The achievement gap in reading competence: the effect of measurement non-invariance across school types

Rohm, Theresa; Carstensen, Claus H.; Fischer, Luise; Gnambs, Timo

doi:10.1186/s40536-021-00116-2

Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

Table 2 Results from the invariance alignment method per measurement occasion

From: The achievement gap in reading competence: the effect of measurement non-invariance across school types

Grade 5 (N = 4885)		Grade 7 (N = 6182)		Grade 9 (N = 4573)
Item	IA	Item	IA	Item	IA
Discrimination		Discrimination		Discrimination
reg50110_c		reg70110_c		reg90610_c
reg5012s_c		reg70120_c		reg90620_c
reg50130_c		reg7013s_c	HS	reg9063s_c
reg50140_c	LS	reg70140_c		reg90640_c
reg50150_c		reg7015s_c		reg90660_c
reg5016s_c		reg7016s_c		reg90670_c
reg50170_c		reg70610_c		reg90680_c
reg50210_c		reg70620_c	HS	reg90810_c
reg50220_c		reg7063s_c		reg90820_c
reg50230_c		reg70640_c		reg9083s_c
reg50240_c		reg70650_c		reg90840_c
reg50250_c		reg7066s_c		reg90850_c
reg5026s_c		reg70210_c		reg90860_c
reg50310_c		reg70220_c		reg90870_c
reg50320_c		reg7023s_c		reg90210_c
reg50330_c		reg7024s_c		reg90220_c
reg50340_c		reg70250_c		reg90230_c
reg50350_c		reg7026s_c		reg90250_c
reg50360_c		reg70310_c		reg90710_c
reg50370_c	MS, HS	reg70320_c		reg90720_c
reg50410_c	LS	reg7033s_c	HS	reg90730_c
reg5042s_c	LS	reg70340_c		reg9074s_c
reg50430_c	LS	reg70350_c		reg90750_c
reg50440_c	HS	reg70360_c		reg9091s_c
reg50460_c	LS	reg70410_c		reg90920_c
reg50510_c		reg70420_c		reg90930_c
reg5052s_c		reg70430_c		reg90940_c
reg50530_c		reg70440_c		reg90950_c
reg50540_c		reg7045s_c		reg90960_c
reg5055s_c		reg70460_c		reg9097s_c
reg50560_c		reg7051s_c		reg90410_c
reg50570_c		reg70520_c		reg90420_c
		reg7053s_c		reg90430_c
		reg7055s_c		reg90440_c
		reg70560_c		reg90450_c
		reg7071s_c	MS	reg90460_c
		reg70720_c	HS	reg9047s_c
		reg70730_c		reg90510_c
		reg70740_c		reg90520_c	LS
		reg7075s_c	LS	reg90530_c	LS
				reg90540_c
				reg90550_c	LS
				reg90560_c	HS
				reg90570_c
Threshold		Threshold		Threshold
reg50110_c		reg70110_c		reg90610_c
reg5012s_c, cat.1	HS	reg70120_c		reg90620_c
reg5012s_c, cat.2		reg7013s_c, cat.1		reg9063s_c, cat.1
reg50130_c		reg7013s_c, cat.2		reg9063s_c, cat.2	AT
reg50140_c	LS	reg70140_c		reg90640_c
reg50150_c		reg7015s_c		reg90660_c
reg5016s_c, cat.1		reg7016s_c, cat.1		reg90670_c
reg5016s_c, cat.2		reg7016s_c, cat.2		reg90680_c
reg5016s_c, cat.3		reg7016s_c, cat.3		reg90810_c
reg5016s_c, cat.4		reg70610_c		reg90820_c	HS
reg5016s_c, cat.5	HS	reg70620_c		reg9083s_c
reg50170_c	HS	reg7063s_c, cat.1		reg90840_c
reg50210_c		reg7063s_c, cat.2		reg90850_c
reg50220_c		reg70640_c		reg90860_c
reg50230_c		reg70650_c		reg90870_c
reg50240_c		reg7066s_c, cat.1		reg90210_c
reg50250_c		reg7066s_c, cat.2		reg90220_c
reg5026s_c		reg7066s_c, cat.3		reg90230_c
reg50310_c		reg7066s_c, cat.4		reg90250_c
reg50320_c		reg70210_c		reg90710_c
reg50330_c		reg70220_c		reg90720_c
reg50340_c		reg7023s_c, cat.1		reg90730_c
reg50350_c		reg7023s_c, cat.2		reg9074s_c, cat.1
reg50360_c		reg7024s_c, cat.1		reg9074s_c, cat.2
reg50370_c	MS, HS	reg7024s_c, cat.2		reg9074s_c, cat.3
reg50410_c	LS	reg70250_c		reg9074s_c, cat.4	LS
reg5042s_c, cat.1	LS	reg7026s_c, cat.1		reg90750_c
reg5042s_c, cat.2	LS	reg7026s_c, cat.2		reg9091s_c, cat.1
reg5042s_c, cat.3	LS	reg7026s_c, cat.3		reg9091s_c, cat.2
reg50430_c	AT, HS	reg7026s_c, cat.4		reg90920_c
reg50440_c	HS	reg70310_c		reg90930_c
reg50460_c	HS	reg70320_c		reg90940_c
reg50510_c		reg7033s_c, cat.1		reg90950_c
reg5052s_c, cat.1		reg7033s_c, cat.2		reg90960_c	LS
reg5052s_c, cat.2		reg7033s_c, cat.3		reg9097s_c, cat.1
reg5052s_c, cat.3		reg70340_c		reg9097s_c, cat.2
reg50530_c		reg70350_c		reg9097s_c, cat.3
reg50540_c	AT	reg70360_c		reg90410_c
reg5055s_c, cat.1		reg70410_c	HS	reg90420_c
reg5055s_c, cat.2		reg70420_c		reg90430_c
reg5055s_c, cat.3		reg70430_c	HS	reg90440_c
reg50560_c		reg70440_c		reg90450_c	HS
reg50570_c		reg7045s_c, cat.1	LS, HS	reg90460_c
		reg7045s_c, cat.2		reg9047s_c, cat.1
		reg7045s_c, cat.3		reg9047s_c, cat.2
		reg70460_c		reg90510_c
		reg7051s_c, cat.1		reg90520_c	LS, HS
		reg7051s_c, cat.2		reg90530_c	HS
		reg70520_c		reg90540_c	HS
		reg7053s_c, cat.1		reg90550_c	LS
		reg7053s_c, cat.2		reg90560_c	HS
		reg7055s_c, cat.1		reg90570_c	LS, HS
		reg7055s_c, cat.2	HS
		reg7055s_c, cat.3
		reg70560_c	HS
		reg7071s_c, cat.1
		reg7071s_c, cat.2	HS
		reg70720_c
		reg70730_c	MS
		reg70740_c
		reg7075s_c, cat.1
		reg7075s_c, cat.2
		reg7075s_c, cat.3
AII grade 5	0.644	AII grade 7	0.631	AII grade 9	0.492

IA invariance alignment method for school types, presenting non-invariant groups (HS high schools, MS middle secondary schools, CS comprehensive schools, AT schools offering all school tracks except high school, LS lower secondary schools). AII Average Invariance Index: Average R² across all parameters ranging from 0 (indicating full non-invariance) to 1 (indicating perfect scalar invariance)

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