Ragin Investigacion

7/30/2019 Ragin Investigacion

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MASTERCLASS: QUALITATIVE COMPARATIVE ANALYSIS

Charles C. RaginDepartment of Sociology

and

Department of Political ScienceUniversity of ArizonaTucson, AZ 85718

http://www.fsqca.comhttp://www.compasss.org

http://www.u.arizona.edu/~cragin


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Why the U-Shaped Pattern?

1. The nature of the discipline, including training, publishing, invisiblecolleges, and so on. Researchers tend to use methods they learn ingraduate school, where training typically is bifurcated.

2. The once common belief that qualitative work is only for themathematically impaired (elitism of quantitative researchers).

3. The underdevelopment of methods for medium-sized Ns.

4. The difficulty of knowing a large number of cases in an in-depthmanner.

5. The difficulty of keeping track of (N)(N-1)/2 paired comparisons.

6. The difficulty of considering 2k

logically possible combinations ofconditions (relevant to counterfactual analysis), where k is the number ofcausal conditions.


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THE CASE-ORIENTED/VARIABLE-ORIENTED DIMENSION

1 2

Single Case Method of Comparative Study QN Study of

Study Agreement of Case Configurations Covariation

Case-Oriented

Small-N

Qualitative

Intensive

With-in Case Analysis

Problem of Representation

Variable-Oriented

Large-N

Quantitative

Extensive

Cross-Case Analysis

Problem of Inference


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Some Assumptions:

1. Social scientists seek generalizations. They are interested in constructingstatements about general patterns.

2. Cross-case analysis is central to the process of constructing generalizations.It is not a necessary ingredient, but is a very common way of arriving at generalstatements. (This assumptions begs the question: What is a case?)

3. The results of cross-case analysis can be very misleading. The spurious

correlation is the best known example of the limitations of cross-case analysis.

4. The best way to address the limitations of cross-case analysis is bycomplementing it with within-case analysis. If possible, it is good to balancecross-case and within-case analysis in social research. (This is a more precise

version of the common admonition to combine qualitative and quantitativeanalysis.)

5. Causal processes are best observed at the level of the single case, through in-depth research.


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SETS ARE CENTRAL TO SOCIAL SCIENTIFIC DISCOURSE

Many, if not most, social scientific statements, especially empirical generalizations aboutcross-case patterns, involve set-theoretic relationships:

A. Religious fundamentalists are politically conservative. (Religious fundamentalists are asubset of politically conservative individuals.)

B. Professionals have advanced degrees. (Professionals are a subset of those withadvanced degrees.)

C. Democracy requires a state with at least medium capacity. (Democratic states are asubset of states with at least medium capacity.)

D. "Elite brokerage" is central to successful democratization. (Instances of successful

democratization are a subset of instances of elite brokerage.)E. "Coercive" nation-building was not an option for "late-forming" states. (States practicingcoercive nation-building are a subset of states that formed "early.")

Usually, but not always (e.g., D), the subset is mentioned first. Sometimes, it takes a little

deciphering to figure out the set-theoretic relationship, as in E.


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CONVENTIONAL VIEW OF SETS

Sets are binary, nominal-scale variables, the lowest and most primitive form ofsocial measurement.

The cross-tabulation of two sets is the simplest and most primitive form of

variable-oriented analysis.

This form of analysis is of limited value because: (1) the strength of theassociation between two binary variables is powerfully influenced by how theyare created (e.g., the choice of cut-off values), and (2) with binary variables

researchers can calculate only relatively simple measures of association.These coefficients may be useful descriptively, but they tell us little about thecontours of relationships.

In short, examining relations between binary variables might be consideredadequate as a descriptive starting point, but this approach is too crude to beconsidered realsocial science.


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Correlational Connections

Correlation is central to conventional quantitative social science. The core principle is

the idea of assessing the degree to which two series of values parallel each otheracross cases.

The simplest form is the 2x2 table cross-tabulating the presence/absence of a causeagainst presence/absence of an outcome:

Cause absent Cause present

Outcome present cases in this cell (#1)contribute to error

many cases should be inthis cell (#2)

Outcome absent many cases should bein this cell (#3)

cases in this cell (#4)contribute to error

Correlation is strong (and in the expected direction) when there are as many cases aspossible in cells #2 and #3 (both count in favor of the causal argument, equally) and as

few cases as possible in cells #1 and #4 (both count against the causal argument,equally).

Correlation is completely symmetrical.


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Correlational Versus Explicit Connections

A correlational connection is a description of tendencies in the evidence:

Presidential form Parliamentary form

3rd

wave democracysurvived

8 11

3rd wave democracycollapsed

16 5

An explicit connection is a subset relation or near-subset relation:

Presidential form Parliamentary form

3rd wave democracysurvived

18 16

3

rd

wave democracycollapsed 6 0

In the second table all democracies with parliamentary systems survived, that is, they area subset of those that survived. The first table is stronger and more interesting from a

correlational viewpoint; the second is stronger and more interesting from the perspectiveof explicit connections.


