Choosing simplified mixed models for simulations when data have a complex hierarchical organization.: An example with some basic properties in Sessile oak wood (Quercus petraea Liebl.)

This paper focuses on the modeling of the variability of some properties in Sessile oak wood (five swelling coefficients and wood density). They are modeled with linear mixed models. The data have a seven-levels hierarchical organization. The variability at each level is modeled with a variance matrix. Unfortunately, a model with all variances has too many parameters to be usable, so preferably only one variance other than the residual is kept. A graphical procedure based on the comparison of residual variance in the different candidate models is used to detect this main level. Result shows that the main level of variability is the "tree" level or the "height within tree" level for five properties. We cannot conclude for the last property. For other properties, the residual variance in the model with a "tree effect" is reduced to 40% of the residual variance of the model without structuring of variability. If the applications of models deal with the variability of properties, this "tree level" cannot be neglected.