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Questions & (tentative) Answers
Disclaimer
This compilation of Questions and Answers around QCA methodology is a
rough copy/paste from e-mail conversations between researchers and Sakura
YAMASAKI unless otherwise mentionned. Therefore, for non-technical questions
(i.e. all questions except software manipulation) we keep the dialogue
open to any comments or criticisms.
TECHNICAL MATTERS (QCA2.0; QCA3.0; TOSMANA)
SIMPLIFYING ASSUMPTIONS
(or Logical Cases, or Remainders)
CONTRADICTORY SIMPLIFYING ASSUMPTIONS
OTHERS
- Are there any micro level analyses published using these methods? Has anyone written about how to adapt QCA to micro-level analysis?
- Why the solution of outputs minimized: "1 Using don't cares: L" does not fully cover all the prime implicants of outputs minimized: "1" ? Doesn't it have to ?
- Why are the "complement"-solutions not the exact complement of the outputs minimized ?
- How do we choose when the software asks us to "choose from the following"?
- Do you usually try out till you find the best ratio between the number of cases and the number of variables/conditions?
RECENTLY ADDED Q&A
TECHNICAL MATTERS
In TOSMANA, how are the thresholds decided when
it is the software who decides (i.e. when not done manually)?
(By Lasse Cronqvist):
If you just change the number of thresholds used, the threshold will be
set so the range of data is cut into equally sized parts (so, if you choose
two thresholds, the range will be cut into three equally sized subranges),
no magic going on there. If you choose to cluster the data by pressing
the cluster button, a simple average linkage cluster will be performed.
How do I perform intersections?
Intersection function is feasible using
QCA 3.0 and TOSMANA softwares.
1- Using QCA3.0 software.
To select the equations to be intersected, put the pointer (arrow on the
left side of the screen) on the equation, go to "Edit" and select
"mark Intersection". A check symbol will appear next to the
selected equation. Repeat the same operation for the corresponding second
equation to be intersected.
NB: when intersecting another pair of equations after a first intersection,
be careful to deselect the previous equations ("Edit", "mark
Intersection"). In other words, the deselection of the equations
is not automatic.
2- Using the TOSMANA software.
Go to "Tools", "Calculator for Boolean Expressions". In the next window,
you should have the conditions on your left, a big "AND" "OR" buttons
and many other things.
Say, for example, that you wish to intersect the following two equations
that you obtained for the minimisation of 1s including logical cases and
0s including logical cases:
AB + cD
Ad + Cb
For the first equation, select condition "A" on your left box, select
its value, therefore "1", in the 2nd box, and since "AB" is the same as
"A AND B", click on the "AND" button.
On the box below,
"A(1) * A(1)"
will appear. Don't worry if A(1) appears twice, just continue:
Select condition "B" on your left box, select its value, therefore "1",
in the 2nd box, by then the box below should read
"A(1) * B(1)".
Since after AB comes a logical OR ("+"), click on the "OR" button.
And you continue until you've introduced the whole equation. When you
are done, click on the 3rd button "Add Expression to list".
On the very bottom box, your first equation should appear.
You do the same thing over for the second equation. When you are done,
select the 2 equations that you've put in the bottom box, click on "Compute
Intersection".
A small window will pop up, with terms (i.e. combinations of conditions)
representing the area where both equations intersect (i.e. share in common).
For more information on intersections:
RAGIN (1987) pp.118-121
WATANABE (2003) (PDF format. COMPASSS Working
Paper2003-13)
YAMASAKI (2003) (PDF format. Conference Proceeding)
In QCA2.0 or QCA3.0, I am not really sure if
i understand the difference between setting the L-cross in the upper or
lower space. And what does the programme exactly do if i set the cross
in the lower space? from my point of view, it turns only those "L"s into
"1" which help minimizing the equation by testing all possible combinations.
But as i already told you i received the most minimized solution when setting the cross in the upper space, and not - as I would expect - in the lower space.
I think i can summarize my problems within one sentence: i don't understand what the program is doing when i am putting the cross in the lower space.
If you want to minimize the "1L", you
have to cross the "1" in the upper space and the "L" in the lower space.
If you cross both the "1" and the "L" in the upper space, the software is going to minimize all the "1" (which is normal) but also ALL the "L". In other words, it will treat the "1" and ALL the "L" as if they were giving the same outcome (ie "1").
Whereas if you cross the "L" in the lower space, the software will SELECT the "L" cases that will allow a minimal equation for the outcome "1".
