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Official Journal of the Japan Wood Research Society

Table 4 Comparison of AIC values in the linear and nonlinear mixed-models for radial variations in relation to cambial age

From: Radial variations of broad-sense heritability in wood properties and classification of load–deflection curves in static bending for six half-sib families of Chamaecyparis obtusa

Model formula

 

Random effect

AIC for each wood property trait

β0

β1

β2

b0j

b1j

b2j

TL

MFA

BD

AD

MOE

MOR

W

CS

 Ia:\(y_{ij} = \beta_{1} + e_{ij}\)

 

    

361

1105

− 1589

− 458

588

1178

812

843

 Ib:\(y_{ij} = \beta_{0} x_{ij} + \beta_{1} + e_{ij}\)

    

67

1044

− 1925

− 528

538

1172

813

840

 Ic:\(y_{ij} = \beta_{0} x_{ij} + \beta_{1} + b_{1j} + e_{ij}\)

  

 

105

1081

− 1977

− 539

505

1144

802

758

 Id:\(y_{ij} = \left( {\beta_{0} + b_{0j} } \right)x_{ij} + \beta_{1} + e_{ij}\)

 

  

367

1026

− 1954

− 582

508

1148

815

795

 Ie:\(y_{ij} = \left( {\beta_{0} + b_{0j} } \right)x_{ij} + \beta_{1} + b_{1j} + e_{ij}\)

 

 

104

1019

− 1975

− 584

503

1149

806

765

 IIa:\(y_{ij} = \frac{{\beta_{0} x_{ij} }}{{\beta_{1} + x_{ij} }} + \beta_{2} + e_{ij}\)

   

− 55

1004

− 2097

− 534

523

1168

 IIb:\(y_{ij} = \frac{{\beta_{0} x_{ij} }}{{\beta_{1} + x_{ij} }} + \beta_{2} + b_{2j} + e_{ij}\)

  

− 74

888

− 2282

− 617

425

 IIc:\(y_{ij} = \frac{{\beta_{0} x_{ij} }}{{(\beta_{1} + b_{1j} ) + x_{ij} }} + \beta_{2} + e_{ij}\)

 

 

− 85

999

− 2255

520

 IId:\(y_{ij} = \frac{{\left( {\beta_{0} + b_{0k} } \right) x_{ij} }}{{\beta_{1} + x_{ij} }} + \beta_{2} + e_{ij}\)

  

− 71

− 2274

− 429

423

  1. - developed model did not converge
  2. Random-effects term b0j in both models corresponded to slope parameters in the regression line or curve. Random-effects terms b1j in Model II and b2j in Model II corresponded to intercept parameters in the regression line or curve
  3. TL tracheid length, MFA microfibril angle, BD basic density, AD air-dry density, MOE modulus of elasticity, MOR modulus of rupture, W bending work, CS compressive strength
  4. The bold style values indicate the smallest AIC values among the developed models for each of the examined wood properties