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
𝐶
𝐼
) and upper limit (
𝑈
𝐶
𝐼
) of 95% equal-tail credible interval (CI) based on the joint modeling (JM), the naive (NV), and the two-step (TS) methods.
Method Model
𝛿
𝜖
𝛿
𝑒
𝛿
𝑎
1
𝛿
𝑎
2
𝛿
𝑎
3
𝛿
𝑏
1
𝛿
𝑏
2
𝛿
𝑏
3
𝜈
𝜖
𝜈
𝑒
𝜈
𝑎
𝜈
𝑏
JM SN PM
0
.
4
1
2
.
3
4
0
.
5
8
0
.
3
4
0
.
2
6
0
.
5
2
−
1
.
8
1
2
.
5
8
— — — —
𝐿
C
I
0
.
2
5
1
.
9
3
−
0
.
6
2
−
0
.
5
8
−
1
6
.
1
−
1
.
9
0
−
1
0
.
1
−
1
0
.
7
— — — —
𝑈
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
— — — — 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
— — — — ST PM
0
.
0
5
2
.
2
6
0
.
8
7
0
.
0
4
−
0
.
5
6
0
.
3
2
−
4
.
7
0
6
.
4
5
3
.
3
2
1
0
.
2
1
4
.
0
1
4
.
4
𝐿
C
I
−0.14
1
.
5
9
−
0
.
3
5
−
0
.
6
0
−
1
6
.
5
−
2
.
2
3
−
1
0
.
1
−
8
.
2
3
3
.
0
1
3
.
0
7
3
.
5
2
3
.
5
2
𝑈
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 SN PM —
2
.
2
4
— — —
0
.
8
0
0
.
1
5
5
.
5
3
— — — —
𝐿
C
I
—
1
.
9
5
— — —
−
1
.
0
5
−1.71
3
.
6
2
— — — —
𝑈
C
I
—
2
.
5
5
— — —
2
.
2
5
2
.
3
0
7
.
7
4
— — — — SD —
0
.
1
5
— — —
0
.
9
2
1
.
0
0
1
.
0
6
— — — — TS SN PM
0
.
1
6
2
.
4
4
0
.
8
9
0
.
2
8
3
.
0
6
0
.
0
4
−
0
.
9
4
5
.
1
8
— — — —
𝐿
C
I
−
0
.
3
9
2
.
0
7
−0.48
−
0
.
5
8
−
1
1
.
7
−
2
.
2
0
−8.53
−
1
2
.
4
— — — —
𝑈
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
— — — — 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
— — — —
