Table 2 Open in new tab Standardised...

Parameter	Estimate	SE		Estimate	SE
Within person level
Autoregressive effects
Social isolation and frailty
FI_T1 ➝ FI_T2	0.653^***	0.023	SI_T1 ➝ SI _T2	0.309^***	0.047
FI_T2 ➝ FI_T3	0.547^***	0.033	SI _T2 ➝ SI _T3	0.216^***	0.058
FI_T3 ➝ FI_T4	0.622^***	0.032	SI _T3 ➝ SI _T4	0.219^***	0.053
FI_T4 ➝ FI_T5	0.742^***	0.028	SI _T4 ➝ SI _T5	0.308^***	0.054
FI_T5 ➝ FI_T6	0.688^***	0.035	SI _T5 ➝ SI _T6	0.562^***	0.049
FI_T6 ➝ FI_T7	0.758^***	0.037	SI _T6 ➝ SI _T7	0.489^***	0.070
Loneliness and frailty
FI_T1 ➝ FI_T2	0.593^***	0.030	L_T1 ➝ L_T2	0.246^***	0.053
FI_T2 ➝ FI_T3	0.519^***	0.034	L_T2 ➝ L_T3	0.211^***	0.059
FI_T3 ➝ FI_T4	0.606^***	0.035	L_T3 ➝ L_T4	0.192^***	0.058
FI_T4 ➝ FI_T5	0.699^***	0.030	L_T4 ➝ L_T5	0.355^***	0.050
FI_T5 ➝ FI_T6	0.706 ^***	0.037	L_T5 ➝ L_T6	0.285^***	0.057
FI_T6 ➝ FI_T7	0.723 ^***	0.042	L_T6 ➝ L_T7	0.512^***	0.071
Cross-lagged effects
Social isolation and frailty	Frailty and social isolation
SI_T1 ➝ FI_T2	0.012	0.024	FI_T1 ➝ SI_T2	−0.138	0.107
SI_T2 ➝ FI_T3	−0.008	0.030	FI_T2 ➝ SI_T3	0.141^***	0.050
SI_T3 ➝ FI_T4	−0.006	0.032	FI_T3 ➝ SI_T4	0.121^*	0.057
SI_T4 ➝ FI_T5	0.031	0.037	FI_T4 ➝ SI_T5	0.227^***	0.049
SI_T5 ➝ FI_T6	0.087^*	0.037	FI_T5 ➝ SI_T6	0.186^***	0.046
SI_T6 ➝ FI_T7	0.040	0.041	FI_T6 ➝ SI_T7	0.102	0.061
Loneliness and frailty	Frailty and loneliness
L_T1 ➝ FI_T2	0.091^***	0.027	FI_T1 ➝ L_T2	0.112	0.107
L_T2 ➝ FI_T3	0.030	0.031	FI_T2 ➝ L_T3	0.225^***	0.055
L_T3 ➝ FI_T4	0.026	0.032	FI_T3 ➝ L_T4	0.275^***	0.060
L_T4 ➝ FI_T5	0.093^***	0.026	FI_T4 ➝ L_T5	0.181^**	0.067
L_T5 ➝ FI_T6	0.001	0.032	FI_T5 ➝ L_T6	0.326^***	0.065
L_T6 ➝ FI_T7	0.098^**	0.042	FI_T6 ➝ L_T7	0.279^***	0.077
Covariances
FI_T1 with SI_T1	0.003	0.067	FI_T1 with L_T1	−0.055	0.078
FI_T2 with SI_T2	0.051	0.035	FI_T2 with L_T2	0.285^***	0.078
FI_T3 with SI_T3	0.091^*	0.039	FI_T3 with L_T3	0.206^***	0.036
FI_T4 with SI_T4	0.107^*	0.047	FI_T4 with L_T4	0.124^***	0.038
FI_T5 with SI_T5	0.045	0.043	FI_T5 with L_T5	0.173^***	0.045
FI_T6 with SI_T6	0.104^*	0.046	FI_T6 with L_T6	0.172	0.046
FI_T7 with SI_T7	0.024	0.062	FI_T7 with L_T7	0.090	0.057
Between person level
Intercept-FI with Intercept-SI	0.112^***	0.037	Intercept-FI with Intercept-L	0.043	0.043

