Pakistani students’ physical activity and psychological well-being: A structural equation modeling approach

Table 3 Measurement model, discriminant validity, and common method bias assessment

Construct	Item	Loading	α	CR	AVE	Fornell-larcker: √AVE & correlations	HTMT
Construct A (e.g., satisfaction)	A1	0.82	0.88	0.89	0.67	0.821
	A2	0.79
	A3	0.85
	A4	0.88
Construct B (e.g., burnout)	B1	0.8	0.86	0.87	0.62	0.45 → 0.791	0.52
	B2	0.76
	B3	0.84
	B4	0.81
Construct C (e.g., intention)	C1	0.77	0.83	0.84	0.64	0.38	0.42 → 0.801	0.44
	C2	0.83
	C3	0.79
Construct D (e.g., support)	D1	0.86	0.89	0.9	0.69	0.52	0.48	0.35 → 0.831	0.56
	D2	0.82
	D3	0.79
	D4	0.85
Construct E (e.g., performance)	E1	0.84	0.87	0.88	0.71	0.61	0.55	0.41	0.44 → 0.841	0.69
	E2	0.81
	E3	0.87

¹√Average variance extracted.

Loading: All factor loadings are standardized and significant at P < 0.001. Fornell-Larcker criterion: Diagonal elements (√average variance extracted) are the square roots of average variance extracted. Off-diagonal elements are inter-construct correlations. Discriminant validity is supported if each √average variance extracted > its row/column correlations. Heterotrait-Monotrait ratio: All values < 0.85, supporting discriminant validity. Common method bias tests: Harman’s single-factor test: 28% of total variance (below 50% threshold). Common latent factor model: All structural path changes < |010|, with no significance changes. Model fit (measurement model): χ²/df = 2.41, comparative fit index = 0.96, root mean square error of approximation = 0.05, standardized root mean square residual = 0.04. α: Cronbach’s alpha; CR: Composite reliability; AVE: Average variance extracted; HTMT: Heterotrait-Monotrait.