Table 1.

Univariate and bivariate change in body mass index and cognitive abilities from age 50–89 in the Health and Retirement Study.

	Univariate		Bivariate
	Estimate	SE	Estimate	SE
(a) Mental status
BMI parameters
Mean intercept level (${\mu }_{{\text{BMI}}_{50}}$)	27.77*	0.07	27.69*	0.07
Mean slope (${\mu }_{{\text{BMI}}_{\text{S}}}$)	− 0.36*	0.11	− 18.04*	1.24
Proportional effect < 70 (βBMI<70)	0.02*	0.00	− 0.45*	0.04
Proportional effect > 70 (βBMI>70)	0.00	0.00	− 0.45*	0.04
Cognition parameters
Mean intercept level (${\mu }_{{\text{COG}}_{50}}$)	51.12*	0.13	50.43*	0.11
Mean slope (${\mu }_{{\text{COG}}_{\text{S}}}$)	− 9.98*	0.72	− 6.25*	1.08
Proportional effect < 70 (βCOG<70)	0.20*	0.01	0.36*	0.04
Proportional effect > 70 (βCOG>70)	0.19*	0.01	0.36*	0.04
Bivariate parameters
Coupling effect BMI on cognition < 70 (γBMI>COG, <70)	–	–	− 0.43*	0.03
Coupling effect BMI on cognition > 70 (γBMI>COG, >70)	–	–	− 0.43*	0.03
Coupling effect cognition on BMI < 70 (γCOG>BMI, <70)	–	–	0.61*	0.04
Coupling effect cognition on BMI > 70 (γCOG>BMI, >70)	–	–	0.61*	0.04
(b) Episodic memory
BMI parameters
Mean intercept level (${\mu }_{{\text{BMI}}_{50}}$)	27.77*	0.07	27.40*	0.08
Mean slope (${\mu }_{{\text{BMI}}_{\text{S}}}$)	− 0.36*	0.11	− 3.67*	0.96
Proportional effect < 70 (βBMI <70)	0.02*	0.00	− 0.02	0.05
Proportional effect > 70 (βBMI >70)	0.00	0.00	− 0.06	0.04
Cognition parameters
Mean intercept level (${\mu }_{{\text{COG}}_{50}}$)	49.88*	0.13	49.51*	0.50
Mean slope (${\mu }_{{\text{COG}}_{\text{S}}}$)	− 3.86*	0.25	− 0.67	3.64
Proportional effect < 65 (βCOG <65)	0.07*	0.01	0.09*	0.01
Proportional effect > 65 (βCOG >65)	0.07*	0.01	0.07*	0.01
Bivariate parameters
Coupling effect BMI on cognition < 65 (γBMI>COG, <65)	–	–	− 0.15	0.11
Coupling effect BMI on cognition > 65 (γBMI>COG, >65)	–	–	− 0.12	0.11
Coupling effect cognition on BMI < 70 (γCOG>BMI, <70)	–	–	0.09	0.05
Coupling effect cognition on BMI > 70 (γCOG>BMI, >70)	–	–	0.12*	0.05
(c) Total cognition
BMI parameters
Mean intercept level (${\mu }_{{\text{BMI}}_{50}}$)	27.77*	0.07	27.49*	0.08
Mean slope (${\mu }_{{\text{BMI}}_{\text{S}}}$)	− 0.36*	0.11	− 2.77*	0.32
Proportional effect < 70 (βBMI <70)	0.02*	0.00	0.00	0.01
Proportional effect > 70 (βBMI >70)	0.00	0.00	− 0.04*	0.01
Cognition parameters
Mean intercept level (${\mu }_{{\text{COG}}_{50}}$)	50.09*	0.14	50.26*	0.14
Mean slope (${\mu }_{{\text{COG}}_{\text{S}}}$)	− 6.23*	0.26	− 4.79*	0.81
Proportional effect < 65 (βCOG <65)	0.12*	0.01	0.15*	0.01
Proportional effect > 65 (βCOG >65)	0.12*	0.01	0.12*	0.01
Bivariate parameters
Coupling effect BMI on cognition < 65 (γBMI>COG, <65)	–	–	− 0.10*	0.03
Coupling effect BMI on cognition > 65 (γBMI>COG, >65)	–	–	− 0.06*	0.03
Coupling effect cognition on BMI < 70 (γCOG>BMI, <70)	–	–	0.06*	0.01
Coupling effect cognition on BMI > 70 (γCOG>BMI, >70)	–	–	0.08*	0.01

SE standard deviation, BMI body mass index, COG cognition.

Parameter estimates and standard deviations from the univariate and bivariate dual change score models of BMI and cognitive abilities in 23,892 individuals of European ancestry from the Health and Retirement Study. The slope parameters represent the mean linear change over 2 years. Proportional and coupling effects represent additional change over 2 years in relation to within and across-trait levels, respectively, at the preceding time point. BMI parameters are in BMI units and cognition parameters in T-score units. Models are adjusted for sex and education. A breakpoint was included to allow for differences in the proportional change and coupling parameters (mean slope is constant across age) before and after age 70 for BMI and mental status, and at 65 for episodic memory and total cognition. *p < 0.05.