Interpretability of Composite Indicators Based on Principal Components

Table 5

Impact of constraints on loadings and pillar characteristics.

Pillar	Input ID	Conventional loadings		Correlation with pillar	Loadings with constraint		Correlation with pillar
		S1	S2		S1	S2
Panel A: Uganda data set
ABS	1	–0.15	0.58	0.30	0.00	1.00	0.59
	2	0.40	–0.33	0.14	0.36	0.00	0.31
	5	0.49	0.34	0.74	0.53	0.00	0.56
	6	0.20	–0.48	–0.17	0.15	0.00	0.09
	7	0.55	0.27	0.74	0.58	0.00	0.62
Variance explained		1.30	1.16		1.29	1.00
AST	1	0.40		0.73	0.40		0.73
	2	0.35		0.64	0.35		0.64
	3	0.35		0.65	0.35		0.65
	4	0.37		0.69	0.37		0.69
Variance explained		1.85			1.85
SSN	1	0.53	–0.03	0.52	0.65	0.00	0.58
	2	0.56	–0.18	0.46	0.64	0.00	0.55
	3	–0.42	–0.10	–0.49	0.00	1.00	0.57
	4	0.07	0.98	0.68	0.06	0.00	0.05
Variance explained		1.29	1.00		1.21	1.00
AC	1	0.38	0.42	0.74	0.53	0.00	0.57
	2	0.18	0.72	0.69	0.35	0.00	0.43
	4	0.35	–0.31	0.22	0.35	0.00	0.31
	5	0.44	–0.12	0.46	0.47	0.00	0.41
	6	–0.42	0.31	–0.31	0.00	1.00	0.46
Variance explained		1.51	1.10		1.34	1.00
Panel B: Chad data set
ABS	1	0.60	0.00	0.54	0.60		0.73
	2	0.27	0.67	0.73	0.27		0.32
	3	0.42	0.16	0.49	0.42		0.51
	4	0.32	–0.07	0.23	0.32		0.39
	8	0.34	–0.66	–0.19	0.34		0.41
Variance explained		1.21	1.10		1.21
AST	1	0.57	–0.10	0.64	0.57		0.85
	2	0.49	0.34	0.81	0.49		0.73
	3	0.31	–0.60	0.01	0.31		0.46
	4	0.11	0.67	0.55	0.11		0.16
Variance explained		1.51	1.07		1.51
SSN	2	0.56		0.65	0.56		0.65
	3	0.39		0.45	0.39		0.45
	5	0.63		0.73	0.63		0.73
Variance explained		1.15			1.15
AC	2	0.69	0.00	0.52	0.70	0.00	0.50
3	–0.43	0.79	0.23	0.00	1.00	0.69
4	0.55	0.62	0.84	0.70	0.00	0.51
Variance explained		1.03	1.00		1.02	1.00