Parameter

Estimate

Within person level

Autoregressive effects

Social isolation and frailty

FI_T1 ➝ FI_T2

0.653^***

0.023

SI_T1 ➝ SI _T2

0.309^***

0.047

FI_T2 ➝ FI_T3

0.547^***

0.033

SI _T2 ➝ SI _T3

0.216^***

0.058

FI_T3 ➝ FI_T4

0.622^***

0.032

SI _T3 ➝ SI _T4

0.219^***

0.053

FI_T4 ➝ FI_T5

0.742^***

0.028

SI _T4 ➝ SI _T5

0.308^***

0.054

FI_T5 ➝ FI_T6

0.688^***

0.035

SI _T5 ➝ SI _T6

0.562^***

0.049

FI_T6 ➝ FI_T7

0.758^***

0.037

SI _T6 ➝ SI _T7

0.489^***

0.070

Loneliness and frailty

FI_T1 ➝ FI_T2

0.593^***

0.030

L_T1 ➝ L_T2

0.246^***

0.053

FI_T2 ➝ FI_T3

0.519^***

0.034

L_T2 ➝ L_T3

0.211^***

0.059

FI_T3 ➝ FI_T4

0.606^***

0.035

L_T3 ➝ L_T4

0.192^***

0.058

FI_T4 ➝ FI_T5

0.699^***

0.030

L_T4 ➝ L_T5

0.355^***

0.050

FI_T5 ➝ FI_T6

0.706 ^***

0.037

L_T5 ➝ L_T6

0.285^***

0.057

FI_T6 ➝ FI_T7

0.723 ^***

0.042

L_T6 ➝ L_T7

0.512^***

0.071

Cross-lagged effects

Social isolation and frailty

Frailty and social isolation

SI_T1 ➝ FI_T2

0.012

0.024

FI_T1 ➝ SI_T2

−0.138

0.107

SI_T2 ➝ FI_T3

−0.008

0.030

FI_T2 ➝ SI_T3

0.141^***

0.050

SI_T3 ➝ FI_T4

−0.006

0.032

FI_T3 ➝ SI_T4

0.121^*

0.057

SI_T4 ➝ FI_T5

0.031

0.037

FI_T4 ➝ SI_T5

0.227^***

0.049

SI_T5 ➝ FI_T6

0.087^*

0.037

FI_T5 ➝ SI_T6

0.186^***

0.046

SI_T6 ➝ FI_T7

0.040

0.041

FI_T6 ➝ SI_T7

0.102

0.061

Loneliness and frailty

Frailty and loneliness

L_T1 ➝ FI_T2

0.091^***

0.027

FI_T1 ➝ L_T2

0.112

0.107

L_T2 ➝ FI_T3

0.030

0.031

FI_T2 ➝ L_T3

0.225^***

0.055

L_T3 ➝ FI_T4

0.026

0.032

FI_T3 ➝ L_T4

0.275^***

0.060

L_T4 ➝ FI_T5

0.093^***

0.026

FI_T4 ➝ L_T5

0.181^**

0.067

L_T5 ➝ FI_T6

0.001

0.032

FI_T5 ➝ L_T6

0.326^***

0.065

L_T6 ➝ FI_T7

0.098^**

0.042

FI_T6 ➝ L_T7

0.279^***

0.077

Covariances

FI_T1 with SI_T1

0.003

0.067

FI_T1 with L_T1

−0.055

0.078

FI_T2 with SI_T2

0.051

0.035

FI_T2 with L_T2

0.285^***

0.078

FI_T3 with SI_T3

0.091^*

0.039

FI_T3 with L_T3

0.206^***

0.036

FI_T4 with SI_T4

0.107^*

0.047

FI_T4 with L_T4

0.124^***

0.038

FI_T5 with SI_T5

0.045

0.043

FI_T5 with L_T5

0.173^***

0.045

FI_T6 with SI_T6

0.104^*

0.046

FI_T6 with L_T6

0.172

0.046

FI_T7 with SI_T7

0.024

0.062

FI_T7 with L_T7

0.090

0.057

Between person level

Intercept-FI with Intercept-SI

0.112^***

0.037

Intercept-FI with Intercept-L

