Estimating a Nonlinear Mixed Volume-age Model with and without Taking into Account Serially-correlated Errors: Differences and Implications

In this study we estimated a lodgepole pine (Pinus contorta var. latifolia Engelm.) volume-age model with and without taking into account serially-correlated errors arisen from permanent sample plots. The estimations were based on the first-order (FO) and first-order conditional expectation (FOCE) methods of the nonlinear mixed model technique. Among the correlated error structures considered, the spatial power structure was found to be the most appropriate. Model predictions were obtained and evaluated on model fitting data, as well as on independent validation data collected from a different ecoregion. Results showed that the model estimated with the independent and identically distributed (iid) error structure performed much better than the model estimated with the correlated error structure. This is true on both model fitting and validation data sets, and for both FO and FOCE methods. It implies that, if the main purpose of a study is to develop models for predictions, there is no real benefit to consider more elaborate and complex error structures to account for the correlated errors. The iid error structure is a sound choice for dealing with correlated errors under the nonlinear mixed model framework.