Using case‐based approaches to analyse large datasets: a comparison of Ragin’s fsQCA and fuzzy cluster analysis

Figures & data

Figure 1 Perfect sufficiency.

Figure 2 Quasi‐sufficiency.

Table 1. Highest qualification better than ‘Ordinary’ level by class, ability and sex (Cooper & Glaesser, 2007).

CLASS_S = service class origin	HIGH_ABILITY = measured ability in top 20% (at age 11)	MALE	Number of cases	HQUAL = highest qualification better than ‘O’ level	Consistency with sufficiency
1	1	1	262	1	0.863
1	1	0	333	1	0.793
0	1	1	359	1	0.691
1	0	1	502	0	0.584
0	1	0	413	0	0.521
1	0	0	458	0	0.485
0	0	1	1676	0	0.358
0	0	0	1797	0	0.224

Table 2. Consistency and coverage indices.

Consistency

Coverage

Table 3. Fuzzy memberships in A and B and derived sets.

Case id	A	B	a	b	AB	Ab	aB	ab
1	1.00	0.00	0.00	1.00	0.00	1.00	0.00	0.00
2	1.00	0.51	0.00	0.49	0.51	0.49	0.00	0.00
3	0.55	0.45	0.45	0.55	0.45	0.55	0.45	0.45
4	0.65	0.55	0.35	0.45	0.55	0.45	0.35	0.35
5	0.20	0.45	0.80	0.55	0.20	0.20	0.45	0.55
6	0.20	0.51	0.80	0.49	0.20	0.20	0.51	0.49

Figure 3 Twelve invented cases with membership in A and B.

Figure 4 Twelve different invented cases with memberships in A and B.

Figure 5 Fuzzy calibration of ability (variable n920 in the NCDS files).

Table 4. Class scheme employed (Erikson & Goldthorpe, 1993) and fuzzy scores.

Class	Label	CLASS_F: fuzzy score
1	Upper service	1.000
2	Lower service	0.830
3	Routine non‐manual	0.583
4	Petty bourgeoisie	0.583
5	Supervisors etc.	0.417
6	Skilled manual	0.170
7	Semi‐ and unskilled manual	0.000

Table 5. Fuzzy scores for highest qualification at age 33.

Highest qualification gained at age 33	HQUAL_F: fuzzy score
Degree or higher NVQ5, 6	1.00
Higher qualification NVQ4	0.83
A Level/equiv NVQ3	0.67
O Level/equiv NVQ2	0.42
CSE 2–5/equiv NVQ1	0.17
No qualification	0.00

Table 6. Cluster centres from FCA.

	Cluster 1	Cluster 2	Cluster 3	Cluster 4	Cluster 5	Cluster 6	Cluster 7	Cluster 8
CLASS_F	0.848	0.743	0.143	0.828	0.117	0.141	0.644	0.113
ABILITY_F	0.940	0.288	0.834	0.928	0.113	0.863	0.420	0.097
MALE	0.003	0.992	0.996	0.997	0.003	0.003	0.008	0.997

Table 7. The fsQCA configurations by best FCA cluster (number of cases).

	FCA cluster where each case has its maximum membership
fsQCA configuration (Class, Ability, Male)	4	1	2	7	3	6	8	5
111	742	0	60	0	0	0	0	0
110	0	784	0	155	0	0	0	0
101	0	0	400	0	0	0	0	0
100	0	0	0	306	0	0	0	0
011	0	0	3	0	705	0	0	0
010	0	0	0	22	0	848	0	0
001	0	0	33	0	29	0	827	0
000	0	0	0	30	0	0	0	856

Figure 6 The 155 cases in both configuration 110 and with maximum membership in fuzzy Cluster 7 (with four cluster centres for females).

Table 8. HQUAL_F = Function(CLASS_F, ABILITY_F, MALE): the resulting truth table.

Most similar FCA cluster	CLASS_F	ABILITY_F	MALE	Number	HQUAL_F	Consistency (from fsQCA software)	Coverage (from Excel calculation)
4	1	1	1	802	1	0.876	0.248
1	1	1	0	939	1	0.830	0.268
3	0	1	1	708	1	0.791	0.233
2	1	0	1	400	0	0.750	0.133
6	0	1	0	870	0	0.721	0.252
7	1	0	0	306	0	0.721	0.118
8	0	0	1	889	0	0.560	0.183
5	0	0	0	886	0	0.496	0.163

Table 9. HQUAL_F as outcome, using FCA clusters as the rows.

fsQCA ‘lookalike’ configuration	FCA cluster	Consistency	Coverage
111	4	0.874	0.208
110	1	0.840	0.218
011	3	0.771	0.190
101	2	0.756	0.132
100	7	0.745	0.137
010	6	0.702	0.198
001	8	0.522	0.145
000	5	0.457	0.126

Cooper , B. and Glaesser , J. Exploring social class compositional effects on educational achievement with fuzzy set methods: A British study . Paper presented at the annual meeting of the American Educational Research Association . Chicago . April .

 Google Scholar

Erikson , R. and Goldthorpe , J.H. 1993 . The constant flux , Oxford : Clarendon Press .

 Google Scholar