0.043

Parameter	Estimate	SE		Estimate	SE
Within person level
Autoregressive effects
Social isolation and frailty
FI_T1 ➝ FI_T2	0.653^***	0.023	SI_T1 ➝ SI _T2	0.309^***	0.047
FI_T2 ➝ FI_T3	0.547^***	0.033	SI _T2 ➝ SI _T3	0.216^***	0.058
FI_T3 ➝ FI_T4	0.622^***	0.032	SI _T3 ➝ SI _T4	0.219^***	0.053
FI_T4 ➝ FI_T5	0.742^***	0.028	SI _T4 ➝ SI _T5	0.308^***	0.054
FI_T5 ➝ FI_T6	0.688^***	0.035	SI _T5 ➝ SI _T6	0.562^***	0.049
FI_T6 ➝ FI_T7	0.758^***	0.037	SI _T6 ➝ SI _T7	0.489^***	0.070
Loneliness and frailty
FI_T1 ➝ FI_T2	0.593^***	0.030	L_T1 ➝ L_T2	0.246^***	0.053
FI_T2 ➝ FI_T3	0.519^***	0.034	L_T2 ➝ L_T3	0.211^***	0.059
FI_T3 ➝ FI_T4	0.606^***	0.035	L_T3 ➝ L_T4	0.192^***	0.058
FI_T4 ➝ FI_T5	0.699^***	0.030	L_T4 ➝ L_T5	0.355^***	0.050
FI_T5 ➝ FI_T6	0.706 ^***	0.037	L_T5 ➝ L_T6	0.285^***	0.057
FI_T6 ➝ FI_T7	0.723 ^***	0.042	L_T6 ➝ L_T7	0.512^***	0.071
Cross-lagged effects
Social isolation and frailty	Frailty and social isolation
SI_T1 ➝ FI_T2	0.012	0.024	FI_T1 ➝ SI_T2	−0.138	0.107
SI_T2 ➝ FI_T3	−0.008	0.030	FI_T2 ➝ SI_T3	0.141^***	0.050
SI_T3 ➝ FI_T4	−0.006	0.032	FI_T3 ➝ SI_T4	0.121^*	0.057
SI_T4 ➝ FI_T5	0.031	0.037	FI_T4 ➝ SI_T5	0.227^***	0.049
SI_T5 ➝ FI_T6	0.087^*	0.037	FI_T5 ➝ SI_T6	0.186^***	0.046
SI_T6 ➝ FI_T7	0.040	0.041	FI_T6 ➝ SI_T7	0.102	0.061
Loneliness and frailty	Frailty and loneliness
L_T1 ➝ FI_T2	0.091^***	0.027	FI_T1 ➝ L_T2	0.112	0.107
L_T2 ➝ FI_T3	0.030	0.031	FI_T2 ➝ L_T3	0.225^***	0.055
L_T3 ➝ FI_T4	0.026	0.032	FI_T3 ➝ L_T4	0.275^***	0.060
L_T4 ➝ FI_T5	0.093^***	0.026	FI_T4 ➝ L_T5	0.181^**	0.067
L_T5 ➝ FI_T6	0.001	0.032	FI_T5 ➝ L_T6	0.326^***	0.065
L_T6 ➝ FI_T7	0.098^**	0.042	FI_T6 ➝ L_T7	0.279^***	0.077
Covariances
FI_T1 with SI_T1	0.003	0.067	FI_T1 with L_T1	−0.055	0.078
FI_T2 with SI_T2	0.051	0.035	FI_T2 with L_T2	0.285^***	0.078
FI_T3 with SI_T3	0.091^*	0.039	FI_T3 with L_T3	0.206^***	0.036
FI_T4 with SI_T4	0.107^*	0.047	FI_T4 with L_T4	0.124^***	0.038
FI_T5 with SI_T5	0.045	0.043	FI_T5 with L_T5	0.173^***	0.045
FI_T6 with SI_T6	0.104^*	0.046	FI_T6 with L_T6	0.172	0.046
FI_T7 with SI_T7	0.024	0.062	FI_T7 with L_T7	0.090	0.057
Between person level
Intercept-FI with Intercept-SI	0.112^***	0.037	Intercept-FI with Intercept-L	0.043	0.043

Table 2

Open in new tab

Standardised estimates of the RI-CLPM for the relationship between social isolation, loneliness and frailty across seven waves