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KINDS OF CONNECTIONS:

QCA VERSUS CONVENTIONAL QUANTITATIVE SOCIAL SCIENCE

Qualitative Comparative Analysis:

Set-Theoretic

Conventional Quantitative Social Science:

Correlational

Explicit

Asymmetric

Case-oriented

Substantively Verified

Tendencies

Symmetric

Model-oriented

Probabilistically Verified


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NECESSITY AND SUFFICIENCY AS SUBSET RELATIONS

Anyone interested in demonstrating necessity and/or sufficiency must address set-theoretic relations. Necessity and sufficiency cannot be assessed using conventionalquantitative methods.

CAUSE IS NECESSARY BUT NOT SUFFICIENT


Outcome present 1. no cases here 2. cases here

Outcome absent 3. not relevant 4. not relevant

CAUSE IS SUFFICIENT BUT NOT NECESSARY


Outcome present 1. not relevant 2. cases here

Outcome absent 3. not relevant 4. no cases here


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SUFFICIENCY (WITHOUT NECESSITY)

I. Expressed as a simple truth table:

Cause | Outcome1 | 10 | 1

0 | 0

II. Expressed as an inequality:

(values of the cause) (value of the outcome)

III. Expressed as a research strategy: Find instances of the causal condition (i.e., selecton the independent variable) and assess their agreement on the outcome (i.e., make surethat the outcome does not vary substantially across instances of the cause). This strategy

is central to most forms of qualitative research.


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NECESSITY (WITHOUT SUFFICIENCY)

I. Expressed as a simple truth table:

Cause | Outcome1 | 1

1 | 00 | 0

II. Expressed as an inequality:

(values of the outcome) (value of the cause)

III. Expressed as a research strategy: Find instances of the outcome (i.e., select on thedependent variable) and assess their agreement on the causal condition (i.e., make surethat the cause does not vary substantially across instances of the outcome).


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Adding Causal Variables in Variable-Oriented Research

If the effects of two variables are additive, then the highest average level orprobability of the outcome should occur when both causes are present, while thelowest should occur when both causes are absent. The main focus is onincreasing the strength of a correlational (tendential) connection, in a symmetric

manner.

Neither parliamentaryform nor multiparty

Only one of the twoattributes present

Both parliamentaryform and multiparty

3rd wavedemocracysurvived

5 8 8

3rd wave

democracycollapsed

10 7 3

The ideal second causal condition has a low correlation with the first, and astrong correlation with the dependent variable.


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ELABORATING EXPLICIT CONNECTIONS:

OUTCOME IS A SUBSET OF THE CAUSEWhen the goal is to establish that the outcome is a subset of a causal condition,the objective is to move cases from cell 1 to cell 2 (i.e., to drain cell 1 of casesand thereby establish an explicit connection). In effect, the causal argument

must be made more inclusive, which can be accomplished using logical or.Generally, this use of logical orentails moving up the ladder of abstraction to amore general conceptualization of the causal condition or construct.

For example, to survive as a third-wave democracy it might be necessary

to have EITHER a parliamentary form OR a multiparty system. At a moreabstract level, these two conditions could be seen as substitutable ways ofaccomplishing political inclusiveness, which in turn could be interpreted as anecessary condition for democratic survival.


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ILLUSTRATION OF USE OF LOGICAL ORTO IDENTIFYEXPLICIT CONNECTION

X Absent X Present bothabsent

X orZPresent

OutcomePresent

5 25 OutcomePresent

0 30

OutcomeAbsent

15 15

before

after

OutcomeAbsent

12 18

By identifying a substitutable causal condition (and moving to a more generalconceptualization), it is possible to identify an explicit connection--the outcome isnow a subset of the reconstituted cause. The second causal condition may bestrongly correlated with the first. The key concern is the impact on the first cell.

It is important to understand that there is a dialogue of ideas and evidence in this

procedure. The goal is not simply to find a causal condition that improves fit withthe outcome, but to use ideas to craft a more encompassing causal condition.

Logical oris central to the process of trying to empty cell 1 of cases. In someinstances, the encompassing causal condition may be interpreted as a necessary

condition.


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ELABORATING EXPLICIT CONNECTIONS:

THE CAUSE IS A SUBSET OF THE OUTCOME

When the goal is to establish that the cause is a subset of the outcome, thegoal is to move cases from cell 4 to cell 3 (i.e., to empty cell 4 of cases andthereby establish an explicit connection). In effect, the causal argument must

be made more restrictive, which is accomplished through the use of logicaland. Generally, this use of logical andalso entails moving toward a morenuanced conceptualization of the causal conditions.

For example, one recipe for survival as a 3rd

wave democracy might be to

combine a party system that permits representation of minorities (i.e., amultiparty system) with an institutional form that fosters coalition building andpolitical bargaining (i.e., the parliamentary form). The set of cases combiningthese two traits might constitute a subset of those that survive.


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The effort to empty cell 4 of cases is connected with greater theoretical nuance

and specificity regarding the nature of the causal mechanisms.

