Table 11 Parameter estimation (standard errors in parentheses) for nonlinear RBAI models using BAL index where competition effect is discriminated as described in Eq. 3

b ₃₀

0.0265 (0.0033)

0.0482 (0.0032)

0.0345 (0.0064)

0.0277 (0.0108)

b ₃₁

−0.2801 (0.1475)

1.8498 (0.4372)

−1.2474 (1.1588)

−0.1874 (0.1004)

b ₃₂

0.0663 (0.0237)

n.s.

0.2176 (0.1598)

0.0281 (0.0104)

b ₃₃

−11.1794 (5.2466)

−5.0813 (0.6626)

−7.4898 (2.0537)

−23.3101 (6.7866)

b ₃₄

1.0504 (0.1562)

1^e

1^e

1^e

b ₃₇

0.3326 (0.0983)

0.1321 (0.0598)

n.s.

n.s.

b ₃₈

1^e

1^e

n.s.

n.s.

b ₃₉

0.0457 (0.0192)

0.0798 (0.0166)

0.0708 (0.0133)

0.0214 (0.0118)

b ₄₀

1.0826 (0.1293)

1^e

1^e

1^e

Random effects

σ _jk ^a

0.0079

0.0147

0.0196

0.0158

σ _k ^b

0.0081

x

x

x

σ ^2c

2.2881

1.2738

0.6273

2.3353

δ ^d

−1.0795

−0.8811

−0.8486

−1.0156