Table 1.

Goodness of fit of maximum likelihood with robust standard errors (MLR) full and partial invariance models.

Invariance model	SBχ2	df	p	SCF	RMSEA	CFI	TLI	cd	TRd	Δdf	p	Mean difference estimate				Simulation					Bias
												α	SE	p	d	AVG	SD	SE avg	95% Cover	% Sig.	M bias (%)	SE Bias (%)
Configural no CUs	97.948	76	0.046	1.112	0.026	0.973	0.967
Configural with CUs	82.052	69	0.135	1.111	0.021	0.984	0.979	1.112	15.889	7	0.026
Weak with CUs	90.371	76	0.125	1.115	0.021	0.982	0.979	1.154	8.319	7	0.305
Strong with CUs	127.238	82	0.001	1.108	0.036	0.944	0.937	1.017	39.534	6	<0.001	−0.341	0.070	<0.001	0.25	−0.344	0.072	0.068	0.938	0.998	0.79	−5.58
Partial1∧ with CUs	108.190	81	0.024	1.110	0.028	0.966	0.962	0.946	22.081	1	<0.001
Partial2* with CUs	94.677	80	0.126	1.110	0.021	0.982	0.979	1.110	13.513	1	<0.001	−0.502	0.075	<0.001	0.35	−0.505	0.079	0.075	0.945	1.000	0.56	−4.20

SBχ², Satorra-Bentler scaled chi-square; df, degrees of freedom; SCF, Scaling Correction Factor; RMSEA, Root Mean Square Error of Approximation; CFI, Comparative Fit Index; TLI, Tucker-Lewis Index; cd, difference test scaling correction; TRd, Satorra-Bentler scaled chi-square difference test; Δdf, degrees of freedom difference; CU, correlated uniquenesses;

^∧Intercept of item 4 was not invariant;

^*Intercepts of items 3 and 4 were not invariant. SB scaled chi-square difference tests are referred to the model in the above line.