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. Author manuscript; available in PMC: 2012 Jul 1.
Published in final edited form as: Dev Sci. 2010 Nov 23;14(4):679–692. doi: 10.1111/j.1467-7687.2010.01012.x

Table 2.

Tests of Invariance by age and sex

Model χ2 Df P RMSEA CFI BIC χ2 difference df difference p difference
Baseline 107.41 53 .0000 0.07 0.91 8122.46 – – –
Tests of invariance by age
M1 166.31 106 .0002 0.08 0.83 8029.67 – – –
M2^ 178.99 113 .0001 0.08 0.81 8005.77 12.68 7 0.080
M3 189.96 121 .0001 0.08 0.80 7974.93 10.97 8 0.203
M4 191.00 122 .0001 0.08 0.80 7970.75 1.04 1 0.308
M5* 196.21 123 .0000 0.08 0.79 7970.74 5.21 1 0.023
M6 194.35 123 .0000 0.08 0.80 7968.87 3.35 1 0.067
M7 194.49 124 .0001 0.08 0.80 7963.78 0.14 1 0.708
M8 196.37 125 .0000 0.08 0.80 7960.44 1.88 1 0.170
M9 196.90 126 .0001 0.08 0.80 7955.75 0.53 1 0.467
Tests of invariance by sex
M1 176.23 106 .0000 0.08 0.88 8259.98 – – –
M2 183.43 114 .0000 0.08 0.88 8225.38 7.2 8 0.515
M3 190.31 122 .0001 0.08 0.88 8190.45 6.88 8 0.550
M4 190.37 123 .0001 0.08 0.89 8185.28 0.06 1 0.807
M5 190.50 124 .0001 0.08 0.89 8180.18 0.13 1 0.718
M6† 204.68 125 .0000 0.08 0.86 8189.14 14.18 1 0.002
M7 190.60 125 .0001 0.08 0.89 8175.06 0.10 1 0.752
M8 192.12 126 .0001 0.08 0.89 8171.35 1.52 1 0.218
M9 199.46 127 .0000 0.08 0.88 8173.47 7.34 1 0.007
^

Partial Metric Invariance. Indicator loading for 6 Boxes was allowed to vary between age groups due to non-invariance.

*

EC factor means were allowed to vary due to non-invariance. M6 model fit statistics are compared to M4 model fit statistics.

†

The latent EC-age path was allowed to vary due to non-invariance. M7 model fit statistics are compared to M5 model fit statistics.

Baseline = entire sample model; M1 = configural invariance; M2 = metric invariance; M3 = scalar invariance; M4 = factor variance invariance; M5 = factor means invariance; M6 = latent EC-Age invariance; M7 = emergent math-EC path invariance; M8 = estimated gC-EC path invariance; M9 = emergent math-estimated gC path invariance.