SIMPLIFYING ASSUMPTIONS
I'm trying to get my head around the simplifying
assumptions while doing QCA. Do you know some good references which illustrate
what these assumptions mean and what they do with the data-analysis.
About simplifying assumptions, they are
the same as "logical cases", and so basically they generate assumptions
that could make the minimal formula even more parsimonious, without ever
contradicting the existing observed cases.
The most recent piece of work by Ragin on them is the one on the COMPASSS website, "Recent advances in fuzzy-set methods and their applications to policy questions". The section II.A. "Limited diversity and simplifying assumptions" has several pages on how to deal with them. See also the recent article by Ragin and Rihoux in the fall 2004 issue of the APSA "Qualitative Methods" Newsletter.
Otherwise, you also have the Vanderborght-Yamasaki piece on the "contradictory simplifying assumptions", presented in ECPR General Conference Marburg, and published in French in the RIPC (see bibliographical section for references).
Other authors mention the issues around these simplifying assumptions, you can find the references in the French manual AQQC-QCA, chapter 4, section on logical cases.
For more information on simplifying
assumptions:
RAGIN (1987) pp.104-113
RAGIN and SONNET (2004) (PDF format.
COMPASSS Working Paper 2004-23)
RAGIN (2003) (PDF format. COMPASSS Working
Paper 2003-9)
On reduction of the number of simplifying assumptions:
SCHNEIDER and WAGEMANN (2004)
(PDF format. Conference Proceeding)
Vanderborght-Yamasaki; Clement; Grassi have treated simplifying assumptions
from different angles in the Special
issue of the RIPC (Vol.11, No.1).
CONTRADICTORY SIMPLIFYING ASSUMPTIONS
My problem is that I cannot remember how to find
out whether any contradictory simplifying assumptions have been used in
the reduction when using the TOSMANA software. How do I control for that?
In Tosmana, there are 2 options to find
out about contradictory simplifying assumptions.
1/ Check by hand and eye (only
suited if you've got no more than a handful of logical cases used in each
equation).
So, you want to check if the logical cases used in the "1 outcome using
L" and the "0 outcome using L" overlap. In order to do so, you have to
check the "compute simplifying assumptions" box when you are in the MVQCA
dialog window and then on "go".
As you know, a new window will appear with the results, and normally the
logical cases used in the minimisation will appear in red letters.
You do this again with the other outcome and then compare the two lists
of logical cases.
If one or more appear on both lists, you have contradictory simplifying
assumptions. This procedure is okay if you don't have that many logical
cases, but it can be quite a pain in the ass if you've got more than a
handful...
2/ Use the Boolean calculator and
intersect equations
In Tosmana, go to "Tools" go to "Calculator for Boolean Expressions".
In the next window, you should have the conditions on your left, a big
"AND" "OR" buttons and many other things.
Say, for example, that you wish to intersect the following two equations
that you obtained for the minimisation of 1s including logical cases and
0s including logical cases:
AB + cD
Ad + Cb
For the first equation, select condition "A" on your left box, select
its value, therefore "1", in the 2nd box, and since "AB" is the same as
"A AND B", click on the "AND" button.
On the box below,
"A(1) * A(1)"
will appear. Don't worry if A(1) appears twice, just continue:
Select condition "B" on your left box, select its value, therefore "1",
in the 2nd box, by then the box below should read
"A(1) * B(1)".
Since after AB comes a logical OR ("+"), click on the "OR" button.
And you continue until you've introduced the whole equation. When you
are done, click on the 3rd button "Add Expression to list".
On the very bottom box, your first equation should appear.
You do the same thing over for the second equation. When you are done,
select the 2 equations that you've put in the bottom box, click on "Compute
Intersection".
A small window will pop up, and if you have equations in it, those are
the overlapping combinations (or contradictory simplifying assumptions).
If you've got "---" it means you are safe! :-)
For more information on contradictory
simplifying assumptions:
VANDERBORGHT and YAMASAKI (2003)
(PDF format. Conference Proceeding)
VANDERBORGHT and YAMASAKI (2004) (In French. See bibliographical section
for references)
What do you do if you have overlapping minimised equations for 1s and 0s including logical cases (in other words contradictory simplifying assumptions or contradictory logical cases)? Exclude certain configurations??
Two possibilities are present:
1- If you had to chose among several simplifying assumptions to obtain your "1 including L" or " 0 including L", then you can always try with the other simplifying assumptions and see if your new equation contains contradictory simplifying assumptions.
2- You can also take a closer look at
your problematic simplifying assumption (the one that overlaps). See what
it means in words ("does it make sense theoretically or empirically?").
