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Table 2 Parameter estimates and fit statistics (standard error (SE), Akaike’s Information Criterion (AIC), logarithm likelihood (log-likelihood)) of models (2) and (3) using generalized least-squares, and model (7) using a nonlinear mixed-effects model approach for Masson pine data from the subtropical China (β 0β 5, k 1, k 2, and L are the model coefficients; σ 2 is the scaling factor of the error dispersion; and u 3 and u 5 represent the random-effect coefficients)

From: Integrating regional climate change into allometric equations for estimating tree aboveground biomass of Masson pine in China

Parameters

Model (2)

Model (3)

Model (7)

Estimates

SE

Estimates

SE

Estimates

SE

β 0

−2.9435

0.2809

−2.7271

1.3385

−1.4544

2.2098

k 1

0.2876

0.0680

−0.0285

0.1079

−0.0175

0.1237

k 2

0.3821

0.0632

0.0077

0.1069

0.0767

0.0819

L

−0.0031

0.0292

0.0240

0.0272

−0.0285

0.0471

β 1

2.5037

0.0760

2.4715

0.0683

2.3697

0.0296

β 2

  

−0.9078

0.4667

−0.7053

0.5677

β 3

  

1.1108

0.4566

0.7337

0.4842

β 4

  

−1.1991

0.3104

−0.3961

0.3679

β 5

  

1.0760

0.4030

0.4973

0.5346

Variance components

σ 2

0.5792

 

0.4380

 

0.0450

 

var(u 3)

    

0.0001

 

var(u 5)

    

0.00003

 

cov(u 3, u 5)

    

0.00001

 

Autocorrelation structure

ρ

    

0.1412

 

Weight (power of D)

γ

    

2.1463

 

AIC

1241.4790

 

1214.1370

 

889.7032

 

Log-likelihood

−614.7396

 

−597.0685

 

−429.8516