FUZZY SET QCA
A SET-THEORETIC APPROACH FOR
UNDERSTANDING AND
INVESTIGATING MAORI RESILIENCE
THROUGH THE CHRISTCHURCH
EARTHQUAKES
SIMON LAMBERT
LINCOLN UNIVERSITY
simon.lamber t@lincoln.ac.nz
WHAT ARE SET-THEORETIC
APPROACHES?
•
Social theory is often verbal and verbal formulations are
largely set theoretic in nature
WHAT ARE SET-THEORETIC
APPROACHES?
•
Social theory is often verbal and verbal formulations are
largely set theoretic in nature
• We often deal with membership of case studies in
researcher-defined sets
• We can understand social phenomena as set relations
• These set relations can be interpreted in terms of
sufficiency and necessity
WHAT ARE SET-THEORETIC
APPROACHES?
•
Social theory is often verbal and verbal formulations are
largely set theoretic in nature
• We often deal with membership of case studies in
researcher-defined sets
• We can understand social phenomena as set relations
• These set relations can be interpreted in terms of
sufficiency and necessity
Maori
WHAT ARE SET-THEORETIC
APPROACHES?
NZ citizens
Maori
WHAT ARE SET-THEORETIC
APPROACHES?
NZ citizens
(Y)
~X,~Y
Maori
(X)
X,Y
~X,Y
WHAT ARE SET-THEORETIC
APPROACHES?
Vulnerable
(Y)
~X,~Y
Maori
(X)
X,Y
~X,Y
WHAT ARE SET-THEORETIC
APPROACHES?
Resilient
(Y)
~X,~Y
Maori
(X)
X,Y
~X,Y
CAUSAL COMPLEXITY
In causal discourse, two terms dominate proceedings: ‘necessity’
and ‘sufficiency’
A cause is necessary if its presence is always required for a
particular outcome.
A cause is sufficient if its presence by itself produces a particular
outcome.
RU WHENUA OTAUTAHI
IDENTIFYING NECESSARY
CONDITIONS
Good design
Building collapses Must be empty…
Building doesn’t
collapse
Not ‘relevant’
Bad design
Cases
IDENTIFYING SUFFICIENT
CONDITIONS
Good design
Cases
Building collapses
Building doesn’t
collapse
Bad design
Not ‘relevant’
Must be empty…
http://www.compasss.org/index.htm
QUALITATIVE COMPARATIVE
ANALYSIS (QCA)
• Designed by Charles Ragin.
• Case-oriented approach.
• Accepts causes will be configurational,
i.e., comprised of several factors…
• …with more than one pathway to
outcomes (equifinality)
• Enables systematic cross-case
comparisons without ignoring complexity
within cases.
QCA IS IDEAL FOR SMALL-TOINTERMEDIATE-N RESEARCH DESIGNS:
QCA can be usefully applied to
research designs involving small
and intermediate-size Ns (e.g., 550).
In this range, there are often too
many cases for researchers to
keep all the case knowledge “in
their heads” but too few cases for
most conventional statistical
techniques.
OPERATIONALISING
QCA …
The first stage begins with the dichotomous coding of
selected variables that are then presented in a ‘data table’.
Case
Variable
1
Variable
2
Variable
3
Outcome
1
1
1
0
1
2
1
0
0
0
3
0
0
1
0
n
0
1
1
1
TRUTH TABLE…
Case
A
B
C
Outcome
1
A
B
c
S
2
A
b
C
s
3
a
B
C
s
ABc → S
BUT IS THE REAL WORLD SO CLEAR CUT?
NZ citizens
(Y)
~X,~Y
Maori
(X)
X,Y
~X,Y
Australian citizens
NZ citizens
Maori
FUZZY-SET/QCA
Designed to capture two aspects of
diversity:
• Differences in kind (as with QCA)
• Differences in degree (i.e., membership b/w
0 and 1)
…thus acknowledging partial
membership in sets, a phenomenon
readily observed in the real world.
LINCOLN RESEARCH
PROJECTS
LURF (Internal Lincoln University funding)
• Quick grab of data = 10 interviews (Maori
emergency workers, managers in CBD Feb 22)
• Detailed email survey (n=40; 21 Maori)
TPK
• Social and economic affects on Whānau
10 + 10 interviews
Ngā Pae o te Māramatanga
• Maori mental health networks
• Partnering with Te Awa o te Ora and Mental
Health Education and Resource Centre
(MHERC)
INTERVIEWS…
When I evacuated the office, my work colleague who was
pregnant needed help... As I was walking past Joe’s Garage, I
could hear screaming in there. I helped this one lady out, I ended
up carrying her. Both her legs were crushed.
