Using Qualitative Comparative Analysis
(QCA) and Fuzzy Sets
Peer C. Fiss
University of Southern California
(Thanks to my co-author Charles Ragin, University of Arizona,
Tucson, for the use of some of his slides—modified for this talk)
The Methodological Divide…
Source: Ragin (2000:25)
The Case-Oriented/VariableOriented Dimension
║
║
Single Case ║
Study
║
Comparative Study
of Configurations
║
║
║
║
QN Study of
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
Textbook Social Science
Comparative Methodology
1. The main goal of social research is to document
general patterns characterizing a large population
of observations.
Comparative researchers focus on the problem of
making sense of a relatively small number of cases,
selected because they are substantively or
theoretically important in some way.
2. Cases and populations are typically seen as
given. The ideal-typic case is the survey
respondent; the ideal-typic population is a national
random sample of adults. The key issue is how to
derive a representative sample from an abundant
supply of given observations.
The comparative researcher's answers to both
"What are my cases?" and "What are these cases
of?" may change throughout the course of the
research, as the investigator learns more about the
phenomenon in question and refines his or her
guiding concepts and analytic schemes.
3. Researchers are encouraged to enlarge their
number of cases whenever possible; more is
always better.
Comparative research is often defined by its focus
on phenomena that are of interest because they are
rare--that is, precisely because the N of cases is
small. Typically, these phenomena are large-scale,
historically delimited, and culturally significant.
Empirical depth is more important than breadth.
4. It is often presumed that researchers have welldefined theories and well-formulated hypotheses at
their disposal from the very outset of their
research; theory testing is the centerpiece of social
research.
Existing theory is rarely well-formulated enough to
provide explicit hypotheses in comparative
research. The primary theoretical objective of
comparative research is not theory testing, but
concept formation, elaboration, and refinement,
and theory development.
Textbook Social Science (cont.)
Comparative Methodology (cont.)
5. Researchers are instructed to assess the relative
importance of competing independent variables in
order to understand causation and test theory.
Comparative researchers usually look at causation in
terms of combinations. A common finding in
comparative research is that different combinations
of causes may produce the same outcome (i.e. there
is equifinality).
6. Researchers study relationships between
variables. They control for the effects of other
variables when looking at the link between any
two.
Comparative researchers examine configurations of
characteristics, seeing how different aspects fit
together in each case and combine to create the
outcome in question.
7. Researchers give priority to cross-case patterns;
the idiosyncrasies of individual cases are
"averaged out" in cross-case analysis.
Comparative researchers try to make sense of cases
through within-case analysis and use cross-case
analysis to strengthen and deepen within-case
analysis.
Using the Comparative Method:
Qualitative Comparative Analysis (QCA)
 Qualitative Comparative Analysis (Ragin, 1987; 2000) lies halfway between the qualitative and quantitative approach
 Allows for the formal analysis of qualitative evidence and
small-N situations using Boolean Algebra rather than
correlational methods
 Relies on sets and uses a language that is half-verbalconceptual, half-mathematical-logical
 Focuses on what conditions are necessary and/or sufficient
for an outcome of interest
 Allows the assessment of equifinality and complex causality
with multiple contingencies in organizations (Ragin & Fiss,
2006; Fiss 2007; Greckhamer et al., 2007; Pajunen, 2008)
How Does QCA Work?
 QCA conceives of cases as combinations of
attributes
 The basic unit of analysis: the set and sub-sets
 Researchers code cases for having membership in
a set of causal conditions (e.g. the set of firms
with formal controls, the set of firms pursuing a
cost leadership strategy etc…)
 This information is then summarized in a truth
table and Boolean logic is used to reduce the table
to a few statements indicating necessary and
sufficient conditions and their combinations
Assessing Causal Complexity
Example: a researcher is interested in the causes of high performance
