Subjective perception of quality of life – multidimensional analysis based on the fuzzy sets approach

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Publishing House of Wrocław University of Economics Wrocław 2016

Quality of Life.

Human and Ecosystem Well-being

PRACE NAUKOWE

Uniwersytetu Ekonomicznego we Wrocławiu

RESEARCH PAPERS

of Wrocław University of Economics

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Copy-editing:RafałGalos Layout:BarbaraŁopusiewicz Proof-reading:BarbaraŁopusiewicz Typesetting:AdamDębski Coverdesign:BeataDębska Informationonsubmittingandreviewingpapersisavailableonwebsites: www.pracenaukowe.ue.wroc.pl www.wydawnictwo.ue.wroc.pl ThepublicationisdistributedundertheCreativeCommonsAttribution3.0 Attribution-NonCommercial-NoderivsCCBY-NC-ND © CopyrightbyWrocławUniversityofEconomics Wrocław2016 ISSN 1899-3192 e-ISSN 2392-0041 ISBN 978-83-7695-590-2 Theoriginalversion:printed PublicationmaybeorderedinPublishingHouse WydawnictwoUniwersytetuEkonomicznegoweWrocławiu ul.Komandorska118/120,53-345Wrocław tel./fax713680602;e-mail:econbook@ue.wroc.pl www.ksiegarnia.ue.wroc.pl Drukioprawa:TOTEM

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Introduction

OnSeptember21-22,2015,6thInternationalScientificConference“QualityofLife 2015.HumanandEcosystemsWell-being”washeldinWrocław. Theconferencewasapartofthecycleoftheconferencesonthetopicofquality oflifethathavebeenorganizedbytheDepartmentofStatistics(WrocławUniversity ofEconomics)since1999.Theaimofthecycleistoparticipateinthestillrising alloverthewordwaveofscientificstudiesonqualityoflife:ethicalbackground anddefinitionsofqualityoflife,investigating(howtomeasureit),presentingthe resultsofdifferencesofqualityoflifeovertimeandspace,itsinterdependences with natural environment, mathematical methods useful for the methodology ofmeasuringqualityoflifeandfinally–possiblemethodsofimprovingit.The conferencesaremeanttointegratethePolishscientificcommunitydoingresearch onthesetopicsaswellastomakecontactswithforeignscientists.

ThisyearourhonoraryguestwasProfessorFilomenaMaggino,pastPresident of International Society for Quality-of-Life Studies (ISQOLS), who presented aplenarylecture. Wehostedabout30participants,amongthemscientistsfromSpain,Romania, ItalyandJapan.Wehad24lecturesonsuchavarietyoftopicsascarbonfootprint andmathematicalpropertiesofsomeestimators.Thecommonbackgroundofall ofthemwastobettercomprehend,measureandpossiblytoimprovethequalityof humans’life. Thepresentvolumecontainstheextendedversionsofsomeselectedlectures presented during the conference. We wish to thank all of the participants of the conference for co-creating very inspiring character of this meeting, stimulating productivediscussionsandresultinginsomepotentiallyfruitfulcooperationover new research problems. We wish also to thank the authors for their prolonged cooperationinpreparingthisvolume,thereviewersfortheirhardworkandformany valuable,althoughanonymous,suggestionsthathelpedsomeofustoimprovetheir works.

Finally, we wish to thank the members of the Editorial Office of Wrocław University of Economics for their hard work while preparing the edition of this volume,continuouskindnessandhelpfulnessexceedingtheirdutiesofthejob.

