Validation of a three-item Fatigue Severity Scale for patients with substance use disorder: a cohort study from Norway for the period 2016–2020

Table 3 Confirmatory factor analysis results at baseline and at the second health assessment

	χ²	df	P	CFI	TLI	RMSEA
	χ²	df	P	CFI	TLI	ε_a	ε_{a 90%CI}	ε_{a p<.05}
Time 1 (baseline)
FSS-9	212.90	27	< 0.001	0.93	0.90	0.10	0.09, 0.12	0.00
FSS-9 ^ResCov	132.80	26	< 0.001	0.96	0.94	0.08	0.07, 0.09	0.00
FSS-9 ^ResCov + VAFS	151.33	34	< 0.001	0.96	0.95	0.07	0.06, 0.09	0.00
FSS-3	0.48	2	0.788	1.00	1.00	0.00	0.00, 0.05	0.95
FSS-3 + VAFS	4.42	4	0.352	1.00	1.00	0.01	0.00, 0.06	0.87
Time 2 (second health assessment)
FSS-9	108.14	27	< 0.001	0.90	0.86	0.12	0.10, 0.14	0.00
FSS-9 ^ResCov	50.16	26	0.003	0.97	0.96	0.06	0.04, 0.10	0.18
FSS-9 ^ResCov + VAFS	65.44	34	< 0.001	0.96	0.95	0.06	0.04, 0.09	0.15
FSS-3	4.20	2	0.122	0.99	0.98	0.07	0.00, 0.17	0.27
FSS-3 + VAFS	5.37	4	0.252	1.00	0.99	0.04	0.00, 0.11	0.50
Time 1–2
FSS-3^a	13.33	8	0.101	0.99	0.99	0.03	0.00, 0.06	0.83
FSS-3^b	14.47	10	0.153	1.00	0.99	0.03	0.00, 0.05	0.92
FSS-3^c	15.48	13	0.278	1.00	1.00	0.02	0.00, 0.04	0.98
FSS-3^d	23.35	16	0.105	0.99	0.99	0.03	0.00, 0.05	0.96

The table shows the confirmatory factor analysis results with variance and model fit of the FSS-9, FSS-9 with ResCov, FSS-9 plus VAFS, FSS-9 with ResCov plus VAFS, FSS-3, and FSS-3 plus VAFS at baseline (Time 1) and at the second health assessment (Time 2). For the FSS-3, a longitudinal confirmatory factor analysis was shown in the period from baseline to the second health assessment (Time 1–2). The mean time interval between baseline and the second health assessment was 11.6 months (SD: 4.2)
CFI Comparative Fit Index, TLI Tucker Lewis Index, VAFS Visual Analog Fatigue Scale, FSS-9 Nine-item Fatigue Severity Scale, FSS-3 Three-item Fatigue Severity Scale, ε_a Root Mean Square Error of Approximation (RMSEA); ε_a P < .05: Probability of close fit (RMSEA = 0.05); ResCov: Residual covariance between items 2 and 3 estimated; SD: Standard deviation
^aFree factor loadings, intercepts, and residuals within and from baseline (time 1) to the second health assessment (time 2)
^bEqual factor loadings from baseline (time 1) to the second health assessment (time 2): Wald test of constraints: 0.77, P = 0.682
^cAnd equal residuals within each indicator from baseline (time 1) to the second health assessment (time 2): Wald test of constraints: 1.25, P = 0.682
^dAnd equal intercepts within each indicator from baseline (time 1) to the second health assessment (time 2): Wald test of constraints: 8.61, P = 0.035

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