Abstract: [Objective] Based on allometric model, individual tree volume model was developed for Larix gmelinii and Pinus sylvestris var. mongolica in Daxing'anling. Error structure and variance function were studied.[Method] Ballantyne(2013)provides the method how to test the error structure by likelihood analysis. For comparison, nonlinear model was fitted using GNLS in S-PLUS. Variance functions (fixed variance, exponential function, power function and constant plus power function) were incorporated into general nonlinear model to reduce heteroscedasticity. Coefficient determination (R²), root mean square error (RMSE), mean absolute bias (Bias), and mean relative error (MRE), were employed to evaluate the precision of different individual volume models.[Result] 1) Through likelihood analysis, error structure of individual tree volume model is multiplicative, therefore, linear regression on the log-transformed data is suitable for individual tree volume model. 2) In order to describe the variance phenomenon in the process of individual tree volume model, variance functions (fixed variance, exponential function, power function and constant plus power function) were incorporated into volume model,and all variance functions could reduce heteroscedasticity, power function and constant plus power function are best for Larix gmelinii and Pinus sylvestris var. mongolica respectively. 3) Model fitting and validation indicated that the result were pretty similar for both error structures of this two species, however, volume model with additive error structure is slightly better than multiplicative error structure.[Conclusion] Error structures of individual tree volume model are multiplicative for this two species. However, through the comparison of model fitting and validation, nonlinear regression is better than linear regression on the log-transformed data. This study did not give an absolute and consistent conclusion from comparison. If model prediction is the first, error structure should be selected based on prediction precision. In summary, additive error structure was favored for individual tree volume model of Larix gmelinii and Pinus sylvestris var. mongolica.

Key words: Larix gmelinii, Pinus sylvestris var, mongolica, individual tree volume, error structure, variance function