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PRACE NAUKOWE UNIWERSYTETU EKONOMICZNEGO WE WROCŁAWIU

RESEARCH PAPERS OF WROCŁAW UNIVERSITY OF ECONOMICS nr 435 ● 2016

Quality of Life. Human and Ecosystem Well-being ISSN 1899-3192 e-ISSN 2392-0041

Hanna Dudek, Wiesław Szczesny

WarsawUniversityofLifeSciences

e-mails:hanna_dudek@sggw.pl;wieslaw_szczesny@sggw.pl

SUBJECTIVE PERCEPTION OF QUALITY OF LIFE –

MULTIDIMENSIONAL ANALYSIS

BASED ON THE FUZZY SETS APPROACH

SUBIEKTYWNE POSTRZEGANIE JAKOŚCI ŻYCIA –

WIELOWYMIAROWA ANALIZA

NA PODSTAWIE PODEJŚCIA WYKORZYSTUJĄCEGO

ZBIORY ROZMYTE

DOI:10.15611/pn.2016.435.03

Summary: The study presents a multidimensional approach to an analysis of subjective assessment of the quality of life using the fuzzy set theory.The analysis uses the survey datafrom“SocialDiagnosis”researchconductedin2013.Itincludes16itemsrelatingtothe evaluationofsatisfactionwithparticularaspectsoflife.Eachoftheseitems,measuredona 7-gradescale,isconvertedintoa[0,1]intervalbyusingamembershipfunction.Toaggregate itemsintosyntheticindicatorsthestudyemploysBettiandVermaweightingproceduretaking intoaccountdifferentiationofitemsandthecorrelationamongthem.Toassesstheanalyzed phenomenoninthewholepopulationandselectedsub-populationssomesummaryindices arecomputed.Forthispurposethecounterpartsofincidence,depthandinequalitymeasures appliedinpovertyanalysisareproposed.Suchanapproachenablestheevaluationoflife satisfactioninthewholesampleofindividuals.ItisfoundthatPoleswerebestsatisfiedwith socialaspectsandworst–withenvironmentalaspects.Moreoverwomenwereslightlyworse-offthanmenandabettereducationcorrespondedtoamorepositivequalityoflifeperception. Keywords:qualityoflife,fuzzysetapproach,multidimensionaldataanalysis. Streszczenie:Wpracypodjętotematwielowymiarowejanalizysubiektywnegopostrzegania jakości życia z zastosowaniem teorii zbiorów rozmytych. W analizie wykorzystano dane z badania „Diagnoza Społeczna” przeprowadzonego w 2013 r. Uwzględniono 16 cech mierzonychnaskaliporządkowejodnoszącychsiędoocenywłasnegozadowoleniazróżnych dziedzin i aspektów życia. Cechy te przekształcono za pomocą funkcji przynależności w cechyowartościachzprzedziału[0,1].ZapomocąwagwyznaczonychmetodąBettiegoi Vermyskonstruowanosyntetycznewskaźnikisubiektywnejpercepcjiżycia.Wceluoceny analizowanegozjawiskawcałejpopulacjiiwwybranychsubpopulacjachobliczonośrednie wartościtychwskaźnikóworazwartościmiarbędącychodpowiednikamiindeksówzasięgu, głębokościinierównomiernościstosowanychwanalizieubóstwa.Stwierdzono,żenajlepiej ocenianoaspektyspołecznejakościżycia,najgorzejzaś–aspektyśrodowiskowe.Ponadto

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56 HannaDudek,WiesławSzczesny oszacowano,żekobietyniecogorzejpostrzegałyswojąsytuacjęniżmężczyźniorazlepsza edukacjaodpowiadałabardziejpozytywnejpercepcjijakościżycia.

Słowa kluczowe: jakośćżycia,zbioryrozmyte,wielowymiarowaanalizadanych.

1. Introduction

Inrecentyears,intheanalyzesofthequalityoflife,agrowinginterestofsubjective indicatorscanbeobserved.Suchanalyzesareconductedbythepublicstatistics,as wellasinternationalorganizationsandresearchcenters.Indicatorsofsatisfaction withvariousaspectsofpersonalandsociallifeareregardedasanimportantpartof monitoringthesocialsituation.Theyallowforacomparisonofsubjectivefeelings ofpeoplewithobjectivedataonlivingconditions.Thustheyareanindispensable andcrucialelementinthemultidimensionalmeasurementandtheanalysisofthe qualityoflife.

The measurement of the subjective quality of life in Poland is carried out, among others, in the “Social Diagnosis” research. Due to the complexity and multidimensionalityofthesubjectmatter,inthequestionnairesofthissurveyalot ofquestionsaboutsatisfactionofrespondentsareincluded.Theyrelatetovarious dimensions referring to the social, material, environmental, health spheres and others.Inourstudyweusethisdatacollectedintheframeofthethisresearchand weconsidersubjectiveperceptionofthequalityoflifetobea“fuzzy”concept.This approachusesamembershipfunctiontocaptureeachindividual’sdegreeofinclusion tothesatisfiedset,yieldingscoresthathavevaluesfrom[0,1]interval.Inorder toassessamultidimensionalphenomenonofsatisfactionwithlife,thescoresare aggregatedintosyntheticindicators.Averagingtheseindicatorsleadstoobtaining summaryindicesforthewholesamplepopulationorforthesuitablesubpopulations. Togetadeeperinsightintotheanalyzedphenomenonameasurementofincidence, depthandinequalityofsatisfactionwithlifecanbeundertaken.Toevaluatethese issuesweproposeourownindices. Intheliteraturethereisasmallnumberofstudiesexamininglifesatisfactionin Polandfromthemultidimensionalperspective1_{.Wehopethatourpaperfillsinthis} gaptosomeextentbycreatingapictureofasubjectiveperceptionofthequalityof lifeforPolandbyadoptingafuzzysetapproach. 1 _{Topapersinthisfieldonecanincluderesearch[Struzik,Struzik,Szwarc2015]onchildren’s} subjectivewell-being.

