. Author manuscript; available in PMC: 2020 Aug 1.

Published in final edited form as: J R Stat Soc Ser C Appl Stat. 2018 Dec 25;68(4):1071–1089. doi: 10.1111/rssc.12333

Table 3.

Estimated standard deviations and correlations of the random effects, and standard deviations of the random spline coefficients from the AQMM for the MCS physical activity data

	Results for the following values of τ:
	τ =0.1	τ =0.5	τ =0.9	τ =0.95	τ =0.99
Standard deviations (random effects)
${\hat{σ}}_{0}$ (intercept weekdays)	2969	3923	2882	2769	4897
${\hat{σ}}_{1}$ (intercept weekend)	3015	3526	2842	2809	5054
${\hat{σ}}_{t_{0}}$ (time of the day weekdays)	2868	3575	2817	2800	5069
${\hat{σ}}_{t 1}$ (time of the day weekend)	2867	3376	2940	2858	5017
Correlations (random effects)
${\hat{ρ}}_{0, 1}$	0.93	0.97	0.73	0.36	0.52
${\hat{ρ}}_{0, t_{0}}$	0.99	0.99	0.94	0.89	0.93
${\hat{ρ}}_{1, t_{0}}$	0.93	0.97	0.71	0.35	0.51
${\hat{ρ}}_{0, t_{1}}$	0.93	0.97	0.73	0.37	0.52
${\hat{ρ}}_{1, t_{1}}$	0.99	0.99	0.93	0.88	0.93
${\hat{ρ}}_{t_{0}, t_{1}}$	0.93	0.97	0.72	0.36	0.51
Standard deviations (smooth terms)
${\hat{ϕ}}_{weekdays}$	4136	15215	4114	4343	1722
${\hat{ϕ}}_{weekend}$	8385	14541	6699	2402	515
${\hat{ϕ}}_{BMI}$	2905	4945	7094	2777	181