Hybrid estimation based on mixed-effects models in forest inventories

In forest inventories, there are many variables of interest that are difficult to measure. Practitioners have to rely on auxiliary variables and models to obtain predictions of these variables. In such contexts, design-based or model-dependent inferences are often ineffective and hybrid estimators are required. Because most models now contain mixed effects, we investigated how the random effects and residual errors affected the inferences in a context of hybrid estimation. We first developed hybrid estimators for the different mixed models. We then tested these estimators through a simulation study. Finally, the estimators were applied to a real-world case study: stone pine (Pinus pinea L.) cone production in central Spain. It turned out that the contributions of the random effects and the residual errors to the variance were constant regardless of the sample size. In our case study, these contributions were rather small when compared with those of the sampling and parameter estimates. The greatest impact came from the underestimation of the variance of the parameter estimates when random effects were not taken into account in the model. As the variance estimators make it possible to distinguish different variance components, they can be useful for identifying the greatest sources of uncertainty.