Parameter	Estimate	SE		Estimate	SE
Within person level
Autoregressive effects
Social isolation and frailty
FI_T1 ➝ FI_T2	0.653^***	0.023	SI_T1 ➝ SI _T2	0.309^***	0.047
FI_T2 ➝ FI_T3	0.547^***	0.033	SI _T2 ➝ SI _T3	0.216^***	0.058
FI_T3 ➝ FI_T4	0.622^***	0.032	SI _T3 ➝ SI _T4	0.219^***	0.053
FI_T4 ➝ FI_T5	0.742^***	0.028	SI _T4 ➝ SI _T5	0.308^***	0.054
FI_T5 ➝ FI_T6	0.688^***	0.035	SI _T5 ➝ SI _T6	0.562^***	0.049
FI_T6 ➝ FI_T7	0.758^***	0.037	SI _T6 ➝ SI _T7	0.489^***	0.070
Loneliness and frailty
FI_T1 ➝ FI_T2	0.593^***	0.030	L_T1 ➝ L_T2	0.246^***	0.053
FI_T2 ➝ FI_T3	0.519^***	0.034	L_T2 ➝ L_T3	0.211^***	0.059
FI_T3 ➝ FI_T4	0.606^***	0.035	L_T3 ➝ L_T4	0.192^***	0.058
FI_T4 ➝ FI_T5	0.699^***	0.030	L_T4 ➝ L_T5	0.355^***	0.050
FI_T5 ➝ FI_T6	0.706 ^***	0.037	L_T5 ➝ L_T6	0.285^***	0.057
FI_T6 ➝ FI_T7	0.723 ^***	0.042	L_T6 ➝ L_T7	0.512^***	0.071
Cross-lagged effects
Social isolation and frailty			Frailty and social isolation
SI_T1 ➝ FI_T2	0.012	0.024	FI_T1 ➝ SI_T2	−0.138	0.107
SI_T2 ➝ FI_T3	−0.008	0.030	FI_T2 ➝ SI_T3	0.141^***	0.050
SI_T3 ➝ FI_T4	−0.006	0.032	FI_T3 ➝ SI_T4	0.121^*	0.057
SI_T4 ➝ FI_T5	0.031	0.037	FI_T4 ➝ SI_T5	0.227^***	0.049
SI_T5 ➝ FI_T6	0.087^*	0.037	FI_T5 ➝ SI_T6	0.186^***	0.046
SI_T6 ➝ FI_T7	0.040	0.041	FI_T6 ➝ SI_T7	0.102	0.061
Loneliness and frailty			Frailty and loneliness
L_T1 ➝ FI_T2	0.091^***	0.027	FI_T1 ➝ L_T2	0.112	0.107
L_T2 ➝ FI_T3	0.030	0.031	FI_T2 ➝ L_T3	0.225^***	0.055
L_T3 ➝ FI_T4	0.026	0.032	FI_T3 ➝ L_T4	0.275^***	0.060
L_T4 ➝ FI_T5	0.093^***	0.026	FI_T4 ➝ L_T5	0.181^**	0.067
L_T5 ➝ FI_T6	0.001	0.032	FI_T5 ➝ L_T6	0.326^***	0.065
L_T6 ➝ FI_T7	0.098^**	0.042	FI_T6 ➝ L_T7	0.279^***	0.077
Covariances
FI_T1 with SI_T1	0.003	0.067	FI_T1 with L_T1	−0.055	0.078
FI_T2 with SI_T2	0.051	0.035	FI_T2 with L_T2	0.285^***	0.078
FI_T3 with SI_T3	0.091^*	0.039	FI_T3 with L_T3	0.206^***	0.036
FI_T4 with SI_T4	0.107^*	0.047	FI_T4 with L_T4	0.124^***	0.038
FI_T5 with SI_T5	0.045	0.043	FI_T5 with L_T5	0.173^***	0.045
FI_T6 with SI_T6	0.104^*	0.046	FI_T6 with L_T6	0.172	0.046
FI_T7 with SI_T7	0.024	0.062	FI_T7 with L_T7	0.090	0.057
Between person level
Intercept-FI with Intercept-SI	0.112^***	0.037	Intercept-FI with Intercept-L	0.043	0.043

