Bootstrap Evaluation of a Young Douglas-Fir Height Growth Model for the Pacific Northwest

Abstract

Abstract We evaluated the stability of a complex regression model developed to predict the annual height growth of young Douglas-fir. This model is highly nonlinear and is fit in an iterative manner for annual growth coefficients from data with multiple periodic remeasurement intervals. The traditional methods for such a sensitivity analysis either involve laborious math or rely on prior knowledge of parameter behavior. To achieve our goals, we incorporate a bootstrap approach to obtain estimates of the distribution of predicted height growth for any set of input variables. This allows for a sensitivity analysis with knowledge of the probability of a given outcome. The bootstrap distributions should approximate the variation we might expect from running the model on numerous independent datasets. From the variation in the model parameters, we are able to produce ranges of height growth prediction error falling under a given probability of occurrence. By evaluating these ranges under several combinations of input variables that represent extreme situations, we are able to visualize the stability of the model under each situation. Each of the four components of the model can be investigated separately, which allows us to determine which components of the model might benefit from reformulation. In this case we find that the model is less stable in extremely high site index, especially under low vegetation competition. Other than the computing time involved with the bootstrap, most of the analysis is fairly quick and easy to perform.