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Subjectiveperceptionofqualityoflife–multidimensionalanalysis… 57

2. Data

Theanalysisusesthesurveydatafrom“SocialDiagnosis”researchconductedin 2013.Themainobjectiveofthissurveyistoprovideanassessmentoftheliving conditionsandthesubjectiveperceptionofqualityoflifeofthePolishpopulation. Twoseparatequestionnairesareusedin“SocialDiagnosis”project.Thefirstisa sourceofinformationaboutahouseholdcompositionandlivingconditionscompleted bytheinterviewerduringameetingwithonebest-informedhouseholdrepresentative. Thesecondquestionnaireiscompletedbyallavailablemembersofagivenhousehold aged16ormoreandcontributesinformationaboutindividualpersons’qualityoflife [Czapiński,Panek2014].In2013thesurveyinvolved12,355householdsand26,307 householdmembersover16yearsofage.Sinceweareinterestedinasubjective assessmentofthequalityoflifeweusethedatabaseincludinginformationfrom individualpersons. AccordingtoCzapiński[2014]themostrealisticintheevaluationofthelevel of well-being is a study of satisfaction with particular areas and aspects of life. “SocialDiagnosis”researchtakesintoaccount16differentitemsexhaustingnearly theentirescopeofinterestsandactivitiesofanaverageperson.Inareportofthe researchtheseitemsareassignedintofivedimensionsregardingto: • socialaspects(satisfactionwithrelationshipswithclosefamilymembers,friends, spousesandchildren), • materialaspects(satisfactionwiththefinancialsituationofthefamilyandwith thehousingconditions), • environmentalaspects(satisfactionwiththesituationinthecountry,theplaceof residence,thelevelofsafetyintheplaceofresidence), • health-relatedaspects(satisfactionwithone’shealthcondition,withtheirsex--lifeandthewayofspendingtheirfreetime), • aspectsrelatedtoaself-assessment(satisfactionwithone’sownachievements, prospectsforthefuture,educationallevel,work). Respondentswereaskedtoassessall16areasoftheirlife andindicatetheextent ofsatisfactionwiththem.Theyhaveachoiceofreplies:1)verysatisfied,2)satisfied, 3) rather satisfied, 4) rather not satisfied, 5) not satisfied, 6) very dissatisfied, 7)notapplicable.Inourstudyweassignvalue3.5tothoseindividualswhoindicated answer“7”andtothosewhodidnotgiveanyanswers,thusweattributethema neutralposition.

3. Methods

Theapplicationofthefuzzysetapproachrequiresthreesteps: 1) identificationoftherelevantitemsandgroupingthemintodimensions, 2) definitionofafunctionalformforthemembershipfunction, 3) choiceofaweightingmethodtoaggregateitemsintoasingleindicator.

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58 HannaDudek,WiesławSzczesny Concerningthefirstpoint,weanalyze16itemsgroupedinto5dimension2_.In thesecondstepweconstructamembershipfunctionforeachitem.Severalmethods havebeenproposedintheliterature3_{(seeforexample[Cerioli,Zani,1990;Betti,} Verma2008])forit.Weoptforamethodusingtheempiricaldistributionfunctionof eachitem.Suchanapproachtakesintoaccountarelativepositioninthesocietyina givenfield.Weusetheformulaproposedin[Cheli,Lemmi1995]: d F c F k j i, , k j i, , ( ) ( ) , = − − 1 1 1 (1)

where: c_k,j,i – category of the j-th item in k-th dimension for the i-th individual, 1≤c_k,j,i ≤6; F –correspondingcumulativedistributionfunctions.

Accordingtoformula(1)theitem’scategoriesareconvertedintoa[0,1]interval. Inthiscontext,thescoredcanbeinterpretedasthemembershiplevelinthevirtual setofsatisfiedpeople,inparticularvalue0referstocompletedissatisfaction(c =6) andvalue1tocompletesatisfaction(c =1).

As in the case of the selection of membership function, there are several approachestochooseweightsforaggregatingdifferentitemsineachdimension(see forexample[Desai,Shah1988;Cheli,Lemmi1995;Filippone,Cheli,D’Agostino 2001; Lazim, Osman 2009]. In the study we use the method proposed by Betti andVerma[1999].Ourchoicemaybesupportedbythefollowingarguments:this methodgiveslessimportancetopoorlydifferentiateditemsandittakesintoaccount theproblemofdataredundancy.Accordingtothesepropertiestheweightscanbe definedasfollows[Betti,Verma1999]: Wk j, =W Wk ja, ⋅ k jb, , (2) where: Wk ja, =Vk j, , (3)

V_k,j–thecoefficientofvariationforj-thscored in the k-thdimension.

BettiandVerma[1999]suggestthatthecoefficientofvariationofeachscored canbeusedasthefirstfactor,andthesecondfactorcanbeobtainedbyapplyingthe followingformula: 2 Toidentifydimensionsonecanusestatisticalmethods(forexamplefactoranalysis)[Betti,Ver-ma2008],butinthisstudyweuseaclassificationappliedin“SocialDiagnosis”Report.Accordingto itwehave5dimensionsencompassing16items. 3 _{Fuzzysettheoryhasbeenappliedinvarioussocio-economicareassuchasmeasurementof} poverty[Cheli,Lemmi1995;Betti,Verma2008;Panek2010],jobsatisfaction[DeBattisti,Marasini, Nicolini2015],qualityoflife[Lazim,Osman2009;Bettietal.2015].

