And 2 , respectively. The AIC and BIC of the single impact model (model 1,two,3, and 4) have been lower than these of the interactive effects model (model 15), which indicated that a substantial proportion with the tree height variations was improved explained by the crossed random effects of the stand density and web site index than the random effects of your stand density alone or maybe a single website index alone.Forests 2021, 12,9 ofTable 7. AIC (Akaike information and facts criterion) score and BIC (Bayesian Information Criterion) score of 36 models derived in the base model. Model 1 2 three four 5 6 7 eight 9 10 11 12 13 14 15 16 17 18 AIC 1798.34 1796.58 1793.00 1804.01 1783.41 1785.13 1785.41 1787.12 1783.41 1785.37 1787.41 1789.37 1787.23 1790.22 1771.64 1773.64 1773.64 1775.64 BIC 1823.72 1817.73 1814.15 1829.34 1804.56 1814.74 1810.80 1820.97 1804.57 1810.76 1817.03 1823.22 1808.39 1811.37 1797.02 1803.25 1803.25 1809.48 Model 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 AIC 1787.53 1792.20 1773.64 1777.64 1789.41 1779.64 1789.22 1794.21 1773.64 1775.64 1777.64 1779.64 1789.53 1796.19 1775.64 1779.64 1779.64 1783.64 BIC 1817.14 1817.58 1803.25 1815.71 1823.26 1821.94 1814.61 1823.82 1803.25 1809.48 1815.71 1821.94 1823.37 1830.03 1809.48 1821.94 1821.94 1834.3.three. The Interactive NLME Height-Diameter Model Model 15 (Table 7) with the random construction variables [M S, M S] that had the best performance (AIC = 1771.64, BIC = 1797.02) was selected as a final model. Model 15 together with the random effects had been the interaction effects of M and S and was defined because the interactive NLME height-diameter model within this post. The expression on the very best interactive NLEM height-diameter model for additional analysis is shown in Equation (11). ( MS) 2 u ( H (ij)k = 1.3 exp 1 u1MS) D 2(ij) (ij)k (ij) (ij)k u(ij) N (0,), (ij) N (0, R(ij)) i = 1, . . . , M1 , j = 1, . . . , M2 , k = 1, . . . , n(ij)(11)exactly where M1 (in this study, M1 = 6) would be the total classes of stand density, M2 (in this study, M2 = five) would be the total classes of internet site index, nij could be the number of observation points contained in the ith stand density class as well as the jth internet site index class. (ij) could be the sample plot with the ith stand density class plus the jth web site index class. The (ij)k could be the error term in the kth tree in sample plot (ij), which we assumed as R(ij) = 2 I (two (two 0) could be the variance in the residual). H will be the tree height measurement value. 3.4. Parameter Estimates All the parameter estimates of your basic model and interactive NLME model have been significant (p 0.05). The parameter estimates of your basic model obtained by an ordinary nonlinear least square (ONLS) function are as Equation (12), which we termed as the NLS model. -6.9169 ^ H = 1.3 exp 3.1194 (12) D ^ exactly where D will be the measured worth of DBH, H would be the estimated total tree height using the NLS model, N (0, 1.952I).Forests 2021, 12,10 ofThe interactive NLEM height-diameter model with all the estimated parameters obtained using the TP003 Description linearization approximation-sequential quadratic ML351 Epigenetic Reader Domain algorithm implemented in the “nonlinear nixed-effects” module on the Forstat computer software in the 2.2 version is provided by:( MS) ^ H(ij)k = 1.3 exp3.1138 u1(ij) -6.8180 u2(ij)D(ij)k( MS) (ij)k (13)with uij = u1ij u2ij0, =0.0053 -0.-0.0981 1., ij N (0, 1.6996I),exactly where (ij) is the sample plot using the ith stand density class plus the jth website index class, and k is the kth observation on the (ij) sample plot. D(ij)k would be the measured value in the DBH of ^ tree k on (ij) sample plot, whilst H(ij)k.