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

Table 1 Demographic characteristics of participants (n = 708)

Characteristic	Category	Frequency (n)	Percentage (%)
Sex	Men	340	48.0
	Women	368	52.0
Age (years)	mean ± SD	21.5 ± 1.9	-
	17-20	280	39.5
	21-23	355	50.1
	24+	73	10.3
University type	Public	425	60.0
	Private	283	40.0
Academic level	Undergraduate (years 1-2)	290	41.0
	Undergraduate (years 3-4)	312	44.1
	Graduate (Masters/PhD)	106	15.0
Field of study	Natural/health sciences	230	32.5
	Social sciences/humanities	255	36.0
	Engineering & IT	135	19.1
	Business & law	88	12.4

Table 2 Psychometric properties of measurement scales

Scale	Number of items	Cronbach’s alpha	CFI	RMSEA	Example item
IPAQ-SF	7	(Test-Retest r = 0.84)	-	-	“During the last 7 days, on how many days did you do vigorous physical activities?”
DASS-21 (total)	21	0.94	0.93	0.05	“I felt that I had nothing to look forward to.” (depression)
GSES	10	0.89	0.95	0.04	“I can always manage to solve difficult problems if I try hard enough.”
PSQI	19	0.82	0.91	0.06	“During the past month, how would you rate your sleep quality overall?”
MSPSS (total)	12	0.92	0.94	0.05	“I get the emotional help and support I need from my family.”

IPAQ: International Physical Activity Questionnaire; DASS: Depression Anxiety Stress Scale; GSES: General Self-Efficacy Scale; PSQI: Pittsburgh Sleep Quality Index; MSPSS: Multidimensional Perceived Social Support Scale; CFI: Comparative fit index; RMSEA: Root mean square error of approximation.

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.

Table 4 Descriptive statistics and inter-correlations of study variables (n = 708)

Variable	mean ± SD	1	2	3	4	5	6
PA (MET-minute/week)	2580 ± 2110	-
Depression (DASS)	12.1 ± 4.5	-0.46b	-
Anxiety (DASS)	11.5 ± 4.2	-0.41b	0.78b	-
Stress (DASS)	13.8 ± 4.8	-0.51b	0.82b	0.75b	-
Self-efficacy (GSES)	28.5 ± 5.1	0.52b	-0.58b	-0.50b	-0.60b	-
Sleep quality (PSQI)	6.8 ± 2.9	-0.38b	0.55b	0.49b	0.57b	-0.48b	-
Social support (MSPSS)	65.2 ± 11.3	0.45b	-0.50b	-0.44b	-0.52b	0.54b	-0.41b

^bP < 0.001, all correlations were in the expected direction and statistically significant (P < 0.001). The pattern of strong correlations provides preliminary support for the proposed relationships in the conceptual model, justifying the use of structural equation modeling.

PA: Physical activity; DASS: Depression Anxiety Stress Scale; GSES: General Self-Efficacy Scale; PSQI: Pittsburgh Sleep Quality Index; MSPSS: Multidimensional Perceived Social Support Scale.

Table 5 Standardized direct and indirect relationships in the structural equation modeling model

Pathway	Standardized estimate (β)	P value	95%CI
Direct relationship
PA → psychological distress	-0.28	< 0.001	-0.37 to -0.19
PA → self-efficacy	0.48	< 0.001	0.40-0.56
PA → sleep quality	-0.35	< 0.001	-0.43 to -0.27
PA → social support	0.42	< 0.001	0.34-0.50
Self-efficacy → distress	-0.33	< 0.001	-0.41 to -0.25
Sleep quality → distress	0.26	< 0.001	0.18-0.34
Social support → distress	-0.21	0.001	-0.29 to -0.13
Sex-specific direct relationship
PA → distress (male)	-0.31	< 0.001	-0.42 to -0.20
PA → distress (female)	-0.24	< 0.001	-0.34 to -0.14
Institution type-specific direct relationship
PA → distress (public university)	-0.25	< 0.001	-0.35 to -0.15
PA → distress (private university)	-0.33	< 0.001	-0.44 to -0.22
Indirect relationship
PA → self-efficacy → distress	-0.16	< 0.001	-0.21 to -0.11
PA → sleep quality → distress	-0.12	< 0.001	-0.16 to -0.08
PA → social support → distress	-0.09	0.002	-0.13 to -0.05
Total indirect relationship	-0.37	< 0.001	-0.45 to -0.29
Total relationship (direct + indirect)	-0.65	< 0.001	-0.73 to -0.57

CI: Confidence interval; PA: Physical activity.

Table 6 Comparison of alternative model structures

Model structure	χ2 (df)	χ2/df	CFI	RMSEA (90%CI)	AIC	BIC	Conclusion
Parallel mediation model (original)	48.32 (24)	2.01	0.96	0.058 (0.035- 0.080)	248.50	312.20	Good fit; preferred for parsimony
Serial mediation model (PA → SE → sleep → MH)	52.17 (23)	2.27	0.94	0.067 (0.045-0.089)	254.30	320.10	Comparable fit but slightly worse
Single-mediator models (average of three)	-	-	-	-	-	-	Inferior to parallel model (by Δχ2)
Null model (no mediation)	156.80 (30)	5.23	0.50	0.142 (0.120-0.164)	-	-	Poor fit

CFI: Comparative fit index; RMSEA: Root mean square error of approximation; CI: Confidence interval; AIC: Akaike information criterion; BIC: Bayesian information criterion; PA: Physical activity; SE: Self-efficacy; MH: Mental health.