Modeling Microibril Angle with Mixed Models for Dahurian Larch

In this study,the sample data was based on 2 790 samples of 9 trees from dahurian larch （Larix gmelinii） plantations located in Qitaihe Forest Bureau in Heilongjiang Province.The modified Logistic model y = b₁ /[1 + exp（b₂ x）]+ b₃ was selected to modeling microfibril angle from six models based on nonlinear regression.Then,the logistic model was fitted using nonlinear mixed-effect modeling approach based on NLME of S-PLUS software.Evaluation statistics,such as AIC,BIC, Log Likelihood and Likelihood ratio test were used for model comparisons.The results showed that the Logistic model with parameters b₁,b₂,b₃ as mixed effects showed the best performance.Correlation structures included compound-symmetry structure （CS）,first-order autoregressive correlation structure AR（1）,moving average correlation structure MA（1） and autoregressive-moving average correlation structure[ARMA（1,1）]were incorprated into the best microfibril angle mixed model.[ARMA（1,1）]significantly improved the precision of mixed model.Validation confirmed that the mixed model with calibration of random parameters could provide more accurate and precise prediction.Therefore,the application of mixed model not only showed the mean trends of microfibril angle,but also showed the individual difference based on variance-covariance structure and correlation structure.