Journal of Probability and Statistics / 2012 / Article / Tab 2

Research Article

Mixed-Effects Tobit Joint Models for Longitudinal Data with Skewness, Detection Limits, and Measurement Errors

Table 2

A summary of the estimated posterior mean (PM) of skewness and degree of freedom parameters, the corresponding standard deviation (SD), and lower limit ( 𝐿 𝐢 𝐼 ) and upper limit ( π‘ˆ 𝐢 𝐼 ) of 95% equal-tail credible interval (CI) based on the joint modeling (JM), the naive (NV), and the two-step (TS) methods.

MethodModel 𝛿 πœ– 𝛿 𝑒 𝛿 π‘Ž 1 𝛿 π‘Ž 2 𝛿 π‘Ž 3 𝛿 𝑏 1 𝛿 𝑏 2 𝛿 𝑏 3 𝜈 πœ– 𝜈 𝑒 𝜈 π‘Ž 𝜈 𝑏

JM SNPM 0 . 4 1 2 . 3 4 0 . 5 8 0 . 3 4 0 . 2 6 0 . 5 2 βˆ’ 1 . 8 1 2 . 5 8 β€” β€”β€”β€”
𝐿 C I 0 . 2 5 1 . 9 3 βˆ’ 0 . 6 2 βˆ’ 0 . 5 8 βˆ’ 1 6 . 1 βˆ’ 1 . 9 0 βˆ’ 1 0 . 1 βˆ’ 1 0 . 7 β€” β€”β€”β€”
π‘ˆ C I 0 . 5 4 2 . 7 3 1 . 4 1 1 . 0 9 1 7 . 0 2 . 3 1 7 . 1 2 1 1 . 0 β€” β€”β€”β€”
SD 0 . 0 7 0 . 2 0 0 . 6 0 0 . 4 7 8 . 5 7 1 . 1 8 5 . 3 0 6 . 9 3 β€” β€”β€”β€”
STPM 0 . 0 5 2 . 2 6 0 . 8 7 0 . 0 4 βˆ’ 0 . 5 6 0 . 3 2 βˆ’ 4 . 7 0 6 . 4 5 3 . 3 2 1 0 . 2 1 4 . 0 1 4 . 4
𝐿 C I βˆ’0.14 1 . 5 9 βˆ’ 0 . 3 5 βˆ’ 0 . 6 0 βˆ’ 1 6 . 5 βˆ’ 2 . 2 3 βˆ’ 1 0 . 1 βˆ’ 8 . 2 3 3 . 0 1 3 . 0 7 3 . 5 2 3 . 5 2
π‘ˆ C I 0 . 2 5 2 . 7 0 1 . 5 4 0 . 6 5 1 4 . 7 2 . 3 7 1 . 9 1 1 2 . 3 4 . 1 8 3 5 . 2 4 1 . 1 4 1 . 9
SD 0 . 1 1 0 . 3 3 0 . 5 0 0 . 3 2 8 . 4 1 1 . 3 1 2 . 9 3 4 . 8 8 0 . 3 2 8 . 9 8 1 0 . 3 1 0 . 3

NV SNPM β€” 2 . 2 4 β€” β€”β€” 0 . 8 0 0 . 1 5 5 . 5 3 β€” β€”β€” β€”
𝐿 C I β€” 1 . 9 5 β€” β€”β€” βˆ’ 1 . 0 5 βˆ’1.71 3 . 6 2 β€” β€”β€” β€”
π‘ˆ C I β€” 2 . 5 5 β€” β€”β€” 2 . 2 5 2 . 3 0 7 . 7 4 β€” β€”β€” β€”
SD β€” 0 . 1 5 β€” β€”β€” 0 . 9 2 1 . 0 0 1 . 0 6 β€” β€”β€”β€”
TS SNPM 0 . 1 6 2 . 4 4 0 . 8 9 0 . 2 8 3 . 0 6 0 . 0 4 βˆ’ 0 . 9 4 5 . 1 8 β€” β€”β€” β€”
𝐿 C I βˆ’ 0 . 3 9 2 . 0 7 βˆ’0.48 βˆ’ 0 . 5 8 βˆ’ 1 1 . 7 βˆ’ 2 . 2 0 βˆ’8.53 βˆ’ 1 2 . 4 β€” β€”β€” β€”
π‘ˆ C I 0 . 5 1 2 . 7 9 1 . 5 5 1 . 0 4 2 1 . 0 2 . 2 3 7 . 4 9 1 2 . 2 β€” β€”β€” β€”
SD 0 . 2 9 0 . 1 8 0 . 5 0 0 . 4 5 8 . 3 0 1 . 3 1 4 . 7 5 6 . 6 7 β€” β€”β€” β€”

We are committed to sharing findings related to COVID-19 as quickly and safely as possible. Any author submitting a COVID-19 paper should notify us at help@hindawi.com to ensure their research is fast-tracked and made available on a preprint server as soon as possible. We will be providing unlimited waivers of publication charges for accepted articles related to COVID-19. Sign up here as a reviewer to help fast-track new submissions.