X Absent X Present X or Zabsent

X*ZPresent

OutcomePresent

16 14 OutcomePresent

18 12

OutcomeAbsent

24 6

before

afterOutcomeAbsent

30 0

Note that when seeking to empty cell 4 of cases, the goal is to refine one ofperhaps severalrecipes for the outcome.

Again the second causal condition may or may not be correlated with the first;the key concern is the impact on the fourth cell.

Note also that this research strategy is the opposite of the previous (using logicalor to derive a more encompassing superset).


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CAUSAL COMPLEXITY

Another important benefit of set theoretic analysis is that it is much more compatible withthe analysis of causal complexity than conventional techniques. For example, aresearcher studies production sites in a strike-prone industry and considers four possiblecauses of strikes:

technology = the introduction of new technologywages = stagnant wages in times of high inflationovertime = reduction in overtime hourssourcing = outsourcing portions of production

Possible findings include:

(1) technology strikes(2) technology*wages strikes(3) technology + wages strikes

(4) technology*wages + overtime*sourcing

strikes

In (1) technology is necessary and sufficient; in (2) technology is necessary but notsufficient; in (3) technology is sufficient but not necessary; in (4) technology is neithernecessary nor sufficient. The fourth is the characteristic form of causal complexity: nosingle cause is either necessary or sufficient.


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ASSESSING CAUSAL COMPLEXITY

I. Logical equation: technology*wages + overtime*sourcing strikes

II. Formulated as a partial crosstabulation:

Causal combinationabsent

Causal combinationpresent

Strike present (1) Cell 1: 20 cases Cell 2: 23 cases

Strike absent (0) Cell 3: 18 cases Cell 4: 0 cases

III. Expressed as a Venn diagram:

StrikesReduction inovertimecombined withoutsourcing

The key to assessing the sufficiency of a combination of conditions, even if it is oneamong many combinations, is to select on instances of the combination and assess

whether these instances agree on the outcome.


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SIMPLE EXAMPLE OF QCA USING HYPOTHETICAL DATA

A. Truth Table:

C L H G U N of Cases

0 0 0 0 0 4

0 0 0 1 0 3

0 0 1 0 0 6

0 0 1 1 1 2

0 1 0 0 1 3

0 1 0 1 1 4

0 1 1 0 0 3

0 1 1 1 1 5

1 0 0 0 0 7

1 0 0 1 0 8

1 0 1 0 0 1

1 0 1 1 1 7

1 1 0 0 1 3

1 1 0 1 1 2

1 1 1 0 0 7

1 1 1 1 1 6

C = Corporatist wage negotiations

L = At least five years of rule by Left or Center-Left parties

H = Ethnic-cultural homogeneity

G = At least ten years of sustained economic growth

U = Adoption of universal pension system


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B. Table simplified through row-wise comparisons (positive outcomes only)

-10- (or L*h: Left rule combined with ethnic diversity)a

-1-1 (or L*G: Left rule combined with economic growth)--11 (or H*G: ethnic homogeneity combined with economic growth)

Dashes indicate that a condition has been eliminated (found to be irrelevant)

C. Finding Redundant Terms:

Terms to be Covered (Rows with Outcome = 1)

0100 1100 0101 1101 0011 1011 0111 1111

Simplified -10- x x x x

Terms (from B) -1-1 x x x x

--11 x x x x

D. Final Results (logically minimal):

U = L*h + H*G

Lower-case letters indicate condition must be absent.

Upper-case letters indicate that condition must be present.

Multiplication (*) indicates combined conditions (logical and).

Addition (+) indicates alternate combinations (logical or).


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THE THREE PHASES OF RESEARCH USING QCA

1. Learn as much as you can about the cases. If possible, construct a narrativefor each case. Use case comparisons to refine and systematize yourunderstandings. This process culminates in the creation of a truth table, whichboth represents what youve learned and disciplines your representations of the

cases.

2. The Analytic Moment: Analyze the evidence using QCA. Actually, preliminaryresults usually send you back to phase 1.

3. Take the results back to the cases. The real test of the results is how usefulthey are. Do they help you understand the cases better? Do the different paths(causal combinations) make sense at the case level? Do the results place thecases in a new light, perhaps revealing something that would not have been

evident before the analysis (phase 2).


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Territorially Based Linguistic Minorities in Western Europe

Austria: Slovenes West Germany: Danes

Magyars North FrisiansCroats

Ireland: GaelsBelgium: Flemings

Walloons Italy: FriuliansGermans Ladins

ValdotiansGreat Britain: Gaels (Scotland) South Tyroleans

Gaels (Isle of Man) SlovenesGaels (N. Ireland) SardsWelsh GreeksChannel Islanders Albanians

Occitans

Denmark: GermansFaroe Islanders Netherlands: West FrisiansGreenlanders

Norway: LappsFinland: Swedes (mainland)

Swedes (Aaland) Spain: CatalansLapps Basques

GaliciansFrance: Occitans

Corsicans Sweden: LappsAlsatians FinnsFlemingsBretons Switzerland: Jurassians


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SUMMARY PRESENTATION OF PREDICTIONS OF THREE THEORIES OF

ETHNIC POLITICAL MOBILIZATION

___________________________________________________________________

Guiding Perspective

Characteristic Developmental Reactive Competitive___________________________________________________________________

Size of Subnation (S) (1)a

(1)a

1

Linguistic Base (L) 1

0

(1)a

Relative Wealth (W) (0)a

0

1

Economic Status (G) 0 ?b ?b___________________________________________________________________

aPredictions in parentheses are only weakly indicated by the theories.

bQuestion marks indicate that no clear prediction is made.


