Application Of Mixed Effects Models In Forest Growth Models

Mixed model technique includes linear mixed effect model and nonlinear mixed effect model. Recently the technique has been extensively applied in medicine, agriculture, economics, forestry and other fields. There are some differences in area or plot aspect, because forest is affected by geographical or physical circumstance, site condition, climate change, tree species characteristic and stand itself. The differences between plots each other or areas are not taken into account in the model we established for simulating forest growths and yields. Remeasured data are often used in the forest growth and yield model for forest research. The method of analyzing the data has been improved greatly, especially for the mixed model. It is more feasible and more credible comparing with ordinary multiple-variable method. But in some literatures, the mixed effect model is mainly used to analyze single variable of remeasured data, and the correlation between data is only existed in the same remeasured variable.Based on understanding theory of the mixed effect model, the model was extablished and improved with fir plantation distributed in jiangxi province for studying its application in remeasured data. Results showed that we not only effectively and embedded digged information included in data and figured out the estimators of fixed effect and random effect, but also obtained the correlation coefficients between response variables themselves or between remeasured response variables and subtly analyzed correlation between data. Additionally, the best model could be gained through developing some different mixed effect models and comparing the goodness of fit and variance-covariance values. The application of mixed effects models in forest growth model was summarized in the thesis firstly, then the mixed models of dominant height stand basal area, stand volume and individual tree diameter increment of fir plantation in jiangxi province were develped taking into account area effect, plot effect and both effect. The main research content, conclusion and innovation of the dissertation were listed as follows:(1) Dominant height:Taking into account plot effect, area effect and both effects, the mixed effect model of the dominant height was established with four often used model forms including Richards and Schumacher, meanwhile error effects including heteroscedasticity and variance covariance matrix of auto-correlation structure were also considerd. Results showed that the mixed model technique for considering the plot effect, area effect or both effect was better than conventional ordinary least square method. The Richards model modified by Fang (2001) was the best when taking into account plot effect of parameterβ1 andβ2. But for area effect, the modified model was the best when parameterβ1 was mixed parameter. Taking into account error effect, the exponent function was fitted best to describe heteroscedasticity and variance covariance matrix of auto-correlation structure with AR(1). Taking into account both plot and area effects, the simulant precise was superior to single effect, also the difference was very significant. When taking into account error effect, the exponent function was fitted best to describe heteroscedasticity and variance covariance matrix of auto-correlation structure with AR(1). In the end, the result was validated with separate data.(2) Stand basal area:The often used models including Richards and Schumacher were used to simulate the stand basal area. Result showed that the accuracy of schumacher equation was the best which independent variables including the number of tree per hectare, age and dominant height. Based on the model, mixed effect model of stand basal area was constructed. The physiognomy character which is qualitative factor could be introduced to the model for improving accuracy. Firstly each parameter was random parameter respectively in establishing mixed model, and then all parameters were considered to be random parameters. Result showed the goodness of fit of model was the best when taking into account the area effect of the parameter of b3 and b5. The goodness of fit of model was the best when taking into account the area effect of parameter b2 and b3. And it was the best with area effect of parameter b3 and plot effect of parameter b3 and b5 simultaneously. The goodness of fit of power function was the best when taking into account heteroscedasticity and the goodness of fit of AR(1) was the best when taking into account variance covariance matrix of auto-correlation structure. The covariance analysis showed that it was better for considering both heteroscedasticity and auto-correlation than single. Also the difference was significant. In the end, the mixed models of three effects were compared with the ordinary least square for validation with independent plot.(3) Stand volume:Stand volume was simulated with two methods. One was simulant of only mixed effect model, the other was simulant of simultaneous function system including the dominant height, stand basal area and stand volume based on mixed model. Results showed the dominant height was the fundamental component in the simultaneous system, which accuracy was critically important in the simultaneous system. The prediction error for dominant height and basal area are the main sources of error in stand volume predictions. In simulant system, taking into account the correlation of three components and random effects of parameters in dominant height and basal area models, then random effect error of stand volume could be ignored. In the end, dominant height, stand basal area and stand volume were predicted.(4) Individual tree diameter increment:The individual tree diameter increment was studied based on linear mixed effect model. Individual tree size, site quality, stand description factor and competition index were considered in the model. Two methods were used. One was plot effect, area effect and both effect of intercept, the other was plot effect, area effect and both effect of random parameters. The heteroscedasticity and variance covariance matrix of autocorrelation structure were all considerd in the two methods. Results showed that:①The simulant goodness of fit of intercept or random parameter based on mixed effect model was better than conventional least square method.②The exponent function was the best form to describe heteroscedasticity and the ARMA(1,1) matrix was the best for describing variance covariance matrix of autocorrelation structure when considering the plot or area effect of intercept. And the power function was the best for describing heteroscedasticity when taking into account plot and area's effect of intercept simultaneousely.③The goodness of fit of all parameters being random was the best considering the plot effect or area effect when analyzing random effect of parameters. The goodness of fit was the best when int and zba were area's random effect parameters and all parameters were plot random effect parameter considering area and plot effect at the same time. Finally, the mixed model of individual tree diameter growth was validated for two methods, respectively.