Qualitative Comparative Analysis Using Fuzzy Sets

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Qualitative Comparative Analysis Using Fuzzy Sets. D r . Adrián Albala FFLCH-USP, São Paulo, November 14 th 2013. Summary. Introduction: Fuzzy Sets, a bridge between two worlds? When can and should we use fuzzy sets analysis? The central principle of “calibration”

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### Qualitative Comparative Analysis Using Fuzzy Sets

FFLCH-USP, São Paulo, November 14th 2013

Summary
• Introduction: Fuzzy Sets, a bridge between two worlds?
• When can and should we use fuzzy sets analysis?
• The central principle of “calibration”
• Using Fuzzy Sets and the notion of “consistency”
• Using Ragin’s Examples
• Through an “imported” example
• Conclusions
• Recommendations: useful and practical softwares and additional bibliography
Introduction: Fuzzy Sets, a bridge between two worlds?

As a comparing method, it inscribes in the Configurational Approach (i.e. “qualititative”) in that it is foundamentaly “case-centered” rather than correlation-centered

It aimes to maintain the “verbality” of the analysis and the demonstration process

As QCA (both cs and mv), it aimes to evidentiate causal relationships for the occurence of “outcomes”, also expressed as “necessary” or “sufficient” conditions or combinations

It constitutes a deepening in the “membership”/ “non-membership” set-relation analysis beyond dichotomy (csQCA) and multivariate (mvQCA) approaches

On the mean time:

> It supposes a higher precision proper to quantitative approaches, while qualitative interpretations and measurments tend to be more implicit

The Principal aim of Fuzzy Sets: clearingthe “brownareas”

Abovethe 1/0 dichotomy, Fuzzy Sets containthreenumericalanchors:

0.0: Full nonmembership

1.0: Full membership

0.5: cross-overvalueseparating “more-in” vs. “more-out” membership

> As toidentifying and differentiating “middle cases”

2. When can and should we use fuzzy sets analysis?

i) Thepurpose of causal inferenceiscloselyrelatedtothenumber of compared cases

> Thehigherthe “N” the more limited as tobetheinterveningconditions

ii) Reverse proportionalrelationshipbetweenthenumber of cases and thedegree of knowledge of every case

> Thehigheristhe “N” the more bluredistheknowledge of every case

Evenifwe can applyFuzzy Sets forsmall N studies, itsrelevanceisnotevident.

Onthesameway, applying QCA (cs/mv) tolarge N comparison, increasestheprobability of “contradictory” cases and so decreasestherelevancy of themethod as to determine “conditionalconfigurations”

2.1 fuzzy sets’ optimalapplicationcorrespondto a “moderat” to “relativelyhigh” N of cases.
3. The central principle of “calibration”
• Fuzzy sets approach supposes a better-fit or precise operationalisation as it allows for “degrees of membership” and variation between the cases.
• In the meantime it goes above empirical benchmarks and the mere “measurment” approach via the elaboration of ranks between cases, where cases are defined relative to each other
• It focuses ont “sets” and “set-memberships”
• E.g: a set of developped countries identifies specific countries that are developped (or not) while a “level of developpement” does not
Thecalibration of diversity as thecoretheoreticalprocess

Case-orientedviewis more compatible withthe idea thatthemeasureshouldbe “calibrated”, forthefocusisonthe “degree” towhich cases satisfy –ornot- membershipcriteria (mostly in/ mostlyout…)

Ideallybasedonthe substantive “objective” theoreticalknowledge > butdoesnotfitwellwith social sciences

Needing of externaldeterminedstandards, ratherthaninductivelydeterminedindicators

A fuzzymembership score attachestruthvalue, notprobabilityto a statement

> Clear specification of the target set, establishedbytheresearcher

4. Using Fuzzy Sets and the notion of “consistency”

Logical AND-combination

Logical OR-combination

negation: ~A = 1 – A

A * B = min (A,B) (i.e. intersection of 2 or more conditions taking the lowst value of one of them)

negation: ~A = 1 – A

A + B = max (A,B) (i.e. union of 2 or more conditions taking the highest value of one of them)

4.2 Theconsistency of the sub-set relation

Theinvestigatormustformulate a rulfordeterminingwhichcombinations are relevantbasedonthenumber of cases and the “consistency” of thecombination

Consistencyexpressed in terms of sufficency/ necessaryrelationshipswhere X≤ Y

Consistencyappliedtosufficientrelation : “ assessesthedegreetowhichthe cases sharing a givenconditionorcombination of conditionsagree in displayingthesameoutcome”

4.2.1 Appliedto “necessaryconditions”

Consistencyappliedtonecessaryconditions: “assessesthedegreetowhichinstances of anoutcomethoughttobenecessary”

Y≤ X

Previousobservation: perfectconsistencyisrare! Thereisalmostalwaysanor a fewexceptions

Importancetodevelopusefuldescriptivemeasures of thedegreetowhich a set relation has beenaroximated > i.ethedegreetowhichtheevidenceis “consistent”

4.4 The set method

Instead of introducing a complexisation of theanalysisthrough a redichotomisation of theconditions > utilisation of thefuzzy sets “crude” datas

Mostgeneralised and “comprehensively” approach

> Whileitbreakswiththe idea of verbality and membership/ non-membershipsystematicalanalysis

Coalitiongovernments in presidentialregimes: un an “accidental” phenomenon?

In thefacts:

+ 50% of southamericangovernmentssince 1979; 85% of themwheremajoritariangovernments at theirinception

Thedichotomous 1/0 relationshipdoesnotreflectthe “precocity” aspect.

>intermediary cases that do notappearor are considered as “totalyout” (‘inrtial’)

ElA= Electoral Alliance, as to know if the cabinet proceeds from an electoral coalition, calibrated using fuzzy sets methodology as follows:

0,0: no electoral alliance, merely post-electoral formation.

0,33 “inertial” alliances

0,60: partially, where most of the participant of the cabinets ran together in the elections, but where some new partners joined the cabinet after the election

0,70: run-off agreement, where all the government partners ran separately in the first “round” of the election but joined for the run-off

0,90: when all the partners of the cabinet ran together in the elections

1.0 when all the partners ran together in the elections and passed, previously by “internship” candidate selection

INST = normas institucionales “favorables” al mantenimiento.

CULT= cultura de acuerdos

CLIV= presencia de un clivaje estructurante fuerte

CONTXT= contexto favorable

5. Conclusions

Fuzzy sets approach enable middle N comparison with broader precision and details than csQCA and mvQCA approaches, due to the calibration process

It remains case-centred in that the calibration process supposes a substantive knowledge of the studied cases.

Enhances the retroduction process through the notion of consistency

Deserves a more generalised approach and consideration

6. Recommendations: useful and practical softwares and additional bibliography

Bibliogaphicsuggestions

Softwares

RAGIN, C., (2006) “Set Relations in Social Research: Evaluating Their Consistencyand Coverage”. Political Analysis 14(3):291-310

RAGIN, C., (2008) « Measurement versus calibration: a set theoretic approach », in BOX STEFFENSMEIER, J., et al.., The Oxford Handbook of Political Methodology, Oxford University Press, pp. 174- 198

RAGIN, C., (2008) Redesigning social inquiry fuzzy sets and beyond, University of Chicago Press

• fsQCA (windows/ mac)
• user-friendlybutnot complete (doesnotpermitcsQCAanalysis)
• Kirq (Linux, Windows) Complete butneeds a little time of adaptation