. Author manuscript; available in PMC: 2012 Feb 1.

Published in final edited form as: Learn Individ Differ. 2011 Feb 1;21(1):85–95. doi: 10.1016/j.lindif.2010.10.005

Table 9.

Measurement and Structural Invariance Tests of the Hierarchical Latent Variable Regression Models Predicting Reading and Spelling Skills at Grade 2 across Orthographies

Model and invariance level	Overall Fit Indexes					Comparative Fit Indexes
Model and invariance level	χ²	df	CFI	RMSEA	SRMR	Δ χ²	Δ df	Δ CFI
Word recognition
1 Baseline	40.678^*	24	.996	.038	.020
2 Factor loadings	51.433^*	27	.993	.043	.027	10.755^*	3	.003
3 Phantom factor loadings	82.820^*	37	.988	.050	.052	31.387^*	10	.006
4 Regression coefficient	83.974^*	41	.988	.046	.052	1.154	4	.000
Phonological decoding
1 Baseline	33.036^*	24	.997	.028	.019
2 Factor loadings	42.316^*	27	.996	.034	.026	9.280^*	3	.001
3 Phantom factor loadings	89.992^*	37	.985	.054	.065	47.676^*	10	.011
4 Regression coefficients	99.557^*	41	.984	.054	.076	9.565^*	4	.001
Spelling
1 Baseline	38.043^*	24	.996	.035	.015
2 Factor loadings	48.586^*	27	.994	.040	.026	10.543^*	3	.002
3 Phantom factor loadings	97.422^*	37	.983	.058	.063	48.836^*	10	.011
4 Regression coefficients	119.438^*	41	.978	.062	.061	22.016^*	4	.005

Note. χ² = chi-square test statistic; CFI = comparative fit index; RMSEA = root-mean-square error of approximation; SRMR = standardized root-mean-square residual; Δ = difference between the comparison and nested model.

p < .001.