among a sample of firms and considers four possible causes of high
performance:
efficient = an efficient production system
innovation = a high rate of product innovation
environment = a stable environment
hierarchy = a hierarchical control structure
• is logical “and”
Possible findings include:
+ is logical “or”
(1) efficient  high performance
(2) efficient • environment  high perf.
(3) efficient + innovation  high perf.
(4) efficient • environment + innovation • hierarchy  high perf.
In (1) efficient
(2) efficient
(3) efficient
(4) efficient
is
is
is
is
necessary and sufficient
necessary but not sufficient
sufficient but not necessary
neither necessary nor sufficient
Organizational Characteristics
Configuration
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
A
Efficient
Production
System
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
No
No
No
No
No
No
No
B
High Rate of
Product
Innovation
Yes
Yes
Yes
Yes
No
No
No
No
Yes
Yes
Yes
Yes
No
No
No
No
C
Heterogeneous
Environment
Yes
Yes
No
No
Yes
Yes
No
No
Yes
Yes
No
No
Yes
Yes
No
No
Outcome
D
Hierarchical
Control
Structure
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Z
High
Performance
Yes
No
Yes
Yes
No
No
Yes
Yes
Yes
No
Yes
No
No
?
?
?
Simplifying Expressions
 Seven combinations may lead to high
performance:
#1.
#3.
#4.
#7.
#8.
#9.
#11.
A•B•C•D
A • B • ~C • D
A • B • ~C • ~D
A • ~B • ~C • D
A • ~B • ~C • ~D
~A • B • C • D
~A • B • ~C • D
• is logical “and”
+ is logical “or”
Simplifying Expressions
 These combinations can be simplified using a
simple algorithm:
A • B • ~C • D + A • B • ~C • ~D
A • B • ~C (D + ~D)
A • B • ~C
=
=
 Using the same algorithm, the seven
expressions can be logically reduced to one
simple expression:
A • ~C + B • D → Z
Set-theoretic Methods and
Equifinality
 Previous research has recommended qualitative
methods, surveys, and factor analysis for assessing
equifinality (Gresov & Drazin 1997)
 Set-theoretic methods such as QCA offer a systematic
approach that at the same time can examine
extensive numbers of different combinations but does
not disaggregate the case as a variable-based
approach would
 Set-theoretic methods allow us to strip away elements
that are not causally involved with the outcome
 Furthermore, these methods allow to measure
“coverage,” i.e. the relative importance of different
paths to an outcome, and “consistency,” i.e. what
proportion of observed cases are consistent with the
pattern
Moving Beyond Crisp Sets:
Fuzzy Sets
 Set membership need not be restricted to binary
values but can be defined using fuzzy sets, e.g.
1.00
0.80
0.60
0.40
0.20
0.00
=
=
=
=
=
=
fully in
mostly in
more in than out
more out than in
mostly out
fully out
 More than merely rescaling variables: fuzzy sets tie
variables to theoretical concepts and substantive
thresholds
What QCA Cannot Do
 QCA involves the imposition of theoretical and
substantive knowledge in examining imperfect
evidence. In this regard, set-theoretic methods are
faced with the same issues of causal inference as all
other methods that use non-experimental data
 QCA is not useful in very small-N situations (e.g. less
than 12 cases)
 Effective use of QCA depends on the ratio of cases to
causal conditions
 QCA is currently is not designed to do truly dynamic
longitudinal analyses
Some promising applications of STMs to
management and strategy research
 Current work on complementarities at the firm
level (e.g. Milgrom & Roberts 1990, 1995; Porter 1996;
Siggelkow 2001, 2002)
 Complementary HR practices (e.g. Huselid 1995;
Ichniowski, Shaw, & Prennushi, 1997; MacDuffie, 1995)
 The resource-based view (e.g. Barney, 1991;
Wernerfelt, 1984; Black & Boal 1994)
 Research on organizational configurations (Meyer,
Tsui & Hinings 1993; Ketchen et al., 1997; Miller, 1986;
Fiss, forthcoming)
 The literature on institutional complementarities
(Hall & Gingerich 2004; Hall & Soskice, 2001; Kogut and
Ragin 2002)
Empirical Analysis: Configurations and
Organizational Performance
 Sample of 205 high-technology manufacturing firms in the
UK (Cosh et al., 2002)
 Data collected in 1999 include items on organizational
structure, strategy, and environment
 Complete data on performance available for 139 firms;
missing values on independent measures imputed using MLE
Outcome of Interest: Membership in
the Set of High-Performing Firms
 Performance is measured based on Return on
Assets (ROA) benchmarked to performance of the
high technology sector (median ROA = 7.2%)
 Fuzzy set of high performing firms
ROA ≥ 16.3% (75th percentile)
ROA = 11.0%
ROA ≤ 7.2% (50th percentile)



