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 5 Results of structural equation models for longitudinal competence measurement ignoring clustered structure (N = 7276)

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

	Model 3a			Model 3b			Model 4a			Model 4b
	M	SD	95% PPI	M	SD	95% PPI	M	SD	95% PPI	M	SD	95% PPI
School Type Covariates
Grade 5
HS				0.627	0.014	(0.600, 0.653)				0.614	0.015	(0.587, 0.644)
MS				− 0.129	0.014	(− 0.156, − 0.101)				− 0.117	0.015	(− 0.145, − 0.089)
CS				− 0.098	0.013	(− 0.124, − 0.073)				− 0.094	0.014	(− 0.119, − 0.066)
AT				− 0.138	0.014	(− 0.165, − 0.109)				− 0.140	0.015	(− 0.170, − 0.112)
LS				− 0.404	0.012	(− 0.427, − 0.380)				− 0.403	0.013	(− 0.428, − 0.378)
Grade 7
HS				0.609	0.012	(0.584, 0.633)				0.615	0.013	(0.589, 0.640)
MS				− 0.156	0.012	(− 0.180, − 0.131)				− 0.158	0.013	(− 0.184, − 0.133)
CS				− 0.053	0.012	(− 0.076, − 0.030)				− 0.054	0.012	(− 0.078, − 0.031)
AT				− 0.111	0.013	(− 0.136, − 0.086)				− 0.113	0.013	(− 0.138, − 0.088)
LS				− 0.406	0.012	(− 0.428, − 0.382)				− 0.406	0.012	(− 0.429, − 0.382)
Grade 9
HS				0.631	0.014	(0.604, 0.658)				0.628	0.014	(0.599, 0.656)
MS				− 0.162	0.014	(− v0.188, − 0.135)				− 0.155	0.014	(− 0.184, − 0.128)
CS				− 0.043	0.013	(− 0.068, − 0.018)				− 0.041	0.013	(− 0.066, − 0.015)
AT				− 0.148	0.014	(− 0.174, − 0.120)				− 0.155	0.014	(− 0.183, − 0.127)
LS				− 0.398	0.013	(− 0.425, − 0.372)				− 0.396	0.013	(− 0.421, − 0.370)
Variance components of the random effects
Grade 5	0.542	0.072	(0.401, 0.689)	0.391	0.050	(0.291, 0.490)	0.490	0.069	(0.368, 0.666)	0.337	0.046	(0.255, 0.438)
Grade 7	0.126	0.015	(0.103, 0.157)	0.094	0.012	(0.074, 0.119)	0.123	0.013	(0.101, 0.152)	0.098	0.014	(0.078, 0.133)
Grade 9	0.307	0.045	(0.216, 0.390)	0.221	0.028	(0.174, 0.282)	0.255	0.035	(0.202, 0.340)	0.204	0.029	(0.154, 0.266)
Correlations and Covariances between latent factors	Correlation		Covariance	Correlation		Covariance	Correlation		Covariance	Correlation		Covariance
Grade 5 with Grade 7	0.754		0.188	0.753		0.194	0.743		0.178	0.751		0.192
Grade 5 with Grade 9	0.771		0.281	0.767		0.304	0.766		0.242	0.766		0.275
Grade 7 with Grade 9	0.810		0.168	0.808		0.155	0.807		0.134	0.809		0.142
PPP	0.005			0.003			0.117			0.045

Standardized results are presented for fixed effects. M posterior mean, SD posterior standard deviation, PPI posterior probability interval (2.5 and 97.5 percentile of the posterior distribution). School type covariates: HS high schools, MS middle secondary schools, CS comprehensive schools, AT schools offering all school tracks except high school, LS lower secondary schools, PPP posterior predictive p value. In Models 3a and 3b, no school-type specific item discrimination or item difficulty estimates were accounted for. In Models 4a and 4b, school-type specific item discrimination and item difficulty estimates were taken into account for items exhibiting DIF
Correlations and covariances were reported based on sample statistics

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