Donal Crilly (LBS) -- An Introduction to Fuzzy Set QCA - Usc

Introduction to Fuzzy-Set
Analysis
Donal Crilly
London Business School
Presentation for QCA PDW, Orlando, 2013

Source: Marx et al. (2012)
Rapid increase
in number of
articles using
fuzzy set
analysis (fsQCA)

Not all Democracies 1 are Equal.
1
Or most other things social scientists care about

Why Fuzzy Sets (fsQCA)?
Social phenomena differ in kind and degree
• Difference in kind: democracy versus
authoritarian regime
• Difference in degree: Norway vs. Italy (equally
democratic?)
fsQCA combines set-theoretic analysis with
gradations in set membership
• Crisp sets (0 or 1): differences in kind
• Fuzzy sets (between 0 and 1): differences in kind and
degree

Calibration
Membership has to be “purposefully calibrated”
(Ragin, 2008: 30)
Calibration =/= measurement

Source: Economist Intelligence Unit Democracy Index, 2010
Norway outscores its neighbors on most dimensions, but these indicators don’t tell us
whether Norway is democratic.
Is the UK (score 8.16) a democracy or a dictatorship?

• Cannot consider a country a democracy simply
because its score is above the sample mean
• Ultimately, must depend on some qualitative
assessment of what warrants being
considered a democracy

Measurement vs. Calibration
Measurement
• Aims for fine gradations between
cases
• Shows relative positions of cases
• All variation treated as important
Calibration
• Aims to make position of a case
interpretable
• Considers how well cases meet
requirements for inclusion in a
category
• Not all variation treated as
important

Calibration Approaches
Crisp set
Three-value
fuzzy set
Four-value
fuzzy set
Six-value fuzzy
set
“Continuous”
fuzzy set
1 = fully in
1 = fully in
1 = fully in
1 = fully out
1 = fully in
0.5 = neither
fully in nor fully
out
0.67 = more in
than out
0.33 = more in
than out
0.8 = mostly
(not fully) in
0.6 = more or
less in
0.4 = more or
less out
0.2 = mostly
(not fully) out
More in than
out
0.5 = cross
over: neither in
nor out
More out than
in
0 = fully out
0 = fully out
0 = fully out
0 = fully out
0 = fully out
Based on Ragin (2008)

Calibration: Examples
• Identify distinct qualitative groupings based on
substantive knowledge
• Not simply ordinal scales!
• Use external standards wherever possible
• For example, democracy classification (EIU)
• Full democracies (1),
• Flawed democracies (0.66),
• Hybrid regimes (0.33), and
• Authoritarian regimes (0)
• Country development (based on UNDP HDI cf. Crilly,
2011)
• Very high (1),
• high( (0.66),
• Medium (0.33), and
• Low (0)

Democracy Index

Continuous Fuzzy Set: Direct
Calibration Method
• Used to transform interval-scale variables into
membership scores between 0 and 1
• Three ‘qualitative’ anchors
1. Threshold for full membership
2. Threshold for full non-membership
3. Cross-over point (maximum ambiguity)
E.g. Firm size based on European Union enterprise size
classes (Fiss, 2011)
1. Full membership: 250 + employees
2. Full non-membership: < 10 employees
3. Cross-over point: 50 employees
• This calibration can be performed using fsQCA software

EMPIRICAL EXAMPLE

Faking it or Muddling Through? Decoupling in
Response to Stakeholder Pressures (Crilly, Zollo &
Hansen)
Aim: To understand why some firms implement CSR
policy consistently whereas others decouple (adopt
without implementing)
• Data: 359 interviews across 17 firms and their
stakeholders, social performance data
• Why QCA? Useful for identifying how
characteristics of firms and their environments
combine to shape firms’ responses
• Why fsQCA? Distinction between
implementation/decoupling is not binary

Steps
• Calibrating set membership
• Constructing truth table
• Reducing number of truth table rows based on
• Minimum acceptable solution frequency
• Minimum acceptable consistency
• Generating simplified combinations from the
truth table rows
• (Optional: Identifying cases that are members
in each configuration)

Conditions
Condition Condition Calibration
Outcome Implementation 0, 0.5, 1
Causal
conditions
Information
asymmetry
Stakeholder
consensus
Organizational
interest
Managerial
consensus
0, 0.33, 0.66, 1
0, 0.5, 1
0, 0.33, 0,66, 1
0, 0.5, 1

Example: Calibrating Managerial
Consensus (based on measure of variance
of responses)
Membership Threshold Evidence from firm at threshold
1 Variance below 0.30 “Agreeing what’s important can’t be
decentralized. You have to do it centrally
and then roll it out.”
0.5 Variance 0.30 – 0.60 Consensus/dissension not a main theme
0 Variance above 0.60 “All our units are very decentralized. We
realize we have to be in greater harmony
because the world doesn’t view us as
these separate functions.”

Calibration Table
Note: Cases with values of 0.5 are dropped from the fuzzy-set analysis in the
fsQCA software program. Transform them by subtracting 0.001 (or adding 0.001).

Sample Truth Table

Configurations Associated with
Implementation and Decoupling

Identifying Case Membership in Configurations
• Assign cases to configurations on the basis of their membership of
at least 0.5 in the configuration

In Closing…
• fsQCA enables you to capture differences in
kind and degree in the phenomena you study
• Middle way between qualitative and
quantitative measurement
• Calibration: simultaneously quantitative and
qualitative
• Fuzzy sets: advantages over conventional variables

And potential applications beyond
social sciences (e.g. athlete selection
for triathlon… but wait until Rio 2016)