Table 4.

Results of Invariance Testing on the Final Model

Type of constraint	df	BIC	AIC	χ2	Δχ2	Δdf	p
Unconstrained	18	7,080.02	6,897.32	12.27
Fully constrained	31	7,430.23	7,297.20	438.15	425.88	13	< .001
Path a (age to PHQ) only	19	7,075.43	6,896.24	13.19	0.92	1	.338
Path b (personal threat to PHQ) only	19	7,080.09	6,900.91	17.86	5.59	1	.018
Path c (regional severity to PHQ) only	19	7,081.21	6,902.02	18.97	6.70	1	.010
Path d (isolation-days to PHQ) only	19	7,075.43	6,896.25	13.20	0.93	1	.336
Path e (isolation-loneliness to PHQ) only	19	7,083.89	6,904.70	21.65	9.38	1	.002
Path f (age to FTE) only	19	7,075.04	6,895.86	12.81	0.53	1	.465
Partially constrained a	21	7,065.87	6,893.71	14.66
Partially constrained + path g (PHQ to FTE)	22	7,060.95	6,892.30	15.25	0.59	1	.442

Note: Change values on a given line are relative to the model the line is nested under (e.g., fully constrained vs. unconstrained, path a vs. unconstrained, etc.). The variable “age” refers to chronological age. Significant p values are given in boldface. BIC = Bayesian information criterion; AIC = Akaike information criterion; PHQ = Patient Health Questionnaire; FTE = future time extension.

^aThe partially constrained model allowed the paths from isolation-loneliness to PHQ, regional severity to PHQ, and personal threat to PHQ to vary across age groups while constraining all other paths from the exogenous variables.