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DATA ON TERRITORIALLY BASED LINGUISTIC MINORITIES

Minority S L W G E

Lapps, Finland 0 0 0 0 0

Finns, Sweden (Torne Valley) 0 0 0 0 0

Lapps, Sweden 0 0 0 0 0Lapps, Norway 0 0 0 0 0

Albanians, Italy 0 0 0 0 0

Greeks, Italy 0 0 0 0 0

North Frisians, Germany 0 0 0 1 1

Danes, Germany 0 0 0 1 1

Basques, France 0 0 0 1 1

Ladins, Italy 0 0 1 0 0

Magyars, Austria 0 1 0 0 0

Croats, Austria 0 1 0 0 0Slovenes, Austria 0 1 0 0 1

Greenlanders, Denmark 0 1 0 0 1

Aalanders, Finland 0 1 1 0 2

Slovenes, Italy 0 1 1 1 1

Valdotians, Italy 0 1 1 1 2

Sards, Italy 1 0 0 0 1

Galicians, Spain 1 0 0 0 1

West Frisians, Netherlands 1 0 0 1 1

Catalans, France 1 0 0 1 1Occitans, France 1 0 0 1 1

Welsh, Great Britain 1 0 0 1 2

Bretons, France 1 0 0 1 2

Corsicans, France 1 0 0 1 2

Friulians, Italy 1 0 1 1 1

Occitans, Italy 1 0 1 1 1

Basques, Spain 1 0 1 1 2

Catalans, Spain 1 0 1 1 2

Flemings, France 1 1 0 0 1Walloons, Belgium 1 1 0 1 2

Swedes, Finland 1 1 1 0 2

South Tyroleans, Italy 1 1 1 0 2

Alsatians, France 1 1 1 1 1

Germans, Belgium 1 1 1 1 2

Flemings, Belgium 1 1 1 1 2

S = Size of subnation

L = Linguistic ability

W = Relative wealth of subnationG = Growth vs. decline of subnational region

E = Degree of ethnic political mobilization

TRUTH TABLE REPRESENTATION OF DATA ON CAUSES OF ETHNIC POLITICAL


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TRUTH TABLE REPRESENTATION OF DATA ON CAUSES OF ETHNIC POLITICALMOBILIZATION

S L W G E N

0 0 0 0 0 60 0 0 1 0 3

0 0 1 0 0 1

0 0 1 1 ? 0

0 1 0 0 0 4

0 1 0 1 ? 0

0 1 1 0 1 10 1 1 1 1 2

1 0 0 0 0 2

1 0 0 1 1 6

1 0 1 0 ? 0

1 0 1 1 1 4

1 1 0 0 0 11 1 0 1 1 1

1 1 1 0 1 2

1 1 1 1 1 3

S = Size of subnation

L = Linguistic ability

W = Relative wealth of subnation

G = Growth vs. decline of subnational region

E = Degree of ethnic political mobilization

EQUATION: E = SG + LW

USING BOOLEAN ALGEBRA TO EVALUATE THEORIES


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USING BOOLEAN ALGEBRA TO EVALUATE THEORIES

1. Intersection with the reactive ethnicity perspective

R = lwE = SG + LWR(E) = SlwG

Conforming cases (6): West Frisians (Netherlands), Catalans (France), Occitans (France), Bretons

(France), Corsicans (France), and Welsh (Great Britain)

2. Intersection with the ethnic competition perspective

C = SWE = SG + LW

C(E) = SW(G + L)

Conforming cases (9): Germans (Belgium), Flemings (Belgium), Swedes (Finland), Alsatians(France), Friulians (Italy), Occitans (Italy), South Tyroleans (Italy), Basques (Spain), Catalans (Spain)

3. Intersection with the developmental perspective

D = LgE = SG + LWD(E) = LWg

One case uniquely covered: Aalanders (Finland)


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4. Cases not covered by any theoretical perspective

H = lw + SW + Lg

h = (L + W)(s + w)(l + G) (using De Morgans Law)= slW + sLG + sWG + LwG

h(E) = (slW + sLG + sWG + LwG)(SG + LW)= sLWG + SLwG

Cases covered by sLWG: Slovenes (Italy) and Valdotians (Italy)Case covered by SLwG: Walloons (Belgium)


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FREQUENCIES AND CODES FOR VARIABLES USED IN BOOLEAN

ANALYSIS OF CHALLENGING GROUPS

Value Freq. Percent

Bureaucracy

0 29 54.71 24 45.3

Lower Strata Constituency0 28 52.81 25 47.2

Displacement as Primary Goal

0 37 69.81 16 30.2

Help From Outsiders0 35 66.01 18 34.0

Acceptance Achieved

0 28 52.81 25 47.2

New Advantages Won0 27 50.91 26 49.1

Values show coding in qualitative comparative analysis: 1 indicates presence; 0 indicates absence.