Then, based on your theoretical/empirical knowledge, you decide whether
this case should be coded "1" or "0". Once you have decided, you add this
case in your truth table (BUT ONLY for the minimizations including Ls,
of course), and minimize. After having done this, it's always safe to
confirm that there are no new contradictory simplifying assumptions that
have been generated by the inclusion of this theoretical case.
More information on contradictory simplifying assumptions:
VANDERBORGHT and YAMASAKI (2003)
(PDF format. Conference Proceeding)
VANDERBORGHT and YAMASAKI (2004) (In French. See bibliographical section
for references)
If the logical combinations are included, I have
to compute intersections . When i compute the intersections between the
two truth tables mentioned above, QCA3 finds the following primes:
A F G +
A B G +
A B D F +
A B c F +
A B e F
What am I supposed to do with this information?
Do I have to change something in my model? Or are those intersections
negligible, because there are only 5 intersections?
YES, it's a problem even if
you had had only one. It means that the software has given to these 5
configurations BOTH values of "1" and "0". It is contradictory, since
it's as if you were saying that the same set of conditions produces different
outcomes.
What you should do:
You have a closer look at these 5 configurations and think what kinds
of cases they represent. Based on your theoretical and empirical knowledge,
you decide to assign a value to these cases (either 1 or 0). You include
these 5 new "theoretical" cases into your truth table and run again the
analysis for 0 and 1, both with inclusion of Ls. (caution: never do this
in an analysis that does not include the Ls).
What you do by this is clearing up the contradiction by assigning yourself
a value to these 5 configurations. Check again by intersecting the newly
obtained minimal formulae.
More information on contradictory
simplifying assumptions:
VANDERBORGHT and YAMASAKI (2003)
(PDF format. Conference Proceeding)
VANDERBORGHT and YAMASAKI (2004) (In French. See bibliographical section
for references)
I am working with 10 cases and 7 inputvariables. I was lucky: no contradictionary cases! but tons of intersections of the simplifying assumptions.
I read in the De Meur-Rihoux handbook that you have to "fix" these logical cases as "real" cases with a clear outcome (0 or 1). But do you think this really works? And what happend afterwards (I didn't try out yet): do I create again new intersections? How do you usually handle this problem?
In fact, it's quite normal that you don't
have any contradictory cases and lots of contradictory simplifying assumptions.
This is because of your ratio between your number of cases and number
of independent variables (10 and 7). You have 128 possible combinations
of cases, and you have 10 cases. Therefore, observing two same combinations
with different outcomes becomes quite rare. Moreover, if you include logical
cases in your minimisation, the software will use lots of them for each
minimisation.
The best advice would therefore be to
either increase the number of cases (for example by dividing them along
timeline) or to reduce your number of conditions. In the first case, if
you keep 7 conditions, maybe 20 cases would be nice. In the latter case,
if you keep 10 cases, maybe 4 or 5 conditions would be nice. But i know
that this is often hard or impossible to do.
So, about the contradictory simplifying assumptions, i am almost sure that you chose to display them with the TOSMANA software. This software is more transparent, but on the other hand, it is more scary...
Let me explain. When you intersect simplifying
assmptions with QCA3.0, you may get something like this:
Model : R = A + B + C
Assumptions used :
AB +
aC+
AbC
In TOSMANA, for the same model and same
analysis, you will get:
Assumptions used:
A B C +
A B c +
a B C +
a b C +
A b C
You see, QCA3.0 "minimises" its assumptions, whereas Tosmana doesn't. The first assumption in QCA3.0 (AB) is the same as the two first ones in Tosmana ( ABC + ABc), it's just a "minimised" version.
Thus, i would advise you to calculate them again using QCA3.0 and add several "theoretical" cases to your truth table to eliminate the contradictions (e.g. just AB- and not ABC and ABc).
After you have added "theoretical" cases to your truth table, you re-run the analysis, and yes, you have to intersect again the new formulae's simplifying assumptions, just to be sure.
(Question continued, reaction
to answer):
In Tosmana, I was also using the Boolean Calculator.
This instrument was suitable to find a "reduced" number of symplifying
assumptions in the way you described for QCA3. With the "reduced" results
of the Boolean Calculator I could go into the results which were generated
by the tool "compute simplifying assumptions" in Tosmana and so it was
easier to find the assumptions who really overlapped.
Still I am not sure if it is methodically "clean" to turn assumptions into "real" cases especially if I don't have any clue which outcome to choose.
