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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