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Subjectiveperceptionofqualityoflife–multidimensionalanalysis… 59 W r r r r r k jb k jj k jj k j m k jj k j k , , ' , ' * ' , ' , | | = + <             ⋅ =

∑

1 1 1 1 j jj k m r k ' * ' , ≥             =

∑

1 (4)

where: isthecorrelationcoefficientbetweentwodifferentscoresd_k,j and d_k,j’; isapredeterminedcut-offcorrelationlevelinthek-thdimension;m_kisthetotal numberofitemsinthek-thdimension. Thresholds canbedeterminedinmanyways,e.g.BettiandVerma[2008] suggesttousethepointofthelargestgapbetweentheorderedsetofcorrelation valuesencountered,whilePanek[2011]proposestoapplythefollowingformula: rk*=min max_j _{j j}_'_≠ rk jj, ' . (5) Theweightsaredeterminedwithineachdimensionseparately.Theyreflectthe relativeimportanceofitemsincontributingtoanindividuallevelofsatisfactionin agivenaspectoflife.Scalingthemtosum1withineachdimensionisconvenient: w W W k j k j k j j mk , , , . = =

∑

1 (6) Theapplicationofthemembershipfunctiontoeachitemproducesanumberof standardizedvariables(scoresd)thatrangebetweenzeroandone.Thereforesuch variablesareexpressedinthesameunitofmeasurementandcanbeaggregated.The indicatorsderivedaccordingtothismaybeconsideredasindicatorsofasubjective perceptionofthequalityoflife.Fori-thindividual,aggregationoverasetofitems in a k-thdimension(k=1,2,…,5)isgivenbyformula[Bettietal.2015]: S_{k i} w d_{k j k j i} j mk , = , , ,, =

∑

1 (7) andanoverallcompositeindicatorforthei-thindividualiscalculatedas: S K S i k i k k = =

∑

1 1 , , (8) where K–numberofdimensions.

For sub-indicators (7) and overall indicator (8) aggregated indices can be typicallyderivedonthebasisofsampledata: S n S k K k k i i n = = =

∑

1 _{1 2} 1 , , , ,.., , ₍₉₎

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60 HannaDudek,WiesławSzczesny S n Si i n = =

∑

1 1 , (10) where n–numberofindividualsinthewholepopulation;K–numberofdimensions. Thisapproachtoconstructindicesisthesimplestandthemostcommonstrategy intheliteratureonmultidimensionalanalysis[Deutsch,Silber2005].Suchsummary indicesenabletoassesstheaveragelifesatisfactioninthewholepopulation. Inthenextstepofanalysis,togetadeeperinsightintotheundertakensubject matter,wemeasureincidence,depthandinequalityoflifesatisfaction.Wepropose to apply counterparts of appropriate summary indices used in classical poverty analyses. In one-dimensional analyses the most popular indices are FGT indices namedafterFoster,GreerandThorbecke4_: P n gi i n α = α =

∑

1 1 , (11) where:g y y y i = i −      

max * _* ,0 ,y_i–incomeofi-thindividual,y*_{–povertythreshold}

(povertyline),α–parameter,α=0,1,2. • With α=0,theformula(11)reducestothepovertyincidence(headcountratio), i.e.thefractionofthepopulationlivingbelowthecertainthresholdnamedthe povertyline:

P n

n

u 0

=

,wherenu–numberofpoorindividuals(i.e.thenumberof thosewhoseincomedoesnotexceedy*_{),n–numberofindividualsinthewhole} population. • With α=1,theformula(11)yieldsdepthofpovertyindex(povertygapindex): P n y y y i i nu 1 1 1 =  −      =

∑

* * .P1takesintoaccounttheextenttowhichindividualsfall belowthepovertylineasaproportionofthepovertyline. • With α=2,theformula(11)givestotheaverageofsquarerelativepovertygap inthepopulationP n y y y i i nu 2 1 2 1 =  −      =

∑

* * . P2iscalledseverityofpovertyindex,it capturesdifferencesinincomelevelsamongthepoor. InthemultidimensionalapproachtopovertytherearesomeextensionsofFGT indices[Alkireetal.2015;Bourguignon,Chakravarty2003;Fosteretal.2010; Panek 4 _{Thisclassofdecomposablepovertyindiceswasproposedinafamouspaper[Foster,Greer,} Thorbecke1984].

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2010].InourstudywefocusonBourguignonandChakravartymethodbecausewe thinkitcanbeadoptedtothemeasurementoflifesatisfaction.

