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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   
  1. 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