Table 1.

Confirmatory Factor Analytic Model of Factorial Invariance Tests Across Mexican American English, Mexican American Spanish, and European American English Groups

		χ2	df	p-Value	Δdf	Δχ2	Δχ2 p-Value	CFI	TLI	RMSEA	SRMR
Model	Dangerous people: Child report
1	Configural invariance model (final configural invariance model)	13.84 (15.33)	6	0.03				0.97	0.92	0.10	0.03
2	Model 1+all factor loadings invariant (final metric invariance model)	18.61 (21.72)	12	0.10	6	5.21a	0.52	0.98	0.97	0.06	0.05
3	Model 2+all measurement intercepts invariant (final strong invariance model)	22.78 (26.34)	18	0.20	6	4.07	0.67	0.98	0.98	0.04	0.05
4	Model 3+all unique variances invariant (strict invariance model)	54.95 (54.66)	26	0.00	8	44.87	0.00***	0.90	0.93	0.09	0.09
5	Model 3+some unique variances invariant (final partially strict invariance model)	41.00 (42.46)	25	0.02	7	22.22b	0.00**	0.95	0.96	0.07	0.08
	Dangerous people: Mother report
6	Configural invariance model (final configural invariance model)	20.42 (23.45)	15	0.16				0.98	0.96	0.05	0.04
7	Model 6+all factor loadings invariant (final metric invariance model)	30.95 (32.85)	23	0.12	8	10.46	0.23	0.97	0.96	0.05	0.07
8	Model 7+all measurement intercepts invariant (final strong invariance model)	45.33 (49.28)	31	0.05	8	14.15	0.08	0.95	0.95	0.06	0.07
9	Model 8+all unique variances invariant (strict invariance model)	92.57 (120.17)	41	0.00	10	36.31	0.00***	0.82	0.87	0.09	0.18
9a	Model 8+some unique variances invariant (final partially strict invariance model)	48.63 (60.73)	37	0.10	6	5.49c	0.48	0.96	0.97	0.05	0.09
	Sense of safety: Mother report
10	Configural invariance model (final configural invariance model)	7.87 (11.98)	6	0.25				0.99	0.98	0.05	0.03
11	Model 10+all factor loadings invariant (final metric invariance model)	12.86 (18.54)	12	0.33	6	4.82	0.57	0.99	1.00	0.01	0.06
12	Model 11+all measurement intercepts invariant (final strong invariance model)	33.96 (44.79)	18	0.01	6	24.46	0.00***	0.94	0.94	0.08	0.07
13	Model 12+all unique variances invariant (strict invariance model)	61.40 (88.05)	26	0.00	8	25.55	0.00**	0.87	0.91	0.10	0.19
13a	Model 12+some unique variances invariant (final partially strict invariance model)	32.95 (47.53)	22	0.06	4	1.37d	0.85	0.96	0.97	0.06	0.09
	Physical environment: Mother report
14	Configural invariance model (final configural invariance model)	32.84 (43.01)	15	0.00				0.97	0.94	0.09	0.04
15	Model 14+all factor loadings invariant (metric invariance model)	48.13 (59.31)	23	0.00	8	14.99	0.06	0.96	0.94	0.09	0.10
15a	Model 14+some factor loadings invariant (final partially metric invariance model)	43.57 (52.72)	22	0.04	7	9.74e	0.20	0.96	0.95	0.08	0.08
16	Model 15a+measurement intercepts invariantg (final partially strong invariance model)	51.76 (59.88)	29	0.01	7	7.23	0.41	0.96	0.96	0.07	0.08
17	Model 16+all unique variances invariant (partially strict invariance model)	76.18 (94.19)	39	0.00	10	23.39	0.01**	0.93	0.95	0.08	0.12
17a	Model 16+some unique variances invariant (final partially strict invariance model)	64.07 (77.96)	36	0.00	7	12.34f	0.09	0.95	0.96	0.07	0.08

Note. χ² values for clustered (non-clustered) models in MPLUS; CFI = Comparative Fit Index; TLI = Tucker-Lewis Index; RMSEA = Root Mean Square Error of Approximation; SRMR = Standardized Root Mean Square Residual.

^aEach chi-square difference test refers to a comparison of the fit of the current model with the immediately preceding model, except where noted by superscripts b through f. For the chi-square difference testing, because of the MLR estimation method; the Satorra-Bentler scaled chi-square statistic is used, which corrects for the scaling factor.

^bCompares models 3 and 5.

^cCompares model 8 and 9a

^dCompares model 12 and 13a.

^eCompares model 14 and 15a.

^fCompares model 16 and 17a.

^gInvariance in intercepts is specified only for those items that demonstrate invariant factor loadings as suggested by Millsap (1997).

^*p<.05

^**p<.01

^***p<.001.