That is one of the reasons why QCA is
sometimes so theory-driven... Yes, if you don't know what could possibly
be the outcome for non-observed cases based on your theoretical/empirical
knowledge, then i can see why attributing a value to these cases is a
problem to you. But maybe just to reassure you, when you attribute a value
to one of more simplifying assumptions, you never present the newly obtained
formula as a minimisation of "observed values". In any cases, there are
generalisations based on your observed cases. Thus, it's not as if you
were saying that these "theoretical cases" are for real. Tell yourself
that you are just helping the programme in not making any mistakes. After
all, when you minimise by including logical cases, the programme chooses
the outcome value of simplifying assumtions for you (without asking your
opinion), too.
More information on contradictory
simplifying assumptions:
VANDERBORGHT and YAMASAKI (2003)
(PDF format. Conference Proceeding)
VANDERBORGHT and YAMASAKI (2004) (In French. See bibliographical section
for references)
OTHERS
Are there any micro level analyses published using these methods? Has anyone written about how to adapt QCA to micro-level analysis?
It is true that QCA is mainly used for
macro or meso-level phenomena so that the cases are often countries or
organisations.
However, there are some studies in which cases are individuals, and i
know of other researchers who are also trying to apply QCA at the micro-level.
DE GRAAF, Theo K. (2001), From Hermeneutics to Empiricism: Extracting Testable Research Hypotheses From the Study of Individual Cases (unpublished manuscript). (Unpublished paper)
Abstract: There is increasing awareness of the lack of both comprehensiveness and specificity of current psychiatric classification systems. Apparently, the old Kraepelinian ideal of nosological entities characterised by the same cause and the same optimal treatment, does not hold. Co-morbidity constitutes a major obstacle for research as well as for evidence-based treatment programs. The author proposes a “bottom-up” approach with the help of multiple N=1 studies of individual cases sharing the same behavioural, cognitive, and/or affective symptoms, in the vein of Ragin’s method of qualitative comparison. In this way, possible psychodynamic, psychotoxic, and genetic influences leading to psychopathology can be mapped and built into hypotheses for subsequent quantitative research. With the help of in-depth observations on a limited number of juvenile delinquents, it can be shown that such a heuristic procedure may result in the establishment of a causal-developmental profile. In comparison with conventional diagnosis, such a causal-developmental profile matches more closely the life experiences and inner world of the patient and will therefore lead to more adequate treatment strategies.
KANOMATA, Nobuo (2001), "Saibankan no Keireki: Kojin Deita heno Ouyou
[Career of Judges: Application [of QCA] to Personal Data]", in KANOMATA,
Nobuo, NOMIYA, Daishiro, and HASEGAWA, Keiji (eds), Shituteki Hikaku Bunseki
[Qualitative Comparative Analysis], Kyoto, Mineruva Syobo, pp. 63-78.
LIEBERSON, Stanley and BELL, Eleanor O. (1992), "Children's First Names : an Empirical Study of Social Taste", American Journal of Sociology, 98, 3, 511-554.
MIETHE, Terance D. and DRASS, Kriss A (1999), "Exploring the Social Context of Instrumental and Expressive Homicides: an Application of Qualitative Comparative Analysis", Journal of Quantitative Criminology, 15, 1, 1-21.
Abstract: Using data from the UCR's Supplementary Homicide Reports, the method of Qualitative Comparative Analysis (QCA) is used to examine whether instrumental and expressive homicides are similar or unique in their social context (i.e., combinations of offender, victim, and situational characteristics). Instrumental and expressive homicides are found to have both common and unique social contexts, but the vast majority of homicide incidents involve combinations of individual and situational factors that are common in both general types of homicides. Among subtypes of instrumental (like rape, prostitution, robbery murders) and expressive homicides (like lovers triangles, brawls and arguments), there is wide variability in their prevalence of unique and common components. After discussing these results, the paper concludes with illustrations of how QCA may be used in other areas within criminology.
MUSHENO, Michael C., GREGWARE, Peter R., and DRASS, Kriss A. (1991), "Court
Management of AIDS Disputes : a Sociolegal Analysis", Law and Social
Inquiry, 16, 4, 737-776.
RANTALA, Kati and HELLSTRÖM, Eeva (2001), "Qualitative Comparative
Analysis - a Hermeneutic Approach to Interview Data", International
Journal of Social Research Methodology, 4, 2, 87-100.
SCHWEIZER, Thomas (1996), "Actor and Event Orderings Across Time:
Lattice Representation and Boolean Analysis of the Political Disputes
in Chen Village, China", Social Networks, 18, 247-266.