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Truth Table For Causes of New Advantages*

Number New No Newof Cases Adv. Adv.

BUR LOW DIS HLP ACP

0 0 0 0 0 4 2 2

0 0 0 0 1 2 2 00 0 0 1 0 2 2 0

0 0 0 1 1 2 2 0

0 0 1 0 0 4 0 4

0 0 1 0 1 1 1 0

0 0 1 1 0 2 0 2

0 0 1 1 1 1 0 10 1 0 0 0 2 0 2

0 1 0 0 1 0 remainder


0 1 0 1 1 2 2 0

0 1 1 0 0 5 0 5

0 1 1 0 1 0 remainder0 1 1 1 0 2 0 2


1 0 0 0 0 3 0 3

1 0 0 0 1 4 1 3

1 0 0 1 0 1 1 0

1 0 0 1 1 1 1 01 0 1 0 0 1 0 1



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1 1 0 0 0 2 1 1

1 1 0 0 1 7 6 11 1 0 1 0 0 remainder

1 1 0 1 1 5 5 0





* Column headings: BUR = bureaucratic organization; LOW = lower strata constituency; DIS =displacement as primary goal; HLP = help from outsiders; ACP = acceptance of the organization. 1indicates presence; 0 indicates absence. The output is coded as follows: U = uniform newadvantages; L = new advantages likely; P = new advantages possible. The dont care output codingis indicated with a dash.


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Sorted Truth Table Spreadsheet for Gamsons Data

BUR LOW DIS HLP ACP freq cumulfreq consistency

1 1 0 0 1 7 7 0.8571430 1 1 0 0 5 12 01 1 0 1 1 5 17 10 0 0 0 0 4 21 0.5

0 0 1 0 0 4 25 01 0 0 0 1 4 29 0.251 0 0 0 0 3 32 00 0 0 0 1 2 34 10 0 0 1 0 2 36 10 0 0 1 1 2 38 1

0 0 1 1 0 2 40 00 1 0 0 0 2 42 00 1 0 1 1 2 44 10 1 1 1 0 2 46 01 1 0 0 0 2 48 0.5

0 0 1 0 1 1 49 10 0 1 1 1 1 50 01 0 0 1 0 1 51 11 0 0 1 1 1 52 11 0 1 0 0 1 53 0

QCA RESULTS: GAMSON DATA


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QCA RESULTS: GAMSON DATA

File: G:/578/05/Gamson/GAMSON.DAT

Model: ADV = BUR + LOW + DIS + HLP + ACP

Algorithm: Quine-McCluskey1 Matrix: 1

- Matrix: R

*** CRISP-SET SOLUTION ***

raw unique

coverage coverage consistency

---------- ---------- -----------dis*HLP+ 0.500000 0.153846 1.000000

bur*ACP+ 0.269231 0.115385 0.875000

LOW*ACP 0.500000 0.230769 0.928571

solution coverage: 0.846154

solution consistency: 0.916667

*************************************************************************

File: G:/578/05/Gamson/GAMSON.DATModel: ADV = BUR + LOW + DIS + HLP + ACP

Algorithm: Quine-McCluskey

1 Matrix: 1

*** CRISP-SET SOLUTION ***

raw uniquecoverage coverage consistency

---------- ---------- -----------

bur*low*dis*HLP+ 0.153846 0.076923 1.000000

bur*low*dis*ACP+ 0.153846 0.076923 1.000000

BUR*LOW*dis*ACP+ 0.423077 0.230769 0.916667

LOW*dis*HLP*ACP 0.269231 0.076923 1.000000

solution coverage: 0.730769

solution consistency: 0.950000

Venn Diagram Showing Results of the Reanalysis of Gamsons Data:


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No Simplifying Assumptions


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PART II: FUZZY SETS


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CRISP VERSUS FUZZY SETS

Crisp set Three-valuefuzzy set

Four-valuefuzzy set

Six-valuefuzzy set

"Continuous"fuzzy set

1 = fully in

0 = fully out

1 = fully in

.5 = neitherfully in norfully out

0 = fully out

1 = fully in

.75 = more inthan out

.25 = more outthan in

0 = fully out

1 = fully in

.8 = mostly butnot fully in

.6 = more orless in

.4 = more orless out

.2 = mostly butnot fully out

0 = fully out

1 = fully in

Degree ofmembership ismore "in" than"out": .5 < xi < 1

.5 = cross-over:neither in nor out

Degree ofmembership ismore "out" than"in": 0 < xi < .5

0 = fully out


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FUZZY MEMBERSHIP IN THE SET OF "RICH COUNTRIES"

GNP/capita:

