Estimating a system of nonlinear simultaneous individual tree models for white spruce in boreal mixed-species stands

A system of three interdependent, tree-level nonlinear equations was fitted. The system was used in an individual tree simulator to predict total tree height, periodic tree diameter increment, and height increment for white spruce (Picea glauca (Moench) Voss) grown in boreal mixed-species stands in Alberta. Because the variables appeared on the left-hand side of the equations also appeared on the right-hand side of the equations in the system, the system was estimated using nonlinear simultaneous techniques. Testing of cross-equation correlations using the Breusch and Pagan statistic indicated that the error terms of the related equations in the system are significantly correlated, suggesting that the parameter estimates obtained from simultaneous techniques are consistent and asymptotically more efficient than those obtained from ordinary least squares procedures applied to individual equations of the system.