Me personally? Oh I didn’t have time to be affected by the
earthquake… on the day we were in the CBD ... I was more
worried about my entire team dying in front of my eyes actually.
I wrapped her up and said a little prayer to myself. ‘If this is it,
please protect my girl.’
EST. CHRISTCHURCH NET MIGRATION YEAR BY
AGE FOR SELECTED ETHNICITIES (JUNE 2011)
5.00%
0.00%
6 yrs 7 yrs 8 yrs 9 yrs
10
yrs
11
yrs
12
yrs
13
yrs
14
yrs
-5.00%
-10.00%
Pakeha
NZ Maori
Samoan
-15.00%
-20.00%
-25.00%
-30.00%
All Ethncities
FAMILY AND EXODUS
NEIGHBOURHOODS
Percent 01Land Area Red Zoned
•
•
.
•
.
~ 410 UX)
(35)
1~510 ~ 4 (3~)
43.310 155 (M)
8210 433 (:Ie)
010 82(31)
SURVEY
• SurveyMonkey
• Sent to participants and through networks
• Ridiculously long, but grabbed considerable detail
• N = 40, 21 Maori
OVER 50 PATAI…
RESULTS…
Personal impacts from the earthquakes (Maori and Pakeha)
RESULTS…
Household impacts from the earthquakes
WELLBEING PRE-QUAKE…
How wou[ld YO'IlIIdescribe your personall weill-beii ngl in eacllil of these fOil I'" areals befol'"e tJIiIe
February 22111d 101[1, earthq[uake?
Vel!)'
sirong
exa
r ail e conomic w ell-being (fo r
Ie, inca e', job, work. hours ,
llIlo rtgag e, b
35. 'k
)
e-I)
.
Owera 's o I well-being (fo r
,e xam
, 'sports, I urch , p ub,
P :e5, cI bs)
Overall renyira
nlal wei being
("Dr ,exam e, beoaeh, Iishi g,
g an::teoni
OYerall cu
e'xa
, wal ing)
25.
.,,.
(5)
.,.
S'tir ong
Good!
~i...eliage
45.0%
01.0%,
(9)
2 .Or ~
(41
45.0%
1 5 . [}i="~
(9)
)
,- .O%. (I
45.0%
15.0i::.
1 •[li=tC>i
(5)
(9)
(3)
( ~
30.0%
25. =.t.
(5)
Ja Gl'%!
(II»
15.0i::.
25.
,~
Wea
~
'1111!1fJ'
ResponsE!
weak
Count
0.0
(Oil
0.0%
to)
!5.0 ' , (t)
0.0
~
I
01.0% ~ ~
0.0
~
I
01.0%
I
1OI.0i::.
~
aJ well-being (fo r
Ie', arts - d crafts.
kapa haka, mus
, wana ngat,
1111
si e)
~S l
)
WELLBEING POST QUAKE…
How woul d you desclribe your persornal well-be,in'9 now?
V ,ery
Slir ongl
Good
A .v erage
2(U )%
25 . %
,41:11.11%,
15 _0%
(4 )
(5 )
(8 )
(3 )
Ht O%
2f 1.O%
201]%
25_G%
20_0%
(2)
(4 )
(4 )
It 5)
(4 )
10_0%
25rJI%
25.0%,
20.[)%
1:5_0%
(2 )
15)
(5 )
(4 )
(3)
0 _0%
1:5 .0%
251]%
30_G%
1:5_0%
(2)
(3)
(:5 )
1(6)
(3)
s t rollg
OV!!Ta eco:nom ic weill-beillg ( for
e xa m ple . i ncom e. j ob. wort hours.
m ortgag e. be:neti )
o".e ral l social weill-b eing ( for
e x am p le. sp orts. c hurc h . pub.
parties. C!lu bs)
Overall enViiro:nme rlital w ell-be in g
(fur e xample. b each v isits . tis h in g .
gardening . walki ng)
Overall cu lrural
w e ll~be i n g
( for
e x am p ie . a rts. a nd c rafts.
