319-54819-7_1

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V. Mitašová et al.

This contribution is focused on the assessment of factors, which affects participation of the Armed Forces of the Slovak Republic in NATO peace support
operations. It is necessary to identify and understand what influences the amount of
finance spent on these operations from state budget of the Slovak Republic (“the
SR”). Based on the input data the multifactor single-equation econometric model is
created and tested. According to the results of each test, the hypothesis, that the
amount of the expenditure which Ministry of defence (“MoD”) of the SR spend on
Armed Forces members’ participation in peace support operations led by NATO is
dependent on the defence expenditures and GDP of the SR, is confirmed or refuted.

1.2

Qualitative Analysis and Input Data

Before econometric model creation, it is necessary to do qualitative analysis, which
means assessing relations between variables. In the contribution it will be verified,
if the estimated correlation among the amount of finance spend on the Slovak
Armed Forces members participation in NATO peace support operations, the
defence expenditures and the level of GDP exists or not.
It can be assumed, that the amount of finance, which states spend on participation of their armed forces in peace operations, is affected by a lot of factors.
Table 1.1 shows some of them.
For the purpose of creating and testing econometric model we should work with
factors mentioned above, but because of many reasons, we will work only with data
listed in the Table 1.2. First factor, variable x1, is defence expenditure of the SR.
This kind of data is publicly available on the official website of MoD of the SR, but
only since 2001. Second factor, variable x2—GDP of the SR, is available on the

Eurostat portal. Third one, variable x3, could be number of completed and ongoing
peace support operations led by NATO. Although the information about number of

Table 1.1 Factors affecting the amount of expenditure spend by MoD of the SR on Armed Forces
members’ participation in peace support operations led by NATO
Variable

Factors

Amount of expenditure spend by MoD of the
SR on Armed Forces members’ participation
in peace support operations led by NATO

Defence expenditure of the SR
GDP of the SR
Number of completed and ongoing peace
support operations led by NATO
Global security environment
Number of military personnel in the SR
Number of Slovak troops deployed in peace
operations led by international crisis
management organizations
Costs of military personnel training
Others


1 Correlational Research of Expenditure Spend on Slovak …

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Table 1.2 Input data
Year

2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
Source

Amount of expenditure spend by
MoD of the SR on Armed Forces
members’ participation in peace
support operations led by NATO in
million Euro (y)

Defence expenditure of
the SR at current prices in
million Euro (x1)

4.35943
632
3.414446

662
12.809034
762
15.170682
762
14.720513
848
23.293318
898
16.069106
929
17.62134
994
32.80862
967
37.572209
853
34.334504
763
38.209909
790
Eurostat (2015), Ivančík (2013), SIPRI (2015)

GDP of the SR at
current prices in
million Euro (x2)

23
25
29

33
38
44
54
64
62
65
68
71

572.9
971.7
489.2
994.6
489.1
501.7
810.8
413.5
794.4
897.0
974.2
096.0

completed and ongoing operations is available, it is difficult and also slightly
mistakenly uses these data as a total number of peace support operations led by
NATO in the individual year. Some operations are ongoing throughout the year,
others only in certain months. More appropriate would be, in this case, to examine
the correlation between the amount of expenditure spend by MoD of the SR on
Armed Forces members’ participation in peace support operations led by NATO
and the number of peace support operations during particular months. However,

because of other data distribution, it is not possible. The same problem is in the case
of another factor, variable x6—the number of Slovak troops deployed in peace
operations led by international crisis management organizations. The number of
troops in peace support operations may change through the operation, and this
number is often slightly different from the mandate. Even though variable x4, which
is global security environment, affects the amount of expenditure spend by MoD of
the SR on Armed Forces members’ participation in peace support operations led by
NATO, it is not a numerical quantity, so it would not be possible to use it in our
econometric multifactor model. Other two variables, x5—the number of military
personnel in the SR and x7—costs of military personnel training, would be
appropriate to examine, but they are not available (Hošková-Mayerová 2017).
The small range of data is influenced by the fact, that the SR is relatively young
country, but also a lot of needed information are confidential or they are not
publicly available.
Based on the data in the Table 1.2, it is possible to notice a growing trend of
expenditure for peace support operations led by NATO. The expenditure had
increased in 12 years more than nine times. A similar trend is in the development of


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GDP, which increased three times during the 12-year period. On the contrary,
defence expenditures of the SR maintain approximately the same level.

1.3

The Construction of Econometric Model
and Its Testing

It is possible to create and to test econometric model in different ways, from
laborious and difficult calculation through different software. The results in this
contribution were gained through MS Office Excel tools and STATISTICA software. Data sources were SIPRI database (Stockholm International Peace Research
Institute) and Eurostat.
The particular regression equation, which expresses the relation between
dependent variable y (expenditure of MoD on participation of the Slovak Armed
Forces in peace support operations led by NATO in million Euro) and explanatory
variables x1 and x2 (defence expenditure at current prices in million Euro and GDP
of the SR at current prices in million Euro), can be written in the form:
y ∧ = 4.1035 − 0.0199x1 + 0.0007x2 + u

