Table 3.

Application of the Bayesian Three Level Mixed Effects Location Scale Model on Adolescent Smoking Study

Parameters	MRM		MRM with HV		MLS
	Estimate	95% Credible Interval	Estimate	95% Credible Interval	Estimate	95% Credible Interval
βintercept	6.6678	(6.3530, 7.0017)	6.6533	(6.3174, 6.9810)	6.6739	(6.3507, 6.9960)
βMale	−0.0409	(−0.3158, 0.2401)	−0.0415	(−0.3353, 0.2464)	−0.0455	(−0.3166, 0.2121)
βsmksubj	0.5538	(−0.5657, 1.6776)	0.5886	(−0.5824, 1.7126)	0.7113	(−0.4083, 1.8347)
βsmkwave	0.0327	(−0.6442, 0.7056)	0.0278	(−0.6352, 0.6695)	0.0385	(−0.6297, 0.7041)
βsmkobs	0.2310	(0.1927, 0.2685)	0.2260	(0.1896, 0.2615)	0.0965	(0.0689, 0.1238)
βwave	0.4498	(0.2594, 0.6428)	0.4465	(0.2594, 0.6445)	0.4463	(0.2523, 0.6411)
αintercept	0.6850	(0.6700, 0.6997)	1.0930	(1.0513, 1.1355)	0.8728	(0.6868, 1.0700)
αMale	—	—	−0.1693	(−0.2007, −0.1375)	−0.1379	(−0.3180, 0.0270)
αsmksubj	—	—	−0.7555	(−0.8816, −0.6342)	−0.5698	(−1.2555, 0.1118)
αsmkwave	—	—	−0.3535	(−0.5465, −0.1635)	−0.0578	(−0.5989, 0.4788)
αsmkobs	—	—	−0.0666	(−0.1043, −0.0284)	−0.0600	(−0.1030, −0.0192)
αwave	—	—	−0.2060	(−0.2380, −0.1734)	−0.3211	(−0.4645, −0.1800)
$\mathit{location}:{\sigma }_{\mathit{subj}\mathit{int}}^2$	0.9808	(0.7293, 1.2807)	0.9689	(0.7087, 1.2978)	1.0020	(0.7583, 1.3068)
$\mathit{location}:{\sigma }_{\mathit{subj}\mathit{slope}}^2$	0.6393	(0.3389, 1.0178)	0.6449	(0.3106, 1.1147)	0.6902	(0.3711, 1.0580)
location : σint slope	−0.1205	(−0.3740, 0.0930)	−0.1171	(−0.4175, 0.1108)	−0.1434	(−0.4051, 0.0698)
$\mathit{location}:{\sigma }_{\mathit{wave}}^2$	0.4080	(0.3597, 0.5058)	0.4582	(0.3563, 0.4919)	0.3794	(0.3201, 0.4505)
$\mathit{scale}:{\sigma }_{\mathit{subj}\mathit{int}}^2$	—	—	—	—	0.2755	(0.1785, 0.3935)
$\mathit{scale}:{\sigma }_{\mathit{subj}\mathit{slope}}^2$	—	—	—	—	0.4298	(0.2518. 0.6570)
scale : σint slope	—	—	—	—	−0.0953	(−0.2263, 0.0135)
$\mathit{scale}:{\sigma }_{\mathit{wave}}^2$	—	—	—	—	0.2729	(0.2218, 0.3138)
elpdLOO	−57755.1 (182.8)		−57532.3 (184.1)		−53721.5 (204.7)