Large-scale Assessments in Education

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Table 5 Distribution of slope parameters \(c_g\), \(c_i\) and \(c_{gi}\) for the indicators of the HRL index

From: Assuming measurement invariance of background indicators in international comparative educational achievement studies: a challenge for the interpretation of achievement differences

Item	Country
	1		2		3		4		5		6		7		8		9		10
	\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)
	Est.	SE	Est.	SE	Est.	SE	Est.	SE	Est.	SE	Est.	SE	Est.	SE	Est.	SE	Est.	SE	Est.	SE
ASBG04	1.08	0.10	3.09	0.20	0.99	0.10	1.86	0.12	1.32	0.11	1.20	0.11	1.58	0.12	1.15	0.11	1.05	0.11	1.40	0.12
ASDG05	0.92	0.14	2.23	0.14	0.52	0.11	2.68	0.16	0.91	0.15	0.50	0.12	0.47	0.11	0.21	0.10	0.42	0.12	1.27	0.13
ASBH15	1.58	0.12	3.43	0.23	0.97	0.10	2.42	0.16	1.90	0.13	1.41	0.12	1.90	0.14	1.25	0.11	0.98	0.10	1.42	0.12
ASDHED	1.98	0.16	6.15	0.30	2.20	0.14	0.78	0.11	1.40	0.13	1.14	0.12	1.63	0.12	1.33	0.11	1.20	0.12	0.97	0.11
ASDHOC	1.86	0.17	2.55	0.16	1.83	0.15	2.73	0.20	1.27	0.13	1.17	0.13	1.78	0.16	1.77	0.15	1.79	0.17	2.38	0.21
\(c_g\)	1.47	0.07	3.05	0.12	1.14	0.06	1.83	0.08	1.43	0.07	1.07	0.06	1.40	0.07	1.02	0.06	1.03	0.06	1.35	0.06

Item	Country
	11		12		13		14		15		16		17		18		19		20
	\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)
	Est.	SE	Est.	SE	Est.	SE	Est.	SE	Est.	SE	Est.	SE	Est.	SE	Est.	SE	Est.	SE	Est.	SE
ASBG04	1.06	0.10	1.38	0.11	2.38	0.14	1.21	0.11	1.03	0.10	0.50	0.10	3.00	0.17	1.13	0.11	0.89	0.09	0.13	0.11
ASDG05	0.40	0.11	0.66	0.11	2.16	0.13	0.56	0.11	0.82	0.12	-0.12	0.10	2.89	0.15	1.94	0.14	0.78	0.11	0.21	0.11
ASBH15	1.03	0.11	1.40	0.11	2.42	0.15	1.53	0.12	1.22	0.11	-0.02	0.11	2.92	0.17	1.95	0.15	0.89	0.09	0.08	0.12
ASDHED	2.84	0.19	4.27	0.24	4.22	0.21	2.12	0.16	1.46	0.12	3.15	0.17	5.01	0.23	3.44	0.19	3.09	0.17	3.83	0.28
ASDHOC	1.34	0.12	2.46	0.18	2.69	0.18	2.03	0.18	2.27	0.19	1.86	0.14	2.17	0.14	1.67	0.13	2.58	0.19	2.07	0.18
\(c_g\)	1.26	0.06	1.74	0.08	2.54	0.10	1.44	0.07	1.20	0.06	1.00	0.06	3.00	0.09	1.83	0.08	1.37	0.06	1.06	0.06

Item	Country
	21		22		23		24		25		26		27		28		\(c_{i}\)
	\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)		\(c_{gi}\)
	Est.	SE	Est.	SE	Est.	SE	Est.	SE	Est.	SE	Est.	SE	Est.	SE	Est.	SE	Est.	SE
ASBG04	2.02	0.13	1.31	0.12	0.95	0.10	1.24	0.11	0.86	0.10	0.98	0.10	1.28	0.10	0.48	0.12	1.48	0.03
ASDG05	1.54	0.12	1.22	0.12	0.27	0.10	0.88	0.12	0.30	0.11	0.34	0.10	1.35	0.17	0.15	0.11	1.02	0.03
ASBH15	2.13	0.14	1.64	0.16	1.25	0.11	1.14	0.10	1.03	0.10	1.03	0.10	1.89	0.13	0.59	0.14	1.65	0.04
ASDHED	2.82	0.15	3.44	0.21	2.29	0.18	1.76	0.12	1.38	0.12	3.32	0.20	1.87	0.15	3.25	0.24	1.89	0.04
ASDHOC	3.15	0.23	1.38	0.12	2.01	0.18	2.04	0.17	1.81	0.16	1.95	0.16	2.10	0.19	1.75	0.16	1.79	0.04
\(c_g\)	2.04	0.08	1.62	0.07	1.24	0.06	1.28	0.06	1.00	0.06	1.31	0.06	1.68	0.08	1.16	0.06	1.55	0.01

Values for Model M1 in the last two columns and the last row, values for Model M2 in the last row of each table, values for Model M3 in the last two columns and values for Model M4 in each of the 28 country columns. ASBG04, number of books in the home (student-reported); ASDG05, number of home study supports (student-reported); ASBH15, number of children’s books in the home (parent-reported); ASDHED, highest level of education of either parent (parent-reported); ASDHOC, highest level of occupation of either parent (parent-reported); 1, Azerbaijan; 2, Australia; 3, Austria; 4, Chinese Taipei; 5, Croatia; 6, Czech Republic; 7, Finland; 8, Georgia; 9, Germany; 10, Honduras; 11, Hungary; 12, Iran, Islamic Rep. of; 13, Ireland; 14, Italy; 15, Lithuania; 16, Malta; 17, Morocco; 18, Oman; 19, Poland; 20, Qatar; 21, Romania; 22, Saudi Arabia; 23, Singapore; 24, Slovak Republic; 25, Slovenia; 26, Spain; 27, Sweden; 28, Abu Dhabi, UAE

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