k.a pahaka. m useum. wammga)
Wea'k
OJ)% (0)
Very'
Respcollse
weak
COllnt
CU I% (O)
20
5.0% ( 1)
20
5 _0% ( 1)
20
5 _0% ( 1)
20
ECONOMIC WELLBEING
Very strong
Very weak
10
9
8
7
6
5
4
3
2
1
0
Strong
pre 22‐2
Weak
Good
Average
ECONOMIC WELLBEING
Very strong
Very weak
10
9
8
7
6
5
4
3
2
1
0
Strong
pre 22‐2
post 22‐2
Weak
Good
Average
SOCIAL WELLBEING
Very
strong
10
9
8
7
Very
weak
6
5
Strong
4
3
2
1
0
pre‐22/2
Weak
Good
Average
post‐22/2
ENVIRONMENTAL WELLBEING
Very strong
Very weak
9
8
7
6
5
4
3
2
1
0
Weak
Strong
pre 22‐2 Envt
post 22‐2 Envt
Good
Average
CULTURAL WELLBEING
Very strong
7
6
5
Very weak
4
Strong
3
2
1
pre 22‐2
0
post 22‐2
Weak
Good
Average
Soooo, we’re not resilient?!
CAUSAL PATHWAYS TO MAORI
RESILIENCE …
Construct sets
Informed by earlier research
Choose variables
Domains, property space
Taken from survey questions
Calibrate memberships…
CAUSAL PATHWAYS TO MAORI
RESILIENCE …
Be
BB
BB
BO
BG
Persincome
Hse income
Bdrm
55,001- 65,000
125,001 - 175 ,000
55,001- 65,000
55,001- 65,000
E less than 18,000
Ove r 80,000
65,001 - Househo ld income
18,000 -
-
less than 18,000
125, 001
Ove r 80,000
90,001 -
Ove r 80,000
Ove r ! 7
Ove r 80,000
65,001
65,001- 80,000
23,001- 28,000
35,001 - 45,000
35,001 - 45,000
3
Ove r 17
90,001
-
90,001 -
Ove rl 7 Wh anau con tact
90,001
-
45,001
-
Persincome
55,001 - 65,000
\.
65,001 -
65,001- 80,000
45,001- 55,000
! less than 18,000
Ove r ! 7
Never
- M oved
30,001 -
Yes
No
I
90,001
Ove r 80,000
125, 001 -
23,001- 28,000
18,001- 23,000
65,001- 90,000
65,001 - 90,000
55,001 - 65,000
45,001 - 65,000
~ /':' , UUU
•
Ove r 80,000
125, 001- 175,000
3
6
2
3
less than 18,000
90,001- 125,000
3
~ .O
0.9
0_8
0.7
0.6
0_5
0.4
0.3
1.0
0.67
0.33
0. 17
0
1
0
Daily
Weekly
Monthly
45,001- 55,000
0 .8
08
55 ,001 . 65,000
>$175,000
$125,001 - $175,000
$90,00 1 - $125,000
$65,00 1 - $90,000
$45,00 1 - $65,000
$30,00 1 - $45,000
$18,000 - $30,000
<$18,000
Once or twice a yea r
persinc
125,001 - 175, 000
90,001- 125,000
Ove r 175,000
65,001 - 90,000
90, 001 - 125, 000
Ove r 175,000
90,001- 125,000
45,001 - 65,000
65,001 - 90,000
Over 175,000
90,001- 125,000
18,001- 23,000
55,001 - 65,000
0 .3
less than 18,000
_ " <;_CIl'I 1_
':; <;_1lClO
165,001 - 90,000
18,000 - 30,000
90,001 - 125,000
b."
BE
Hseincom e
125,001- 175,000
Ove r 175,000
3 23 001 - 28, 000
Ove r 80,000
BO
30,001 - 45,000
125,001- 175,000
65,001- 90,000
0 .8
1
0 .2
65,001- 90,000
45,001 - 65,000
125,001 - 175,000
90,001- 125,000
no
CI.,,, L 1.3<;.1\C1('l
hse inc
•I
0.9
0.7
1
0."
0.8
0.9
0.8
1
0.7
0.8
1
0.8
0.6
0.7
1
0.8
0.5
0.9
0.7
0. 7
0.6
0.9
0.8
1,1.