Bourguignon and Chakravarty [2003] build a class of multidimensional povertymeasuresthatextendstheFGTindicestomanydimensions.Theytakeas afundamentalstartingpointshortfallsfromthresholdsoneachdimensionofan individual’swell-being:

MP

n

w g

k ki i n k K α

=

α = =

∑

1

1 1

,

(12) where:g y y y ki k ki k = _ −    

max * _* ,0 ;y_ki–attributeofpovertyofi-thindividualink-th dimension,i=1,..,n,k=1,…,K; –povertythresholdink-thdimension;w_k–weight for k-th dimension, k=1,..,K; K – number of dimensions in poverty analysis; n – numberofindividualsinthewholepopulation;α–parameter,α=0,1,2. Weadoptformula(12)inthemeasurementoflifesatisfaction.Inourstudywe have2obviousthresholdsforanswer“3”meaning“rathersatisfied”andtoanswer “4”–“rathernotsatisfied”.Foreachofthesethresholdsforj-thitemink-thdimension wecancomputecorresponding“criticalvalues”ds_{(for3–rathersatisfied)andd}ns (for4–rathernotsatisfied).Moreformally,forscored_k,_j,_iobtainedbyformula(1),

wedefine: and .Valueg_k,_j,_i

meansarelativegapfori-thindividualwhichissatisfied(relativedistanceofvalue d_k,_j,_ifromthresholdds_)andh

k,j,idenotesarelativegapfori-thindividualwhichis

unsatisfied (relative distance of value d_k,_j,_i from threshold dns_{). We construct life}

satisfactionindicesas:

LS

nK

w g

k j k j i j m k K n n k α

=

α = = =

∑

1

1 1 1 , , , (13) andsimilarlylifedissatisfactionindicescanbedefinedas:

LDS

nK

w h

k j k j i j m k K n n k α

=

α = = =

∑

1

1 1 1 , , ,

,

(14) where:w_k,j–theweightassignedtoj-thiteminthek-thdimension;m_k–thetotal numberofitemsinthek-thdimension;K–numberofdimensions;n–numberof individualsinpopulation;α–parameter,α=0,1,2.

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62 HannaDudek,WiesławSzczesny

Inparticular,

• for α=0wehaveLS₀ and LDS₀ –incidenceofsatisfactionandincidenceofdis-satisfaction,denoting,respectively,percentageshareinpopulationofsatisfied individualsandunsatisfiedindividuals;

• for α=1weobtainLS₁ and LDS₁ –depthofsatisfactionanddepthofdissatisfac-tion; • for α=2–inequalityofsatisfactionandinequalityofdissatisfaction. Inouropinionsuchindicesareusefulinthequalityoflifemeasurement.

4. Results

Inouranalysisweinvestigate5dimensionsencompassing16items.Allitemsare convertedbymembershipfunction(1)intoscores.Inordertocalculateweightsfor themweappliedtheStataproceduremdepriv5_{[PiAlperin,VanKerm2014].These}

weights are used to obtain synthetic indicators of a subjective perception of the qualityoflife.Next,toassesstheanalyzedphenomenoninagivenpopulation,some summaryindicesarecomputed.

Theempiricalresultsofthestudyarereportedintables1-3.Alltablespresent thediversityofsatisfactionwithlifeduetothegenderandeducationalstatus.Two groups regarding educational status are examined: the first refers to those who attained secondary, post-secondary or higher level of education and the second concerns poorly educated people involving persons with basic, lower secondary, vocationallevelorwithouteducationalattainment.

Table1reportstheoverallaggregateindexSandtheindicesS₁,S₂,S₃,S₄,S₅ corresponding to the five dimensions (computed accordingly by (10) and (9) formulas). Moreover it provides information about incidence of satisfaction and dissatisfaction. Asshownintable1Poleswerebestsatisfiedinrelationshipswithotherpeople (socialaspects)andtheworst–withenvironmentalaspects.Ourresultsindicatethat near60%ofthepopulationexhibitedpositiveassessmentoflifeandonly3%ofthe samplepopulation–anegativeperceptionoflife.Theremainingpart,containing 37%,relatestoneutralattitudes6_{.Whatisinteresting,onlylessthan1%ofthepeople} hadabadopinionabouttheirownrelationshipswithotherpeopleandmorethan70% –positivelyvaluatedthesesocialaspects.Theincidenceofsatisfactionisespecially lowinthedimensionreferringtotheaspectsrelatedtoaself-assessment–lessthan 40%ofindividualsevaluatedwelltheirownachievements,prospectsforthefuture, theireducationallevelandwork.Ontheotherhand,headcountratios,placedinthe 5 _{Wefoundamongallpairsofscoresingivendimensionweakormoderatelystrongpositive} correlations.Foralldimensionsthresholdr*=0.3isused. 6 _{NeutralattitudesconcernsuchcasesforwhichLS0waslessthan“criticalvalue”corresponding} toanswer“3–rathersatisfied”andLDS0wasgreaterthan“criticalvalue”correspondingtoanswer “4–rathernotsatisfied”.LS0andLDS0aredefinedrespectivelybyformulas(13)and(14).