100 ----> 1,999

2,000 ----> 7,9998,000

8,001 ----> 17,99918,000 ----> 30,000

Membership (M):

M = 0

0 < M < .5M = .5

.5 < M < 1.0M = 1.0

Verbal Labels:

clearly not-rich

more or less not-richin between

more or less richclearly rich


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FUZZY MEMBERSHIP IN THE SET OF "POOR COUNTRIES"

GNP/capita (US$):

100 ----> 499500 ----> 999

1,0001,001 ----> 4,9995,000 ----> 30,000

Membership (M):

M = 1.0.5 < M < .1

M = .50 < M < .5

M = 0

Verbal Labels:

clearly poormore or less poor

in betweenmore or less not-poor

clearly not-poor


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Calibrating Degree of Membership in the Set of Developed Countries


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Country Nationalincome

Qualitativecoding*

Predictedlog odds

Degree ofmembership

Switzerland 40110 4 4.41 0.99United States 34400 4 3.97 0.98Netherlands 25200 4 3.45 0.97Finland 24920 4 3.43 0.97Australia 20060 2 2.95 0.95Israel 17090 2 2.49 0.92Spain 15320 2 2.14 0.89

New Zealand 13680 2 1.76 0.85Cyprus 11720 0.5 1.22 0.77Greece 11290 0.5 1.09 0.75Portugal 10940 0.5 0.98 0.73Korea, Rep 9800 0.5 0.60 0.65Argentina 7470 -0.5 -0.29 0.43Hungary 4670 -0.5 -1.59 0.17Venezuela 4100 -0.5 -1.89 0.13

Estonia 4070 -0.5 -1.90 0.13Panama 3740 -2 -2.08 0.11Mauritius 3690 -2 -2.11 0.11Brazil 3590 -2 -2.16 0.10Turkey 2980 -2 -2.51 0.08Bolivia 1000 -4 -3.71 0.02Cote dIvoire 650 -4 -3.94 0.02Senegal 450 -4 -4.07 0.02

Burundi 110 -4 -4.30 0.01

*4.0 = in the target set; 2.0 = probably in the target set; 0.5 = more inthan out of the target set; -0.5 more out than in the target set; -2.0probably out of the target set; -4.0 = out of the target set.


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Mathematical Transformations of Qualitative Codings

1. Qualitativeinterpretation

2. Numerical value(estimated log of odds)

3. Odds ofmembership

4. Degree ofmembership

In 4.0 54.60 .98

Probably in 2.0 7.39 .88More in than out 0.5 1.65 .62

More out than in -0.5 .607 .38

Probably out -2.0 .135 .12

Out -4.0 .018 .02

DECONSTRUCTING THE CONVENTIONAL SCATTERPLOT


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100 x

x

error x

O x

U x

T x

C 67 x

O x

M x

E x

x

Y x

x

33 x

x

x

x

x error

0 x

0 100

CAUSE (X)

In conventional quantitative analysis, points in the lower-right corner and theupper-left corner of this plot are "errors," just as cases in cells 1 and 4 of the

2X2 crisp-set crosstabulation are errors.

With fuzzy sets, cases in these regions of the plot have differentinterpretations: Cases in the lower-right corner violate the argument that thecause is a subset of the outcome; cases in the upper-left corner violate theargument that the outcome is a subset of the cause.


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THE CAUSE (X) IS A SUBSET OF THE OUTCOME (Y)

100 x x x x

x x xx xx

x x x xxx x

O x x x x x

U x x

T x x x

C 67 x xx x x x

O x xxx x

M x xx

E x xxxx x

x x x

Y x

x x x

33 xxx x

x x

x x

xxxx

x x

0 x

0 100

CAUSE (X)

This plot illustrates the characteristic upper-triangular plot indicating the fuzzysubset relation: X Y (cause is a subset of the outcome). This also can be

viewed as a plot supporting the contention that X is sufficient for Y.

Cases in the upper left region are not errors as they would be in a


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Cases in the upper-left region are not errors, as they would be in aconventional quantitative analysis. Rather, these are cases with high

membership in the outcome due to the operation of other causes. After all, theargument here is that X is a subset of Y (i.e., X is one of perhaps several waysto generate or achieve Y). Therefore, cases of Y without X (i.e., highmembership in Y coupled with low membership in X) are to be expected.

In this plot, cases in the lower-right region would be serious errors becausethese would be instances of high membership in the cause coupled with lowmembership in the outcome. Such cases would undermine the argument thatthere is an explicit connection between X and Y such that X is a subset of Y.

THE OUTCOME (Y) IS A SUBSET OF THE CAUSE (X)


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THE OUTCOME (Y) IS A SUBSET OF THE CAUSE (X)

100 x

xx

x x

O x x x

U x x

T xx xx

C 67 x

O x x x x

E x x x

x x x

Y x x x

xx x x x

x x x x x

33 x xxxx x x

xx x x

x x x x x x

x x x x

xxx x x x xx x x

0 x xxx x x x xxx x x

0 100

CAUSE (X)

This plot illustrates the characteristic lower-triangular plot indicating the fuzzysuperset relation: X Y (outcome is a subset of the cause). This also can be

viewed as a plot supporting the contention that X is necessary for Y.