Parameter	Estimate	SE		Estimate	SE
Within person level
Autoregressive effects
Social isolation and frailty
FI_T1 ➝ FI_T2	0.653^***	0.023	SI_T1 ➝ SI _T2	0.309^***	0.047
FI_T2 ➝ FI_T3	0.547^***	0.033	SI _T2 ➝ SI _T3	0.216^***	0.058
FI_T3 ➝ FI_T4	0.622^***	0.032	SI _T3 ➝ SI _T4	0.219^***	0.053
FI_T4 ➝ FI_T5	0.742^***	0.028	SI _T4 ➝ SI _T5	0.308^***	0.054
FI_T5 ➝ FI_T6	0.688^***	0.035	SI _T5 ➝ SI _T6	0.562^***	0.049
FI_T6 ➝ FI_T7	0.758^***	0.037	SI _T6 ➝ SI _T7	0.489^***	0.070
Loneliness and frailty
FI_T1 ➝ FI_T2	0.593^***	0.030	L_T1 ➝ L_T2	0.246^***	0.053
FI_T2 ➝ FI_T3	0.519^***	0.034	L_T2 ➝ L_T3	0.211^***	0.059
FI_T3 ➝ FI_T4	0.606^***	0.035	L_T3 ➝ L_T4	0.192^***	0.058
FI_T4 ➝ FI_T5	0.699^***	0.030	L_T4 ➝ L_T5	0.355^***	0.050
FI_T5 ➝ FI_T6	0.706 ^***	0.037	L_T5 ➝ L_T6	0.285^***	0.057
FI_T6 ➝ FI_T7	0.723 ^***	0.042	L_T6 ➝ L_T7	0.512^***	0.071
Cross-lagged effects
Social isolation and frailty			Frailty and social isolation
SI_T1 ➝ FI_T2	0.012	0.024	FI_T1 ➝ SI_T2	−0.138	0.107
SI_T2 ➝ FI_T3	−0.008	0.030	FI_T2 ➝ SI_T3	0.141^***	0.050
SI_T3 ➝ FI_T4	−0.006	0.032	FI_T3 ➝ SI_T4	0.121^*	0.057
SI_T4 ➝ FI_T5	0.031	0.037	FI_T4 ➝ SI_T5	0.227^***	0.049
SI_T5 ➝ FI_T6	0.087^*	0.037	FI_T5 ➝ SI_T6	0.186^***	0.046
SI_T6 ➝ FI_T7	0.040	0.041	FI_T6 ➝ SI_T7	0.102	0.061
Loneliness and frailty			Frailty and loneliness
L_T1 ➝ FI_T2	0.091^***	0.027	FI_T1 ➝ L_T2	0.112	0.107
L_T2 ➝ FI_T3	0.030	0.031	FI_T2 ➝ L_T3	0.225^***	0.055
L_T3 ➝ FI_T4	0.026	0.032	FI_T3 ➝ L_T4	0.275^***	0.060
L_T4 ➝ FI_T5	0.093^***	0.026	FI_T4 ➝ L_T5	0.181^**	0.067
L_T5 ➝ FI_T6	0.001	0.032	FI_T5 ➝ L_T6	0.326^***	0.065
L_T6 ➝ FI_T7	0.098^**	0.042	FI_T6 ➝ L_T7	0.279^***	0.077
Covariances
FI_T1 with SI_T1	0.003	0.067	FI_T1 with L_T1	−0.055	0.078
FI_T2 with SI_T2	0.051	0.035	FI_T2 with L_T2	0.285^***	0.078
FI_T3 with SI_T3	0.091^*	0.039	FI_T3 with L_T3	0.206^***	0.036
FI_T4 with SI_T4	0.107^*	0.047	FI_T4 with L_T4	0.124^***	0.038
FI_T5 with SI_T5	0.045	0.043	FI_T5 with L_T5	0.173^***	0.045
FI_T6 with SI_T6	0.104^*	0.046	FI_T6 with L_T6	0.172	0.046
FI_T7 with SI_T7	0.024	0.062	FI_T7 with L_T7	0.090	0.057
Between person level
Intercept-FI with Intercept-SI	0.112^***	0.037	Intercept-FI with Intercept-L	0.043	0.043

Notes: FI: Frailty Index, L: Loneliness, SI: Social Isolation, SE: standard error, RI-CLPM = random intercept cross-lagged panel model. T1 = Time 1 (1995–1996); T2 (1998–1999); T3 (2001–2002); T4 (2005–2006), T5 (2008–2009); T6 (2011–2012); T7 (2015–2016). Models were controlled for age, sex, education and depressive symptoms at baseline. Autoregressive effects capture the stability of each variable over time. Cross-lagged effects represent the impact of one variable at a previous wave on the current value of another variable. Model fit indices for RI-CLPM of social isolation and frailty: χ² = 289, df = 84, P value ≤ 0.001, CFI = 0.984, TLI = 0.971, RMSEA = 0.033, and SRMR = 0.040. Model fit indices for RI-CLPM of loneliness and frailty: χ² = 162, df = 79, P value ≤ 0.001, CFI = 0.993, TLI = 0.986, RMSEA = 0.021, and SRMR = 0.023. ^*^*^*P < 0.001; ^*^*P < 0.01; ^*P < 0.0 5.

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