Response shift in health-related quality of life measures in the presence of formative indicators

Table 3 Fit statistics for the formative indicator models

Model	χ²	df	p-value	RMSEA	CFI	Δχ²	Δdf	p-value
Step 1: invariance of reflective indicators (OH, QoL, FC) used for identification Purpose
Baseline	2.59	3	0.458	0	1	–	–	–
Constrained model^a	16.06	11	0.139	0.04	0.99	13.13	8	0.108
Step 2: invariance of items used to create the two domain-level formative indicators (PA, FA)
Baseline	30.30	24	0.175	0.03	0.99	–	–	–
Constrained model^b	74.14	35	< 0.001	0.07	0.97	44.56	11	< 0.001
Constrained model^c	43.26	33	0.109	0.03	0.99	13.01	9	0.162
Step 3: RS detection—invariance in the formative indicator model
Baseline	51.59	30	0.01	0.05	0.98	–	–	–
Constrained model^d	54.80	33	0.01	0.05	0.98	3.59	3	0.310

Step 1–step 3 are illustrated in Fig. 3
OH, overall health; QoL, overall quality of life; FC, functioning scales; PA, pain; FA, fatigue; RMSEA, root mean square approximation; CFI, comparative fit index
^aLoadings, intercepts and residual variances of the three indicators, OH, QoL and FC, are constrained to be equal across the two time points; the mean of the latent variable is set to zero at t = 1 and freely estimated at t = 2
^bLoadings, intercepts and residual variances of the five items measuring the latent variables PA and FA are constrained to be equal across the two time points; the means of the latent variables are set to zero at t = 1 and freely estimated at t = 2
^cAfter removing two error variance equality constraints
^dPA and FA regression coefficients and the unexplained variance of the latent variable is constrained to be equal across the two time points and the model intercept is set to zero at t = 1 and freely estimated at t = 2

ISSN: 1477-7525