Table 5: Maximum likelihood estimates (standard errors) of the parameters 𝛽 of the BMI model 𝑌 𝑖 𝑏 𝑖 , 𝑍 𝑖 , 𝛽 N P Q M ( 𝛽 0 + 𝛽 1 𝑏 𝑖 + 𝛽 2 1 { 𝑍 𝑖 = 0 } , 𝛽 3 , 𝛽 4 , 𝛽 5 ) .

Likelihood 𝑘 ̂ 𝛽 0 ̂ 𝛽 1 ̂ 𝛽 2 ̂ 𝛽 3 ̂ 𝛽 l o g ( 3 / 𝜋 ) ̂ 𝛽 4 ̂ 𝛽 5 ̂ 𝛽 l o g 5

Conditional10026.91 (0.14) 0 . 0 7 (0.02) 0 . 6 4 (0.27)4.270.88 (0.02)0.14 (0.03)0.37 1 . 0 0 (0.05)
(6.2)100026.92 (0.14) 0 . 0 7 (0.02) 0 . 6 4 (0.27)4.270.88 (0.02)0.14 (0.03)0.37 1 . 0 0 (0.05)
500026.92 (0.14) 0 . 0 7 (0.02) 0 . 6 4 (0.27)4.270.88 (0.02)0.14 (0.03)0.37 1 . 0 0 (0.05)
Conditional10026.93 (0.13) 0 . 0 7 (0.02) 0 . 6 3 (0.26)4.250.87 (0.02)0.14 (0.03)0.37 1 . 0 0 (0.05)
(6.3)100026.93 (0.13) 0 . 0 7 (0.02) 0 . 6 3 (0.26)4.250.87 (0.02)0.14 (0.03)0.37 1 . 0 0 (0.05)
500026.93 (0.13) 0 . 0 7 (0.02) 0 . 6 3 (0.26)4.250.87 (0.02)0.14 (0.03)0.37 1 . 0 0 (0.05)
Full26.94 (0.07) 0 . 0 7 (0.01) 0 . 6 0 (0.25)4.060.83 (0.01)0.13 (0.01)0.35 1 . 0 6 (0.03)
Weighted26.94 (0.15) 0 . 0 6 (0.03) 0 . 6 8 (0.33)4.300.88 (0.04)0.17 (0.05)0.41 0 . 8 9 (0.11)