Plot size related measurement error bias in tree growth models

Abstract

Local tree density around a tree affects tree growth because neighboring trees compete for the same resources. In forestry trees are often sampled by measuring all the trees in sample plots. The total number of the trees in a sample plot or in a larger plot that also encompasses a border zone is often used as the density measurement for all trees in the plot. When the plot density is used as the measurement of local density around a sample tree, the measurement error is correlated both with the measured value and with the true value. Thus none of the standard measurement error assumptions hold. The bias in the estimated density effect is related to the plot size. Assuming random tree locations and a simple linear model including both overall stand density and local density as predictor variables, the bias is analyzed analytically using weighted distributions. The plot size producing the highest coefficient of determination is rather close to the size of the influence zone, but much larger plot sizes are needed for unbiased estimation. It is safe to measure density from a larger plot than that used for sample tree selection. The analysis may give insight for other cases in multilevel modeling where group variables are used to explain individual responses.