ð1:1Þ

The value of the parameter b1 = −0.0199 indicates, that the increase of defence
expenditure by 1 million Euro will reduce the amount of expenditure on the Slovak
Armed Forces participation in NATO peace support operations by 19,900 Euro,
while GDP remains unchanged. The value of the parameter b2 = 0.0007 indicates,
that increase of GDP by 1 million Euro will increase the expenditure on the Slovak
Armed Forces participation in NATO peace support operations by 700 Euro,
providing defence expenditure remained unchanged.
Multiple R = 0.8949 means, that there occurs a very strong positive correlation
in the econometric model. The value of reliability R2 = 0.8008 can be interpreted,
that about 80% of the explaining variable variability is explained by the variability
of explanatory variables. Remaining 20% of the explaining variable variability,
which is amount of expenditure spend by MoD of the SR on Armed Forces
members’ participation in peace support operations led by NATO, is explained by
other variables (Table 1.3).
Graphical representation of variables y, x1, x2 distribution is in the Figs. 1.1, 1.2
and 1.3. On the right side of these figures are values characterizing variables,

namely minimum, maximum, standard deviation or median.

Table 1.3 Basic statistical
values of the econometric
model

Summary statistics
Multiple R
Multiple R2
Adjusted R2

0.8949
0.8008
0.7566


1 Correlational Research of Expenditure Spend on Slovak …

Fig. 1.1 Graphical summary for variable y

Fig. 1.2 Graphical summary for variable x1

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Fig. 1.3 Graphical summary for variable x2

Econometric model must be tested after its creation, thus it is possible to conclude whether the model is applicable for practical needs. These tests are testing
model as a whole through the coefficient of determination R2 tested by Fisher’s
statistics (F-statistic), testing parameters of variables through Student’s probability
distribution (t-statistics), testing of residuals autocorrelation (we have <15 observations, so we will use Von-Neumann ratio and D-statistics). Verification of
heteroscedasticity, respectively homoscedasticity, is made by Goldfield and Quandt
test. The last test is used to find out the presence of multicollinearity in the model.
For this purpose, we will use Farrar and Glauber method, where the correlation
matrix is tested through Chi-square (Mikolaj and Vančo 2004; Ristvej and
Kampová 2009).
Because of comprehensive testing procedures, there will be stated only particular
resultant values of tests and conclusions related to them.

1.3.1

Testing of Econometric Model as a Whole

The value of determination coefficient R2 is 0.8008. It means, that approximately
80% of the amount of expenditure spend by MoD of the SR on Armed Forces
members’ participation in peace support operations led by NATO variability is
explained by the variability of defence expenditure and GDP in the SR. Remaining
nearly 20% of the explaining variable variability is affected by other factors, which


1 Correlational Research of Expenditure Spend on Slovak …

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are not included in the model. F-statistic test was performed at a significance level
0.05.

Therefore, if the model would be significant as a whole, the inequality (1.2) has
to be valid.
Fr > Fα; k; ½n − ðk + 1ފ

ð1:2Þ

The value of Fr = 18.0938 and F0,05, 2, 9 = 4.2565, consequently, the determination coefficient of on the significance level 0.05 is considered as a significant and
the model as a whole is considered as a statistically significant too.

1.3.2

Testing of Variables Parameters Through t-Statistics

Both of parameters, b1 = 0.0199 and b2 = 0, 0.0007, are tested at the significance
level 0.05. To consider parameter as a statistically significant, the inequality (1.3)
has to be valid.
jti j > tα; ½n − ðk + 1ފ

ð1:3Þ

In the case of parameter b1, after substituting into inequality 0.9811 < 2.2622, it
does not apply. It means that the parameter b1 at the significance level 0.05 is not
considered as statistically significant. After substituting into inequality in the case
of parameter b2, inequality form is 5.2772 > 2.2622. Based on it, we can formulate
conclusion that inequality applies, therefore, the parameter b2 at significance level
0.05 is considered as statistically significant.

1.3.3

Testing of Residuals Autocorrelation

Testing of residuals autocorrelation for <15 observations is carried out by
Von-Neumann ratio. To autocorrelation verification the calculated value is compared to the tabulated one, while the inequality (1.4) has to apply.
D+ < D < D−

ð1:4Þ

Value of D+ = 1.2301, D− = 3.1335 and D = 2.0705, therefore, the inequality
applies. We conclude autocorrelation of residuals absents in our econometric
model.


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1.3.4

V. Mitašová et al.

Testing of Heteroscedasticity

It is necessary to test heteroscedasticity for each variable x (x1 and x2). For the
hypothesis “scatter of residuals is constant, there is homoscedasticity of residuals in
the model” acceptation, inequality (1.5) has to apply, whereby the value v means
degree of freedom.
F2, 1 ≤ Fαðv, vÞ

ð1:5Þ

It is calculated according to Eq. (1.6). The value v = 2 and tabulated value
F0.05;(2,2) = 19.

v=½

ðn − M Þ
Š − ðk + 1Þ
2

ð1:6Þ

After substituting into inequality in the case of variable x1, it is 1.6852 < 19, in
the case of variable x2, it is 1.4757 < 19. Therefore, the inequality applies in both
cases, we conclude, that heteroscedasticity of residuals absents in our model. For
better expression of values, in the Fig. 1.4 are shown predicted and observed values
of variable y.

Fig. 1.4 Graph of predicted and observed values of variable y