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

Wendt, Heike; Kasper, Daniel; Trendtel, Matthias

doi:10.1186/s40536-017-0043-9

Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

Table 11 Distribution of random effects \(\varvec{G}\) across scaling models and countries (part II)

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

Country	Effect	1		2		3		4
Country	Effect	\(\hat{\alpha }_{0}\)	\(\hat{\alpha }_{1}\)	\(\hat{\alpha }_{0}\)	\(\hat{\alpha }_{1}\)	\(\hat{\alpha }_{0}\)	\(\hat{\alpha }_{1}\)	\(\hat{\alpha }_{0}\)	\(\hat{\alpha }_{1}\)
Morocco	\(\hat{\alpha }_{0}\)	4358.44	85.63	4433.22	104.05	4314.43	53.49	4311.60	−97.25
Morocco	\(\hat{\alpha }_{1}\)	85.63	432.09	104.05	959.00	53.49	392.12	−97.25	825.05
Oman	\(\hat{\alpha }_{0}\)	2187.73	17.59	2186.26	15.53	2176.12	−38.90	2217.85	−108.31
Oman	\(\hat{\alpha }_{1}\)	17.59	319.17	15.53	377.71	−38.90	294.01	−108.31	349.03
Poland	\(\hat{\alpha }_{0}\)	322.04	−40.50	322.36	−37.82	321.52	−44.02	317.37	−36.29
Poland	\(\hat{\alpha }_{1}\)	−40.50	42.59	−37.82	39.27	−44.02	40.80	−36.29	37.58
Qatar	\(\hat{\alpha }_{0}\)	1823.03	124.61	1824.27	107.88	1843.10	124.99	2290.76	154.27
Qatar	\(\hat{\alpha }_{1}\)	124.61	217.05	107.88	169.92	124.99	186.00	154.27	181.57
Romania	\(\hat{\alpha }_{0}\)	3132.69	−574.41	3133.08	−652.34	3119.28	−558.05	3138.69	−577.43
Romania	\(\hat{\alpha }_{1}\)	−574.41	863.19	−652.34	1159.58	−558.05	818.38	−577.43	1098.26
Saudi Arabia	\(\hat{\alpha }_{0}\)	3929.55	−146.25	3930.06	−147.93	3891.32	−174.19	3900.55	−180.56
Saudi Arabia	\(\hat{\alpha }_{1}\)	−146.25	379.72	−147.93	392.95	−174.19	340.87	−180.56	290.76
Singapore	\(\hat{\alpha }_{0}\)	275.71	−9.82	273.85	−10.80	275.53	−16.42	281.66	−19.49
Singapore	\(\hat{\alpha }_{1}\)	−9.82	134.89	−10.80	112.66	−16.42	123.45	−19.49	86.69
Slovak Republic	\(\hat{\alpha }_{0}\)	1359.48	−314.15	1353.27	−287.64	1355.48	−318.11	1381.23	−298.18
Slovak Republic	\(\hat{\alpha }_{1}\)	−314.15	308.61	−287.64	256.59	−318.11	304.41	−298.18	250.48
Slovenia	\(\hat{\alpha }_{0}\)	234.97	−33.21	234.17	−32.55	232.33	−43.19	234.77	−61.34
Slovenia	\(\hat{\alpha }_{1}\)	−33.21	123.54	−32.55	91.74	−43.19	126.89	−61.34	98.47
Spain	\(\hat{\alpha }_{0}\)	454.26	−8.45	453.99	−7.85	459.55	−9.76	494.53	−8.72
Spain	\(\hat{\alpha }_{1}\)	−8.45	94.17	−7.85	80.19	−9.76	81.59	−8.72	74.55
Sweden	\(\hat{\alpha }_{0}\)	134.78	−11.58	134.80	−11.66	135.76	−14.16	139.87	−15.65
Sweden	\(\hat{\alpha }_{1}\)	−11.58	159.41	−11.66	172.39	−14.16	167.74	−15.65	163.90
Abu Dhabi, UAE	\(\hat{\alpha }_{0}\)	2138.29	46.38	2136.88	43.58	2006.65	28.57	1795.27	−51.16
Abu Dhabi, UAE	\(\hat{\alpha }_{1}\)	46.38	210.85	43.58	170.91	28.57	219.04	−51.16	221.58

1, scaling model 1; 2, scaling model 2; 3, scaling model 3; 4, scaling model 4; \(\hat{\alpha }_{0}\), random intercept; \(\hat{\alpha }_{1}\), random slope of home resource for learning index

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