Table 5.

Scalar Invariance Alignment Findings for Loadings Averaged Across the 100 Datasets.

Structure and items	Percentage of approximate non-invariance across the 100 datasets							Average % of non-invariance	Weighted average loading across invariant groups		R 2
	18–25	26–35	36–45	46–55	56–65	66–75	76+		M	SD	M	SD
UCLA-LS-4 Russell et al. (1980)								0.07%
1	0	0	0	0	0	1	0		0.41	0.01	0.40	0.22
13	0	0	0	0	0	0	0		0.70	0.01	0.57	0.22
15	0	0	0	0	1	0	0		0.50	0.01	0.03	0.07
18	0	0	0	0	0	0	0		0.67	0.01	0.31	0.28
UCLA-LS-8 Hays & DiMatteo (1987)								0.05%
2	0	0	0	0	0	0	0		0.62	0.01	0.53	0.10
3	0	0	0	0	0	0	0		0.65	0.01	0.58	0.19
9	0	0	0	0	0	2	0		0.33	0.01	0.27	0.17
11	0	0	0	0	0	0	0		0.57	0.01	0.43	0.27
14	0	0	0	0	0	1	0		0.75	0.01	0.32	0.27
15	0	0	0	0	0	0	0		0.48	0.01	0.45	0.23
17	0	0	0	0	0	0	0		0.63	0.01	0.46	0.19
18	0	0	0	0	0	0	0		0.60	0.01	0.02	0.07
15	0	0	0	0	0	0	0		0.53	0.01	0.37	0.25
UCLA-LS-8 Roberts et al. (1993)								5.8%
1	0	0	0	0	0	1	0		0.36	0.01	0.07	0.09
2	1	0	0	0	0	4	0		0.64	0.01	0.26	0.14
4	86	54	19	4	20	35	97		0.30	0.08	0.00	0.01
5	0	0	0	0	0	0	0		0.56	0.01	0.33	0.23
7	0	0	0	1	0	0	1		0.70	0.01	0.35	0.20
11	0	0	0	0	0	0	0		0.57	0.01	0.42	0.26
14	0	0	0	0	0	1	0		0.76	0.01	0.38	0.23
15	0	0	0	0	0	0	0		0.53	0.01	0.37	0.25
UCLA-LS-9 Hawkley et al. (2005)
F1: 2	0	0	0	0	0	0	0	0%	0.57	0.01	0.62	0.09
11	0	0	0	0	0	0	0		0.57	0.00	0.80	0.15
14	0	0	0	0	0	0	0		0.78	0.01	0.02	0.07
F3: 1	0	0	0	0	0	0	0	0%	0.42	0.01	0.39	0.19
5	0	0	0	0	0	0	0		0.66	0.01	0.26	0.26
6	0	0	0	0	0	0	0		0.69	0.01	0.33	0.30
UCLA-LS-10 Knight et al. (1988) Version 1 – two-factor								4% a
F1: 1	0	0	0	0	0	0	0		0.43	0.01	0.55	0.21
4	98	34	14	6	6	27	93		0.29	0.07	0.08	0.03
6	0	0	0	0	0	0	0		0.56	0.01	0.26	0.23
16	0	0	0	0	0	0	0		0.62	0.01	0.40	0.33
19	0	0	0	0	0	0	0		0.55	0.01	0.50	0.27
F2: 2	0	0	0	0	0	0	0		0.58	0.01	0.52	0.11
7	0	0	0	0	0	0	0		0.71	0.01	0.51	0.24
8	0	4	0	0	0	0	0		0.46	0.01	0.06	0.13
11	0	0	0	0	0	0	1		0.51	0.01	0.44	0.22
18	0	0	0	0	0	0	0		0.61	0.01	0.09	0.17
UCLA-LS-10 Knight et al. (1988) Version 2 – two-factor								0.16%
F1: 3	1	0	0	0	0	0	0		0.73	0.27	0.52	0.28
12	1	0	0	0	0	0	0		0.52	0.19	0.43	0.27
13	1	0	0	0	0	0	0		0.70	0.25	0.05	0.11
14	1	0	0	0	0	0	0		0.76	0.28	0.51	0.24
17	1	0	0	0	0	0	0		0.60	0.23	0.31	0.14
F2: 5	1	0	0	0	0	0	0		0.63	0.22	0.36	0.26
9	1	0	0	0	0	0	0		0.41	0.14	0.34	0.22
10	1	0	0	0	0	0	0		0.49	0.17	0.42	0.24
15	1	0	0	0	0	0	1		0.58	0.20	0.37	0.25
20	1	0	0	0	0	0	0		0.59	0.20	0.18	0.20

Note. Versions that achieved full measurement invariance (UCLA-LS9 and its factor 2) are not presented here, as they did not receive alignment testing. UCLA-LS-4 = University of California Los Angeles, Loneliness Scale-4-item measures; UCLA-LS-8 = University of California Los Angeles, Loneliness Scale-8-item measures; UCLA-LS-9 = University of California Los Angeles, Loneliness Scale-9-item measures; UCLA-LS-10 = University of California Los Angeles, Loneliness Scale-10-item measures.

^aFormula used to calculate the average % of non-invariance: 283 non-invariant parameters across the 100 datasets/7,000 calculated parameters*100.