Longitudinal beta regression models for analyzing health-related quality of life scores over time

Table 1 Parameter estimates of LMM, beta GLMM and beta GEE in the KORA data (N = 1945)

Parameter coefficients	LMM		Beta GLMM		Beta GEE
	Estimate	p value	Estimate	p value	Estimate	p value
Intercept	0.7808	<0.0001	1.3534	<0.0001	1.2816	<0.0001
Age at baseline (centered)	−0.0036	<0.0001	−0.0185	0.0007	−0.0209	<0.0001
Male sex	0.0525	<0.0001	0.3483	<0.0001	0.3000	<0.0001
Time	−0.0140	0.0002	−0.0788	0.0004	−0.0815	0.0002
Diabetes	−0.0267	<0.0001	−0.1538	0.0002	−0.1586	<0.0001
Diabetes*Time	−0.0300	0.0544	−0.1837	0.0608	−0.1513	0.0813
σ²	0.0091
ϕ			14.45
Variance of random effects	Estimate	SE	Estimate	SE	Estimate	SE
Variance	0.0095	0.0007	0.3854	0.0309
Covariance estimates
Variance					0.0536	0.0028
Compound symmetry					0.0564	0.0042
Scale					0.0240
Fit statistics
−2LogL	−2457		−2739		-
AIC	−2441		−2723		-
BIC	−2401		−2682		-
Pseudo-R²†	0.0535		0.1812		-

LMM Linear mixed model, GLMM Generalized linear mixed model, GEE Generalized estimating equations, SE Standard error, CS Compound Symmetry, AIC Akaike information criterion. BIC Bayesian information criterion.
†Compared to linear random-intercept model with -2LogL = −2350.

ISSN: 1471-2288