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Subjectiveperceptionofqualityoflife–multidimensionalanalysis… 63 Tables 1. Basicsummarystatisticsforcompositeindicatorsoflifesatisfaction

Index

Overall 1Social ₂Material

3 Environmental ₄Health-related 5 Self-assessment Aggregateindexoflifesatisfaction 0.4012 0.4357 0.4040 0.3740 0.4112 0.3811 –women 0.3963 0.4438 0.4030 0.3715 0.3939 0.3690 –men 0.4062 0.4212 0.4053 0.3770 0.4323 0.3952 –atleastsecondarylevelofeducation 0.4318 0.4570 0.4358 0.3800 0.4469 0.4391 –pooreducationallevel 0.3719 0.4154 0.3735 0.3682 0.3770 0.3254 Incidenceofsatisfaction 58.91% 72.84% 69.95% 43.17% 63.12% 35.93% –women 58.01% 74.60% 69.89% 42.87% 59.84% 33.24% –men 60.04% 70.63% 70.03% 43.53% 67.22% 39.30% –atleastsecondarylevelofeducation 67.08% 75.35% 75.69% 45.61% 70.40% 47.11% –pooreducationallevel 51.08% 70.44% 64.44% 40.83% 56.13% 25.21% Incidenceofdissatisfaction 3.09% 0.72% 17.55% 24.11% 7.20% 11.87% –women 2.97% 0.62% 17.75% 24.41% 7.54% 12.21% –men 3.25% 0.85% 17.31% 23.74% 6.76% 11.55% –atleastsecondarylevelofeducation 1.64% 0.44% 13.09% 23.61% 4.68% 6.72% –pooreducationallevel 4.49% 0.98% 21.84% 24.60% 9.61% 16.80% Source:owncalculation. bottomofthetable1,indicatethatafractionofdissatisfiedindividualswiththese aspectswasabout12%.Itmeansthatabout50%ofindividualsexpresseddecidedly neitherapositivenoranegativeopiniononthismatter.Itshouldalsobenotedthat almost a quarter of the sample population was dissatisfied with environmental aspectstakingintoaccountthesituationinthecountry,theplaceofresidenceand thelevelofsafetyintheplaceofresidence.

Dividingthepopulationintosub-groupsaccordingtogender,itcanbeobserved thatwomenareslightlyworse-offthanmen.Onenotableexceptionisthesocial aspect. Taking into account educational status one can state that well-educated peopledefinitelybetterperceivedtheirqualityoflifethanpoorlyeducatedpeople. Thebiggestdifferencesbetweenthesetwogroupsrefertoaspectsrelatedtoaself-assessmentandthesmallest–toenvironmentalaspects.

Figure 1 presents cumulative distribution functions of overall composite indicators S for well-educated and poorly educated people. It highlights a few salientfacts.First,onecanfindthatincidenceofdissatisfactionforwell-educated peopleequalsabout1%andforpoorlyeducatedpeople–about4%(seevalueson verticalaxiscorrespondingtothresholdSds_=0.147_{),secondly,theseheadcountratios}

7 _{Weightedthresholdsd}us_{correspondingtoanswer“4”–“rathernotsatisfied”yieldthresholdsS}us

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64 HannaDudek,WiesławSzczesny

for satisfaction are about 67% and 51% respectively (see values on vertical axis correspondingtothresholdSs_{=0.35andsubtractthemfrom1).Moreoveritcanbe} seenthatmedianofoverallcompositeindicatorSforthefirstgroupisabout0.43and forthesecond–0.37.Generally,aworsesubjectiveassessmentofthequalityoflife amongpoorlyeducatedpeoplethanwell-educatedpeopleisvisible. Figure 1. ComparisonofoverallcompositeindicatorsSforwell-educatedandpoorlyeducatedpeople Source:owncomputation. Next,inordertoassessthedepthofsatisfactionanddissatisfactionwithlife valuesofLS₁ and LUS₁,definedrespectivelybyformulas(13)and(14),arecomputed andreportedintable2.

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Subjectiveperceptionofqualityoflife–multidimensionalanalysis… 65 Tables 2. Depthofsatisfactionanddissatisfaction

Indicator

3 Environmental ₄Health-related 5 Self-assessment Depthoflifesatisfaction 24.76% 63.92% 48.29% 17.38% 38.50% 12.12% – women 23.65% 65.80% 48.07% 17.08% 34.52% 11.03% – men 26.14% 61.57% 48.57% 17.75% 43.48% 13.50% – atleastsecondarylevelofeducation 30.17% 69.96% 55.28% 18.37% 45.52% 17.17% – pooreducationallevel 19.56% 58.13% 41.59% 16.43% 31.76% 7.28% Depthoflifedissatisfaction 0.84% 0.28% 7.32% 11.16% 2.62% 4.03% – women 0.77% 0.25% 7.41% 11.29% 2.64% 3.98% – men 0.91% 0.30% 7.21% 11.00% 2.61% 4.10% – atleastsecondarylevelofeducation 0.42% 0.19% 5.06% 11.01% 1.69% 2.21% – pooreducationallevel 1.23% 0.36% 9.49% 11.30% 3.52% 5.78% Source:owncalculation.

