Table 3.

Tests for Factorial Invariance of the Four Models across Different Age Groups: Goodness-of-Fit Statistics

Model	S-B χ2	Df	CFIa	Changes in CFIa	RMSEA (90%CI)a	SRMRa
Enjoyment-Competence Model
1: Configual model	138.11	30	0.95		0.05(0.04–0.06)	0.03
2: Measurement model	177.06	37	0.93	0.02	0.05(0.04–0.06)	0.04
Partial measurement modelb	152.00	34	0.94	0.01	0.05(0.04–0.06)	0.04
3. Structural model	151.80	35	0.94	0.01	0.05(0.04–0.06)	0.04
Outcome expectation Model
1: Configual model	148.87	49	0.95		0.04(0.03–0.05)	0.03
2: Measurement model	206.11	56	0.92	0.03	0.04(0.04–0.05)	0.05
Partial measurement modelc	172.05	54	0.94	0.01	0.04(0.03–0.05)	0.04
3. Structural model	196.65	55	0.93	0.02	0.04(0.04–0.05)	0.05
Social Support Model
1: Configual model	249.55	76	0.97		0.04(0.04–0.05)	0.03
2: Measurement model	296.44	83	0.96	0.01	0.04(0.04–0.05)	0.04
Partial measurement modeld	253.31	81	0.97	0.00	0.04(0.03–0.04)	0.03
3. Structural model	281.42	87	0.96	0.01	0.04(0.04–0.05)	0.05
Environment Model
1: Configual model	54.93	20	0.97		0.04(0.02–0.05)	0.03
2: Measurement model	72.25	24	0.96	0.01	0.04(0.03–0.05)	0.03
Partial measurement modele	68.13	23	0.96	0.01	0.04(0.03–0.05)	0.03
3. Structural model	104.83	26	0.94	0.03	0.05(0.04–0.06)	0.03

Based on the univariate χ² incremental values (p < 0.05)

a: The cut-off points of model fit: CFI greater than .90, Changes in CFI equal or less than 0.01, the point estimate of RMSEA less than 0.05 and the 90%CI of RMSEA less than 0.08, SRMR less than 0.08.

b: Equality constraints related to item Enjoy3 and item Enjoy5 were removed sequentially

c: Equality constraints related to item Socbel3 and item Socbel4 were removed sequentially

d: Equality constraints related to item Parsupp3 and item Teacher2 were removed sequentially

e: Equality constraints related to item Opp2 were removed