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Cases in the lower-right region are not errors, as they would be in aconventional quantitative analysis. Rather, these are cases with lowmembership in the outcome, despite having high membership in the cause.This pattern indicates that Y is a subset of X: condition X must be present for Yto occur, but X is not capable of generating Y by itself. Other conditions may

be required as well. Therefore, cases of X without Y (i.e., high membership inX coupled with low membership in Y) are to be expected.

Cases in the upper-left region would be serious errors because these would be

instances of low membership in the cause coupled with high membership in theoutcome. In this plot, such cases would undermine the argument that there isan explicit connection between X and Y such that Y is a subset of X.

REFINING THE FUZZY SUBSET RELATION:


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REFINING THE FUZZY SUBSET RELATION:1. CAUSE IS A SUBSET OF THE OUTCOME

When elaborating the subset relation X Y with fuzzy sets, the goal is to move

cases to the left side of the main diagonal of the scatterplot (i.e., above it).

When the argument is that the cause (X) is a subset of the outcome (Y), cases

below the diagonal are "errors" because these X scores exceed thecorresponding outcome (Y) scores.

As with crisp set analysis, logical andcan be used to move scores to the

correct side of the diagonal. With logical and, conditions are compounded,which in turn involves taking the minimum membership score of thecompounded sets as the membership of a case in the combinations.Mathematically, A*B must be less than or equal to A.

Thus, the elaboration of a subset relation through additional compoundedconditions lowers the X values and thus may move cases toward the left sideof the diagonal.


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FUZZY-SET DATA ON CLASS VOTING INTHE ADVANCED INDUSTRIAL SOCIETIES

Country Weak Classvoting (W)

Affluent(A)

IncomeInequality (I)

Manufacturing(M)

StrongUnions (U)

Australia 0.6 0.8 0.6 0.4 0.6

Belgium 0.6 0.6 0.2 0.2 0.8

Denmark 0.2 0.6 0.4 0.2 0.8

France 0.8 0.6 0.8 0.2 0.2

Germany 0.6 0.6 0.8 0.4 0.4

Ireland 0.8 0.2 0.6 0.8 0.6

Italy 0.6 0.4 0.8 0.2 0.6

Netherlands 0.8 0.6 0.4 0.2 0.4

Norway 0.2 0.6 0.4 0.6 0.8

Sweden 0.0 0.8 0.4 0.8 1.0

United Kingdom 0.4 0.6 0.6 0.8 0.6

United States 1.0 1.0 0.8 0.4 0.2


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ILLUSTRATION OF LOGICAL AND(COMBINED CONDITIONS)

Country Affluent

(A)

Income

Inequality (I)

Manufacturing

(M)

Strong

Unions (U)

Affluent*

Income

Inequality

Affluent*

Income

Inequality*

Weak Unions

A a I i M m U u A*I A*I*u

Australia 0.8 0.2 0.6 0.4 0.4 0.6 0.6 0.4 0.6 0.4

Belgium 0.6 0.4 0.2 0.8 0.2 0.8 0.8 0.2 0.2 0.2Denmark 0.6 0.4 0.4 0.6 0.2 0.8 0.8 0.2 0.4 0.2

France 0.6 0.4 0.8 0.2 0.2 0.8 0.2 0.8 0.6 0.6

Germany 0.6 0.4 0.8 0.2 0.4 0.6 0.4 0.6 0.6 0.6

Ireland 0.2 0.8 0.6 0.4 0.8 0.2 0.6 0.4 0.2 0.2

Italy 0.4 0.6 0.8 0.2 0.2 0.8 0.6 0.4 0.4 0.4

Netherlands 0.6 0.4 0.4 0.6 0.2 0.8 0.4 0.6 0.4 0.4

Norway 0.6 0.4 0.4 0.6 0.6 0.4 0.8 0.2 0.4 0.2

Sweden 0.8 0.2 0.4 0.6 0.8 0.2 1.0 0.0 0.4 0.0

Ukingdom 0.6 0.4 0.6 0.4 0.8 0.2 0.6 0.4 0.6 0.4

Ustates 1.0 0.0 0.8 0.2 0.4 0.6 0.2 0.8 0.8 0.8

REFINING THE FUZZY SUBSET RELATION:


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REFINING THE FUZZY SUBSET RELATION:2. OUTCOME IS A SUBSET OF THE CAUSE

When elaborating the subset relation Y X with fuzzy sets, the goal is to move

cases toward the right side of the main diagonal of the scatterplot (i.e., belowit).

When the argument is that the outcome (Y) is a subset of the cause (X), casesabove the diagonal are "errors" because these X scores are less than thecorresponding outcome (Y) scores.

As with crisp set analysis, logical orcan be used to move scores to thecorrect side of the diagonal. With logical orconditions are substitutable,which in turn involves taking the maximum membership score of thesubstitutable sets. It follows mathematically that A + B A.