FS = 1.0
FS = 0.5
FS = 0.0
 Fuzzy set of very high performing firms
ROA ≥ 25.0%
ROA = 16.3% (75th percentile)
ROA ≤ 7.2% (50th percentile)



FS = 1.0
FS = 0.5
FS = 0.0
Organizational Structure
 Formalization is measured using a set of 9 survey
items that assess to what extent e.g.




Formal policies and procedures guide decisions
Communications are documented by memos
Reporting relationships are formally defined
Plans are formal and written
 Items combined into a scale (Cronbach’s  = .83)
 Fuzzy set of firms with high degree of formalization
“Nearly always”
“About half the time”
“Almost never”



FS = 1.0
FS = 0.5
FS = 0.0
Organizational Structure
 Centralization is measured using a set of 5 survey
items that assess who is the last person whose
permission must be obtained (“department head,
division head, CEO, Board of Directors”) for e.g.
 Addition of a new product or service
 Unbudgeted expenses
 Selection of type or brand of new equipment
 Items combined into a scale ( = .74)
 Fuzzy set of firms with high degree of centralization
“Board of Directors”
scale mid-point
“Department Head”



FS = 1.0
FS = 0.5
FS = 0.0
Organizational Structure
 Complexity is measured using a combined measure
of vertical and horizontal differentiation
 Vertical differentiation was measured as the number of
levels in the longest line between direct worker and CEO
(Pugh et al., 1968)
 Horizontal differentiation was measured using the number of
functions with at least one full-time employee (Pugh et al.,
1968)
 Complexity is calculated as the product of horizontal and vertical
differentiation (Singh, 1986; Wong & Birnbaum More, 1994)
 Fuzzy set of firms with high degree of complexity
99th percentile (6 Levels / 17 Functions)
50th percentile (3 Levels / 9 Functions)
1st percentile (1 Level / 1 Function)



FS = 1.0
FS = 0.5
FS = 0.0
Organizational Structure
 Size is measured as average number of full time
employees, with fuzzy set membership tied to US SME
categories
 Fuzzy set of large firms
250+ employees
50 employees
10 or less employees



FS = 1.0
FS = 0.5
FS = 0.0
Strategy
 Differentiation strategy measured as competitive
capability based on product features and new product
introduction, combined into 5-point scale ( = .80)
 Low cost strategy measured as competitive
capability based on low labor cost, material cost,
energy consumption, inventory cost, combined into 5point scale ( = .86)
 Recoded into two fuzzy sets of firms with a
differentiation strategy and low cost strategy
(5) “Critically important”
(3) scale mid-point
(1) “Not important”



FS = 1.0
FS = 0.5
FS = 0.0
Environment
 Velocity assesses the speed of change (Bourgeois &
Eisenhardt, 1988) and is measured as length of main product
life cycle in months, recoded into fuzzy set of firms
operating in a high velocity environment
1 months
36 months
360 months



FS = 1.0
FS = 0.5
FS = 0.0
 Uncertainty is measured using two items that assess how
predictable were technological changes in the environment,
combined into a scale ( = .74) and recoded into a fuzzy
set of firms operating in a highly uncertain environment
“Completely unpredictable”
scale mid-point
“Easily predictable”



FS = 1.0
FS = 0.5
FS = 0.0
Calibration
 All variables were transformed into fuzzy sets using the
“direct” method of calibration (Ragin, 2008)
 The variables are assigned thresholds for full membership, full nonmembership, and the crossover point
 Variables scores are translated into the metric of log odds
 Membership scores are calculated using the formula below
Degree of Membership = exp(log odds)/(1 + exp(log odds))
where “ exp” stands for the exponentiation of log odds to simple odds
 The rescaled measures range from 0 to 1 and are tied to
their respective membership thresholds and crossover
points
Fuzzy Set Analysis
 The Inclusion algorithm described in Ragin (2000) is
the one used in most previous analyses using fuzzy
sets
 However, this algorithm circumvents the creation of a
truth table and thus forfeits some analytical
advantages when e.g. analyzing limited diversity
 To overcome this limitation, Ragin (2005) introduced a
Truth Table algorithm that is now implemented in the
fs/QCA software package (Ragin, Drass, & Davies 2006). This
algorithm additionally allows the calculation of
consistency and coverage scores
Modeling the Negation of the
Outcome
 In fuzzy set analysis, an important aspect relates to
modeling the absence of the outcome
 In this case that means modeling the absence of high
performance; note that this is different from modeling causes
leading to low performance
 Using the negation of the outcome here leads to
consistency scores considerably below the acceptable level
of 0.75, indicating the absence of a clear set-theoretic
relationship
 Put differently: there are few configurations that
consistently lead to high performance, but many
configurations that lead to no high performance
 Note that QCA thus allows for Causal Asymmetry, a
concept foreign to correlational methods that always
conceive of causal relations in symmetric terms
If you are interested in using
STMs or want to learn more…
Visit the fs/QCA homepage:
www.fsqca.com
(you can also download the fs/QCA software package here for free)
Or, visit my homepage:
http://www-rcf.usc.edu/~fiss/
(for links, papers, etc.)