Psychometric assessment of scales for measuring loneliness and social isolation: an analysis of the household, income and labour dynamics in Australia (HILDA) survey

Table 4 Measurement invariance for the three-factor model across waves and gender

	AIC	aBIC	χ²	Δ χ²	p-value	CFI	ΔCFI	RMSEA	ΔRMSEA	SRMR	ΔSRMR
Across waves (17 and 19)
Configural invariance	933,079.20	933,399.13	4931.2			0.95		0.07		0.04
Metric invariance	933,074.19	933,363.16	4938.2	7.0	0.60	0.95	0.00	0.06	-0.01	0.04	0.00
Scalar invariance	933,068.25	933,326.27	4944.2	6.0	0.42	0.95	0.00	0.06	0.00	0.04	0.00
Strict invariance	933,069.55	933,281.12	4963.5	19.3	0.58	0.95	0.00	0.06	0.00	0.04	0.00
Across sex in Wave 19 (male and female)
Configural invariance	427,284.77	427,556.50	2353.1			0.95		0.07		0.04
Metric invariance	427,332.53	427,577.96	2412.9	59.8	< 0.001	0.94	− 0.01	0.07	0.00	0.05	0.01
Partial metric invariance	427,383.94	427,642.52	2458.3	45.4	< 0.001	0.94	0.00	0.07	0.00	0.05	0.00
Scalar invariance	427,597.94	427,817.08	2690.3	232.0	< 0.001	0.94	0.00	0.07	0.00	0.05	0.00
Partial scalar invariance	427,343.91	427,576.19	2413.3	0.4	0.79	0.94	0.00	0.07	0.00	0.05	0.00
Strict invariance	427,769.40	427,949.09	2879.8	466.5	< 0.001	0.94	0.00	0.06	0.01	0.07	0.02
Across age categories
Configural invariance	459,166.47	459,834.67	2858.5			0.95		0.07		0.05
Metric invariance	459,288.70	459,849.99	3028.7	170.2	< 0.001	0.95	0.00	0.07	0.00	0.05	0.00
Partial metric invariance	459,170.39	459,802.96	2869.0	10.5	0.08	0.94	− 0.01	0.07	0.00	0.05	0.00
Scalar invariance	459,616.90	460,071.27	3404.9	535.9	< 0.001	0.94	0.00	0.07	0.00	0.06	0.01
Partial scalar invariance	460,232.25	460,472.81	2602.2	− 266.8	< 0.001	0.94	0.00	0.07	0.00	0.06	0.00
Strict invariance	460,800.67	460,983.31	3196.6	594.4	< 0.001	0.94	0.00	0.07	0.00	0.06	0.00

AIC, Akaike information criterion; aBIC, sample size corrected Bayesian information criterion; CFI, comparative fit index; RMSEA, root mean square error of approximation; SRMR, standardised root mean squared residual; Δ, change

ISSN: 1477-7525