Thus, the elaboration of a superset relation through additional substitutableconditions raises the X values and thus moves cases toward the right side ofthe diagonal.


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ILLUSTRATION OF LOGICAL OR(SUBSTITUTABLE CAUSES)

Country Affluent (A) Income

Inequality (I)

Manufacturing

(M)

Strong Unions

(U)

Manufacturing +

Strong Unions

A a I i M m U u M+U

Australia 0.8 0.2 0.6 0.4 0.4 0.6 0.6 0.4 0.6

Belgium 0.6 0.4 0.2 0.8 0.2 0.8 0.8 0.2 0.8

Denmark 0.6 0.4 0.4 0.6 0.2 0.8 0.8 0.2 0.8

France 0.6 0.4 0.8 0.2 0.2 0.8 0.2 0.8 0.2

Germany 0.6 0.4 0.8 0.2 0.4 0.6 0.4 0.6 0.4

Ireland 0.2 0.8 0.6 0.4 0.8 0.2 0.6 0.4 0.8

Italy 0.4 0.6 0.8 0.2 0.2 0.8 0.6 0.4 0.6

Netherlands 0.6 0.4 0.4 0.6 0.2 0.8 0.4 0.6 0.4

Norway 0.6 0.4 0.4 0.6 0.6 0.4 0.8 0.2 0.8Sweden 0.8 0.2 0.4 0.6 0.8 0.2 1.0 0.0 1.0

UKingdom 0.6 0.4 0.6 0.4 0.8 0.2 0.6 0.4 0.8

UStates 1.0 0.0 0.8 0.2 0.4 0.6 0.2 0.8 0.4

FUZZY SETS AND CONFIGURATIONS


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Country Income Inequality Manufacturing Strong Unions

I i M m U u i*m*u i*m*U i*M*u i*M*U I*m*u I*m*U I*M*u I*M*U

Australia 0.6 0.4 0.4 0.6 0.6 0.4 0.4 0.4 0.4 0.4 0.4 0.6 0.4 0.4Belgium 0.2 0.8 0.2 0.8 0.8 0.2 0.2 0.8 0.2 0.2 0.2 0.2 0.2 0.2

Denmark 0.4 0.6 0.2 0.8 0.8 0.2 0.2 0.6 0.2 0.2 0.2 0.4 0.2 0.2

France 0.8 0.2 0.2 0.8 0.2 0.8 0.2 0.2 0.2 0.2 0.8 0.2 0.2 0.2

Germany 0.8 0.2 0.4 0.6 0.4 0.6 0.2 0.2 0.2 0.2 0.6 0.4 0.4 0.4

Ireland 0.6 0.4 0.8 0.2 0.6 0.4 0.2 0.2 0.4 0.4 0.2 0.2 0.4 0.6

Italy 0.8 0.2 0.2 0.8 0.6 0.4 0.2 0.2 0.2 0.2 0.4 0.6 0.2 0.2

Netherlands 0.4 0.6 0.2 0.8 0.4 0.6 0.6 0.4 0.2 0.2 0.4 0.4 0.2 0.2

Norway 0.4 0.6 0.6 0.4 0.8 0.2 0.2 0.4 0.2 0.6 0.2 0.4 0.2 0.4Sweden 0.4 0.6 0.8 0.2 1.0 0.0 0.0 0.2 0.0 0.6 0.0 0.2 0.0 0.4

UKingdom 0.6 0.4 0.8 0.2 0.6 0.4 0.2 0.2 0.4 0.4 0.2 0.2 0.4 0.6

UStates 0.8 0.2 0.4 0.6 0.2 0.8 0.2 0.2 0.2 0.2 0.6 0.2 0.4 0.2

With three fuzzy sets, the vector space has eight corners. It is possible to calculate themembership of each case in each corner.

The corners can be viewed as ideal typic cases; the membership of a case is a corner isthe degree to which it conforms to the ideal type represented by the corner.

In crisp-set analysis, by contrast, membership in a corner is either 1 or 0 and a case canhave nonzero membership in only one corner.


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The Fuzzy-Set Procedure

f f


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1. The researcher calibrates fuzzy membership scores for all relevant causal conditions and theoutcome. It is OK to mix crisp and fuzzy causal conditions.

2. fsQCA calculates the membership of each case in all the logically possible combinations ofmembership. In each calculation the minimum membership score is used.

3. fsQCA calculates the degree to which membership in each combination of conditions is a

consistent subset of membership in the outcome.

4. The results of these 2k analyses are recorded in a truth table. In effect, each row of the(crisp) truth table represents a corner of the multidimensional space defined by the causalconditions.

5. fsQCA also calculates the number of cases with greater than .5 membership in eachcombination of conditions. This information is used to assess patterns of limited diversity.

6. The researcher uses the information in the truth table (from #4 and #5) to code the outcomein the truth table. This involves decisions about frequency and consistency thresholds.

7. fsQCA analyzes the truth table. Usually, two solutions are derived, one with remainders setto false (0), the other with remainders set to dont care. These two solutions establish therange of plausible solutions (the complexity/parsimony continuum).

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