Table 3.

Fit statistics for the random-intercepts cross-lagged panel model (RI-CLPM)

	Fit statistics								Model comparisons (compared to the full model)
	χ2	df	p	CFI	TLI	RSMEA	90% CI	SMRS	∆ χ2(df)a	∆ p
Step 0: Fit statistics for the full reciprocal model
i. Reciprocal model with stability paths, within-wave correlations and bidirectional cross-lagged paths	2.80	1	0.094	0.999	0.992	0.026	0.000–0.063	0.009
Step 1: Testing invariance of full model
1. Both contemporaneous and cross-lagged paths constrained to be equal (= no change over time)	12.96	5	0.024	0.998	0.993	0.024	0.008–0.040	0.026	10.21 (4)	0.037
2. Model with auto-regressive paths to be constraint to be equal
a. ASD paths	1.83	2	0.402	1.00	1.00	0.000	0.000–0.037	0.010	0.12 (1)	0.729
b. Prosocial paths	8.76	2	0.013	0.998	0.986	0.035	0.014–0.060	0.024	6.02 (1)	0.014
3. Model with cross-lagged paths constrained to be equal over time
a. ASD → prosocial path constrained	9.62	2	0.008	0.998	0.984	0.037	0.016–0.062	0.015	7.01 (1)	0.008
b. Prosocial → ASD constrained	4.87	2	0.088	0.999	0.994	0.023	0.000–0.049	0.013	2.08 (1)	0.149
Step 2: Select optimal model
ii. Reciprocal model with constrained auto-regressive ASD paths, unconstrained auto-regressive prosocial skills paths, unconstrained cross-lagged paths from ASD symptoms to prosocial skills and constrained cross-lagged paths from prosocial skills to ASD symptoms	3.48	3	0.322	1.00	0.999	0.008	0.000–0.034	0.013

CFI comparative fit index, TLI Tucker-Lewis Fit Index, RSMEA Root Mean Square Error of Approximation, 90% CI 90% confidence interval of the RSMEA; ∆ symbolizes difference scores between current model and model #1. Model comparison based on difference scores for AIC, BIC and χ² values

^aChi-square difference calculated using the Satorra–Bentler Scale Chi-square difference test