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Scientia Silvae Sinicae ›› 2015, Vol. 51 ›› Issue (3): 25-33.doi: 10.11707/j.1001-7488.20150304

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Based on Mixed-Effects Model and Empirical Best Linear Unbiased Predictor to Predict Growth Profile of Dominant Height

Zu Xiaofeng1,2, Ni Chengcai2, Gorden Nigh3, Qin Xianlin1   

  1. 1. Institute of Forest Resources Information Techniques, CAF Beijing 100091;
    2. College of Forestry, Beihua University Jilin 132013;
    3. British Columbia Ministry of Forests, Lands and Natural Resources Operations, Forest Analysis and Inventory Branch, P. O. BOX9512, Stn. Prov. Govt. Victoria, B. C. V8W 9C2, Canada
  • Received:2014-05-20 Revised:2014-09-19 Online:2015-03-25 Published:2015-04-10

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Abstract:

【Objective】 This study analyzed prediction accuracy of empirical best linear unbiased predictor(EBLUP), and effects of previous observations, age interval of observations and prediction span on prediction accuracy, based upon height data from 79 dominant trees of ponderosa pine in British Columbia, Canada. 【Method】We randomly selected 49 trees for fitting mixed-effects models and 30 trees for validating EBLUP. The base models were Richards, Logistic, and Korf. Fit statistics, AIC, BIC and Loglik, were used as evaluation criteria, and mean squared prediction error (MSPE) for analyzing effects of previous observations, age interval of observations and prediction span on prediction accuracy. We used the nlme function in R for model fitting, and the IML procedure in SAS for analyzing EBLUP prediction. To isolate the effect of one factor, we kept two other factors fixed.【Result】Fitting results showed the Logistic model had the best criteria among the three models of under investigation, indicating that it was the best-fitted model and was chosen for EBLUP prediction analysis. In the analysis of EBLUP prediction, we first introduced how to use EBLUP to predict random effects associated with a stand through a detailed example. Data from six trees, which deviated significantly from population-mean growth process, were used to present relationships among individual growth, population-mean growth, and adjusted values given by EBLUP. The results indicated that EBLUP prediction could fully follow individual growth process, given that there were multiple previous observations with long-enough age intervals. EBLUP analysis results also presented the number of previous observations, age interval of observations and prediction span significantly affected prediction accuracy. MSPE decreased as the number of previous observations increased, particularly when observations separated long enough in age so that they could give more efficient growth information. With respect to prediction span, prediction accuracy decreased as prediction span extended further away from the ages at which observations were obtained. 【Conclusion】 We concluded that EBLUP could be taken as the second stage of a two-stage fitting process. The first stage was used to estimate fixed model parameters, whereas the second stage to predict random effects associated with a stand on the basis of parameter estimators obtained in the first stage, and then to predict the height growth process of the stand.

Key words: mixed-effects model, EBLUP, dominant height growth model, ponderosa pine

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