TYRKKO, Arya (2.2002), "The Intersection Between Working Life and
Parenthood. A Boolean Approach", Economic and Industrial Democracy.
An International Journal, 23, 1,
Abstract: This article aims at investigating the research concerning the interplay between working life and parenthood in an effort to sort out what is interesting to discuss and study further. The relationship between working life and parenthood is discussed focusing on the working life. Parenthood puts into focus the extent to which there is room for adjusting to demands from other life spheres when engaged in paid work. The investigation shows the importance of taking into account the gendered structures and practices in working life when trying to explain individual adjustment strategies. Approaches which are built upon a holistic research design, have proven to be valuable strategies in analyses of such complex phenomena as the adjustment between working life and family life.
WILLIAMS, Linda Meyer and FARRELL, Ronald A. (1990), "Legal Response
to Child Sexual Abuse in Daycare", Criminal Justice and Behavior,
17, 3, 284-302.
Why the solution of outputs minimized: "1
Using don't cares: L" does not fully cover all the prime implicants
of outputs minimized: "1" ?
Doesn't it have to ?
In fact, the Prime Implicants for 1 using
don't cares L do cover all the Prime Implicants for 1s.
It's just that it's not visible with the eye. If you:
- list all the configurations (the raw configurations, not the Prime Implicants)
for the 1s ; and
- try to cover them with the Prime Implicants of 1s using don't cares
L,
You'll see they match.
Concretely, i guess you were talking
about, for example,
a B C E F
in table 1 that is not covered, right?
Well, this term is equal to
a B C d E F +
a B C D E F
which are covered by Prime Implicants
D F
and
a d
Why are the "complement"-solutions not the exact complement of the outputs minimized ?
You don't get the exact same complements
because there isn't a causal symmetry in your data. In other words, the
explanations for 1s are not the exact opposite of the explanations for
0s. There are some rare cases where you can find a causal symmetry in
your analysis of 1s and 0s with Don't Cares L. It might mean that your
conditions are quite relevant vis-à-vis the outcome phenomena (cf
QCA manual from Gisele and Benoit, p. 78).
But let me explain about causal symmetry.
Because QCA uses 1s and 0s, it's true that we may think that all that
is not associated to 0s are associated to 1s. Take for example the variables
"good" (it's a good weather), "rich" (the person is wealthy), and "need"
(the person needs something) for the outcome "shopping" (the person goes
for shopping). The results may indicate that people go shopping when it's
sunny (with logical cases). So the weather is a strong predictor for people
going shopping. But does this mean that we can say people DON't go shopping
when it's not good weather? Or let's say that the results indicate that
people don't go shopping when they are not rich AND not in need of something
(s = rn). Would this mean that people do go shopping only when they are
rich OR in need of something? We cannot say. This is because there is
not neccessarily a causal symmetry in human behaviour.
How do we choose when the software
asks us to "choose from the following"?
Here's my QCA 3.0 output:
_____
Model:
OUTCOME = A + B + C + D + E + F + G
Outputs Minimized: 1 Using Don't Cares: L
Method: Quine-McCluskey (Minimal)
F G + B G
*****One From The Following Group*****
B D F
a B F
B c F
B e F
******************************
Outputs Minimized: 0 Using Don't Cares: L
Method: Quine-McCluskey (Minimal)
A + b g
_____
Here's my questions:
In the upper part (outputs minimized: 1) it says "one from the following
group". So what I did was to choose the one, that fits the best (with
regard to content) with the case that is covered by this prime. Is this
right? And what if I chose each of those primes? Would that mean, that
my solution is wrong or would it just mean, that I don't have the most
minimal solution?
Yes, you are right to select one implicant
based on your case knowledge. If you decide to chose each of these primes,
it would mean that you do not chose the most minimal solution. But doing
so is not logically wrong.
Do you usually try out till you find the best ratio between the number of cases and the number of variables/conditions?
Well, as would Benoit say, "i don't have a clear cut answer to this one". :-) The "best ratio" is an abstract concept, and we don't have any reference table to decide whether a truth table has a good ratio or not.
For more information on independent
variable selection in QCA:
AMENTA & POULSEN (1994) (See bibliographical section
for reference).
RECENTLY ADDED Q&A
Last modified: 06-Jan-2008
Benoît RIHOUX, Centre de Politique Comparée
Gisèle
DE MEUR, Lab.
de recherche en MAThématiques et sciences humaines
Afdeling
Arbeids- en Organisatiesociologie
Peter BURSENS,
Onderzoeksgroep
Internationale Politiek