In general, it is found the depth of life satisfaction exceeds the depth of life dissatisfaction.Itmeansthatatleastgoodassessmentsofownlife(whichcorresponds totheanswer1or2)wereobservedmorefrequentlythanbadevaluationoflife (whichcorrespondstotheanswer5and6).Inotherwords,ontheaverage,theextent ofsatisfactionwasgreaterthantheextentofdissatisfaction8_{.Thisresultrelatestoall} dimensions,butparticularlyitisevidentforsocialaspects. Itisworthnoticingthatapoorassessmentofthefifthdimensionwasaccompanied bylowvaluesofdepths(seelastcolumnsintables1and2).Itmeansthatsatisfaction anddissatisfactionwere“shallow”here,whichonecaninterpretthatmostofpeople hadmoderate(neitherverygoodnorverybad)opinionsinthefieldoftheirown achievements,prospectsforthefuture,educationallevel,work.Takingintoaccount gender,onecanobservethatmenmorefrequentlythanwomenexhibitedextreme judgmentsonthismatter.

Turning to comparison groups with different educational status it was found thatinallaspectssatisfactionofwell-educatedpeoplewasdeeperthansatisfaction ofpoorlyeducatedpeopleandoppositerelationshipheldinregardstothedepthof dissatisfaction.

The next table provides information about diversities among satisfied and dissatisfiedpeople.

8 _{Amongsatisfiedpeopledistancesfromthresholdrelatingtoanswer“3–rathersatisfied”were}

greater,onaverage,thandistancesfromthresholdrelatingtoanswer“4–rathernotsatisfied”among unsatisfiedpeople.

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66 HannaDudek,WiesławSzczesny Tables 3. Inequalityofsatisfactionanddissatisfaction

Indicator

3 Environmental ₄Health-related 5 Self-assessment Inequalityoflifesatisfaction 3.1694 8.7776 1.5817 4.0885 0.9346 0.4644 – women 3.2283 9.1673 1.6075 4.0244 0.8796 0.4629 – men 3.0956 8.2898 1.5494 4.1688 1.0033 0.4664 – atleastsecondarylevelofeducation 3.4148 9.5541 1.7848 4.0991 1.0399 0.5963 – pooreducationallevel 2.9331 8.0306 1.3862 4.0777 0.8332 0.3378 Inequalityoflifedissatisfaction 0.0830 0.0168 0.0963 0.1485 0.0724 0.0810 – women 0.0833 0.0163 0.0968 0.1481 0.0749 0.0804 – men 0.0827 0.0175 0.0956 0.1491 0.0692 0.0819 – atleastsecondarylevelofeducation 0.0684 0.0131 0.0702 0.1402 0.0555 0.0630 – pooreducationallevel 0.0970 0.0204 0.1213 0.1566 0.0885 0.0984 Source:owncalculation. Table3showsgreaterinequalitiesinapositiveassessmentthaninanegative evaluationofallaspectsoflife.Thegreatestdiversitiesamongthesatisfiedrefer tosocialaspects,thelowest–toself-assessmentaspects.Asindicatedintable3 inequalitiesinagroupofthedissatisfiedareverysmall.Thisisduetothefactthat answer“4–rathernotsatisfied”dominatedamongthenegativeopinions. Takingintoaccountgender,onecanobservethat,withtheexceptionofsocial aspects, inequalities for women were less than for men. Dividing the population intosub-groupsaccordingtoeducationallevelitcanbeseenthatinawell-educated groupinequalitiesofsatisfactionweregreaterthaninapoorlyeducatedgroupand theoppositerelationshipheldforinequalitiesofdissatisfaction.

Finally, it is important to underline that the application of multidimensional analysisinasubjectiveperceptionofthequalityoflifeisrelativelynew.Inorder topresenttheuseofafuzzysetapproachtotheundertakenissue,thispapershows introductory results for the data from one year and includes a comparison of satisfactionintheselectedgroupsregardinggenderandeducationalstatus.

5. Concluding remarks

The increasing interest in a well-being analysis has caused growth of different measurementapproaches.Thisstudypresentsamethodologicalframeworkforthe assessmentofsubjectiveperceptionoflifebyusingthemethodsoffuzzysettheory appliedinamultidimensionalpovertyanalysis.Thedatausedfortheanalysiscome fromthe“SocialDiagnosis”researchconductedin2013.Inthisresearchalotof

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questionnaires’itemsaredevotedtoaspectsofpersonallifethatcanbemeaningfully describedinordinalterms.Inourframeworktheordereddatarelatingtosubjective assessmentsareconvertedbyamembershipfunctionintoa[0,1]interval.Inthe nextstep,inordertoobtainasyntheticindicatorencompassingalotofareasand aspects of life, weights reflecting the relative importance of partial satisfaction scoresareused.Themainwaytoasynthesisintheevaluationoflifesatisfactionin thewholesamplepopulationisthecomputationofcompositeindices.Thepaper exploreshowtomeasuretheincidence,depthandinequalityinmultivariateanalysis ofsatisfactionwithlife.

