Psychometric properties and measurement invariance of the Beck hopelessness scale (BHS): results from a German representative population sample

Table 5 Results of the Multi Group Confirmatory Factor Analysis

	Model	X ²	df	CFI	RMSEA	95% CI	ΔCFI	ΔRMSEA
	Group = Gender
One factor	Configural	1.635.501	238	0.945	0.063	[0.060,0.066]	–	–
	Weak / strong	1.625.190	254	0.948	0.066	[0.063,0.070]	0.003	0.003
	Strict	1.480.973	270	0.954	0.061	[0.058,0.064]	0.006	−0.005
bi-factor	Configural	682.7209	299	0.986	0.032	[0.029,0.036]	–	–
	Weak / strong	711.6125	336	0.986	0.030	[0.0278,0.033]	< 0.001	−0.002
	Strict	674.5467	354	0.989	0.027	[0.024,0.030]	0.003	−0.003
	Goup = Depression (PHQ-2 score < 3, PHQ-2 score ≥ 3)
One factor	Configural	1.613.255	238	0.927	0.069	[0.066,0.072]	–	–
	Weak / strong	1.618.950	254	0.927	0.066	[0.063,0.069]	< 0.001	−0.003
	Strict	1.520.225	270	0.933	0.062	[0.059, 0.065]	0.006	−0.004
bi-factor	Configural	673.1354	299	0.981	0.032	[0.029, 0.035]	–	–
	Weak / strong	1023.4319	336	0.965	0.041	[0.038, 0.044]	−0.016	0.009
	Strict	961.7185	354	0.969	0.037	[0.035, 0.040]	0.004	−0.004

Note. All fit statistics are robust.; configural = (for identification purposes) one marker variable per factor fixed to 1, unique variances of marker variables fixed as 1; all thresholds equally constrained across groups, unique variance of first group fixed as 1, factor means of first group fixed as 0; weak/strong = additionally all free loadings constrained to be equal across group; strict = additionally all unique variances of all groups fixed to 1; CFI = Comparative Fit Index, RMSEA = Root Means Square Error of Approximation, *** = p < .001

ISSN: 1471-244X