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Table 4 Parameter estimates with their standard error in parenthesis of the models (3) to (8) for both datasets

From: Comparison of models for estimating bark thickness of Picea abies in southwest Germany: the role of tree, stand, and environmental factors

Dataset

Parameter

Eq. (3)

Eq. (4)

Eq. (5)

Eq. (6)

Eq. (7)

Eq. (8)

LME

LME

LME

LME

LME

NLME

1 (1970s)

β 0

6.2946 (0.2051)

3.2089 (0.1734)

−0.4314 (0.03)

 

5.0932 (0.2224)

−4.6534 (0.0251)

β 1

0.0371 (1.54E−04)

0.0105 (2.02E−04)

−7.87E−04 (1.98E−05)

0.0707 (6.21E−04)

0.052 (0.001)

0.9896 (0.0062)

β 2

 

0.0342 (1.55E−04)

0.6017 (0.0054)

−0.0447 (4.76E−04)

−5.00E−05 (3.35E−06)

7.1147 (0.047)

β 3

  

0.1566 (9.38E−04)

0.0889 (6.88E−04)

4.69E−08 (3.22E-09)

1.867 (0.0144)

β 4

   

−6.03E−04 (1.72E−05)

 

0.0119 (1.27E−04)

β 5

     

0.004 (1.99E−04)

β 6

     

0.313 (0.0102)

δ

0.5612

0.6193

−0.1385

0.5981

0.5616

−0.1679

CAR1

0.9189

0.9046

0.848

0.9101

0.9173

0.8538

σ

0.1048

0.0704

0.2144

0.075

0.1036

0.2681

2 (2014–2016)

β 0

5.2856 (0.4166)

−0.4969 (0.5058)

−0.7606 (0.1266)

 

7.3826 (0.5450)

−4.8984 (0.1814)

β 1

0.0345 (5.498E−04)

0.0140 (0.0011)

−6.380E−04 (1.002E−04)

0.0747 (0.0029)

0.0116 (0.0044)

1.3541 (0.0398)

β 2

 

0.0339 (5.452E−04)

0.6323 (2.668E−02)

−0.0595 (0.0019)

6.246E−05 (1.419E−05)

5.8692 (0.1561)

β 3

  

0.2028 (0.0052)

0.1015 (0.0028)

−4.035E−08 (1.354E−08)

2.2051 (0.0904)

β 4

   

−7.480E−04 (8.818E−05)

 

0.0125 (6.841E−04)

β 5

     

0.0056 (0.0015)

β 6

     

−0.0855 (0.1123)

δ

0.6855

0.7144

−0.2041

0.6222

0.6489

−0.2032

CAR1

0.8937

0.8909

0.799

0.8493

0.902

0.7973

σ

0.0552

0.0464

0.4019

0.0626

0.0701

0.4074

  1. LME linear mixed-effects model, NLME nonlinear mixed-effects model, δ variance parameter, CAR1 first-order continuous autoregressive term, σ residual standard error