CAUSAL PATHWAYS TO MAORI
RESILIENCE …
EN
EO
EP
EQ
ER
ES
fT
EU
EV
EW
EX
EY
EZ
Strong
0.8
Very strong
1
Ave rage
0.4
Ave rage
0.4
Very w eak
o
Very w eak
o
V ery weak
FA
0.6
0.4
Strong
0.8
Ve ry strong
1
Very strong
1
Good
0.6
Very strong
1
Ve ry strong
1
Very strong
1
Ve ry st rong
Ve ry strong
1
Good
0.8
Strong
Strong
0.6
0.8
Ave rage
Strong
0.6
0.8
Good
Good
0.4
0.6
Strong
1
0.4
0.8
o
well2
Weak
0.2
Weak
0.2
Good
Strong
0.8
Good
0.6
Av erage
Weak
0.2
Average
0.4
Average
Good
0.6
Good
0.6
1
Good
0.6
Good
0.6
Average
0.4
Ve ry strong
1
Good
0.6
Good
0.6
Average
0.4
Ve ry strong
1
Strong
0.8
Good
Very strong
1
Ve ry strong
1
Strong
0.8
Strong
0.8
Strong
Strong
O.S
Strong
0.8
Strong
0.8
0.8
Good
Strong
0.6
0.8
Strong
0.6
0.8
Strong
0.8
Ve ry strong
1
Good
0.6
Strong
0.8
Ve ry strong
1
Strong
0.8
Strong
very strong
1
Strong
0.8
very strong
1
Ve ry strong
1
v ery strong
1
Strong
0.8
0.8
Ve ry strong
1
Good
0.6
Average
0.4
Very strong
1
Good
0.6
Ave rage
0.4
Good
0.6
Very strong
1
Ve ry strong
1
Very strong
1
Good
0.8
Very strong
1
Good
Very w eak
o
weak
1
0.8
Strong
o
0.6
0.2
Very strong
Ve ry w eak
Ve ry w eak
o
Very w eak
o
Very weak
Good
0.6
Strong
0.8
Strong
Strong
0.8
Av erage
Strong
Good
Ave rage
0.6
0.4
Good
Strong
0.8
0.6
Good
0.8
0.8
O.S
Strong
Strong
0.8
0.4
Good
0.6
0.6
Strong
0.8
Strong
0.8
Strong
0.8
Strong
0.8
Ave rage
0.4
Strong
0.8
Strong
0.8
Strong
0.8
Strong
0.8
Strong
Strong
0.8
Average
0.6
0.4
Strong
Strong
0.6
0.4
Good
0.6
0.8
0.8
Good
Av erage
0.8
0.4
0.8
0.4
St rong
0.8
Strong
0.8
Good
Strong
Good
0.6
Good
0.6
Good
0.6
0.6
Weak
0.2
Average
0.4
Good
0.6
Good
Strong
Good
0.8
Strong
Very strong
0.8
Strong
Strong
Strong
Good
Ave rage
Good
0.6
0.6
Weak
0.2
We ak
0.4
Average
Weak
0.2
Strong
Good
Good
0.8
Ave rage
0.4
0.4
Ave rage
Good
0.8
Av erage
0.8
0.4
Ave rage
0.4
Strong
Ave rage
0.6
o
Good
0.6
0.6
Weak
0.2
Good
Very strong
0.8
Ave rage
0.4
Olicome
•
Se!
Se! N....,ted
II
I
Ci>JSoj Coodib:."
CAUSAL PATHWAYS TO MAORI
RESILIENCE …
econ1*~move*hseinc*~impacts
econ1*move*hseinc*impacts
raw
unique
coverage coverage consistency
0.741344 0.741344 0.709552
0.133401
0.133401
R
solution coverage: 0.874745
solution consistency: 0.722456
0.803681
e1*~m*hseinc*~i
e1*m*hseinc*i
CAUSAL PATHWAYS TO MAORI
RESILIENCE …
In plain language: resilient individuals displayed…
1. No impacts, not moving, high household income,
strong pre-quake economic wellbeing
2. Significant impacts, moving away, high household
income, strong pre-quake economic wellbeing
PATHWAYS TO NON-RESILIENCE?
impacts*~move
raw
unique
coverage coverage consistency
0.467800 0.121646 0.895548
~impacts*move
0.089445
0.071556
1.000000
~persinc
0.398032
0.051878
0.855769
~mcult*~cult1
0.275492
0.063506
0.708046
solution coverage: 0.702147
solution consistency: 0.813471
CONCLUSIONS
• Resilience is yet to be demonstrated
• But that is to be expected!
• It is preceded by endurance…
• Set theoretic methods are powerful tools
in social research.
• fsQCA is a useful tool in understanding,
investigating and communicating Maori
resilience contexts.