Itwasfoundthatthebestsatisfactionreferredtosocialaspect,theworst–to environmental and self-assessment aspects. Incidence of life satisfaction equals about60%foroveralllifesatisfaction,70%forsatisfactioninsocialandmaterial aspects, 60% – in health-related, 40% – in environmental and self-assessment aspects.Theoveralldepthandinequalityoflifesatisfactionwasgreaterthanoverall depthandinequalityofdissatisfaction. Theuseofmicro-leveldataisusefulandhasthepotentialtoyieldimportant insightintodisparitiesregardinggenderandeducationalstatus.Itwasfoundthat, exceptforsocialaspects,subjectivequalityoflifewasslightlybetteranddeeper amongmenthanamongwomen.Moreoverwell-educatedpeopledefinitelybetter perceivedtheirqualityoflifethanpoorlyeducatedpeople. Theapplicationoffuzzysetstoissuesofsatisfactionwithlifeisrelativelynew. Weplanvariousextensionsofourstudy.Amongotherthings,thefuturedirections of the research should include an analysis of the data from several years and comparingtheobtainedresults,anapplicationofpaneldatamodelsforcontrolling unobserved heterogeneity of individuals, an analysis of the influence of various socio-demographiccharacteristicsonasubjectiveperceptionofthequalityoflife.

References

Alkire S., Foster J., Seth S., Santos M.E., Roche J.M., Ballon P., 2015, Multidimensional Poverty

Measurement and Analysis,OxfordUniversityPress,Oxford.

BourguignonF.,ChakravartyS.R.,2003,The measurement of multidimensional poverty,Journalof EconomicInequality,vol.1,pp.25-49.

BettiG.,VermaV.,1999,Measuring the degree of poverty in a dynamic and comparative context:

A multidimensional approach using fuzzy set theory, Proceedings of the ICCS-VI. Lahore.

Pakistan,vol.11,pp.289-301.

BettiG.,VermaV.2008,Fuzzy measures of the incidence of relative poverty and deprivation: A

multi-dimensional perspective,StatisticalMethodsandApplications,vol.17(3),pp.225-250.

BettiG.,SoldiR.,TalevI.,2015,Fuzzy multidimensional indicators of quality of life: The empirical

case of Macedonia,SocialIndicatorsResearch,vol.127(1),pp.39-53.

CerioliA.,ZaniS.,1990,A Fuzzy approach to the measurement of poverty,[in:]DagumC.,ZengaM. (eds.), Income and Wealth Distribution, Inequality and Poverty, Studies in Contemporary Economics,SpringerVerlag,Berlin,pp.272-284.

(18)

68 HannaDudek,WiesławSzczesny CheliB.,LemmiA.,1995,A “totally” fuzzy and relative approach to the multidimensional analysis of

poverty,EconomicNotes,Vol.24(1),pp.115-134.

CzapińskiJ.,2014,Individual quality of life and lifestyle.[in:]CzapińskiJ.,PanekT.(eds.), Diagnosis

2013 –The objective and subjective quality of life in Poland – Report,Warsaw.

CzapińskiJ.,PanekT.(eds.),2014,Social Diagnosis 2013 –The objective and subjective quality of life

in Poland – Report,Warsaw.

DeBattistiF.,MarasiniD.,NicoliniG.,2015,A measure of job satisfaction by means of fuzzy set

theory,StatisticaApplicata–ItalianJournalofAppliedStatistics,vol.23(3),pp.361-374.

DesaiM.,ShahA.,1988,An econometric approach to the measurement of poverty,OxfordEconomic Papers,vol.40(3),pp.505-522.

DeutschJ.,SilberJ.,2005,Measuring multidimensional poverty: an empirical comparison of various

approaches,ReviewofIncomeandWealth,vol.51(1),pp.145-174.

Filippone A., Cheli B., D’Agostino A., 2001, Addressing the interpretation and the aggregation

problems in totally fuzzy and relative poverty measures,ISERWorkingPaperSeriesnr2001–22,

UniversityofEssex.

FosterJ.,GreerJ.,ThorbeckeE.,1984, A class of decomposable poverty measures, Econometrica, vol.3(52),pp.761-766.

Foster J., Greer J., Thorbecke E., 2010, The Foster–Greer–Thorbecke (FGT) poverty measures:

25 years later,TheJournalofEconomicInequality,vol.8,pp.491-524.

LazimM.A.,OsmanM.T.A.,2009,A new Malaysian quality of life index based on fuzzy sets and

hierarchical needs,SocialIndicatorsResearch,94(3),pp.499-508.

PanekT.,2010,Multidimensional approach to poverty measurement: Fuzzy measures of the incidence

and the depth of poverty,StatisticsinTransition,vol.11(2),pp.361-379.

PanekT.,2011,Ubóstwo. wykluczenie społeczne i nierówności. Teoria i praktyka pomiaru,Oficyna WydawniczaSzkołyGłównejHandlowejwWarszawie,Warszawa.

PiAlperin M.N.,Van Kerm P., 2014, MDEPRIV: Stata module to compute synthetic indicators of

multiple deprivation,StatisticalSoftwareComponentsS457806,BostonCollegeDepartmentof

Economics.

StrózikD.,StrózikT.,SzwarcK.,2015,The subjective well-being of school children. The first findings