Biased predictions for tree height increment models developed from smoothed ‘data’

Only two basic methods exist for obtaining tree height (H) increment data: felled tree measurements and remeasured height or height increment on standing forest trees. Because the former method is expensive (but reliable), and the latter has a large measurement error relative to the actual height increment, it is difficult to obtain good height increment data. The contradictory occurrence of high coefficients of determination for height increment models that are not based on felled-tree samples can only be explained by so-called height increment ‘data’ that is actually predicted from some heuristic function, usually of diameter. Such smoothed ‘data’ are not observable, not measurable, and have much variation removed. Use of smoothed data reduces the apparent problem of height increment modeling to a simplistic problem of using one function to estimate the smoothed predictions from another function. We illustrate this phenomenon with a controlled experiment. Using more than 7500 Norway spruce trees from the Austrian National Forest Inventory with remeasured heights (5 year interval), we built height increment models: (1) based on the difference in observed heights; (2) based on the difference in predicted heights using a heuristic function of diameter. Using the same model and input variables, the coefficient of determination was 3 times higher (0.44 vs. 0.14) using the smoothed increment ‘data’ than with the observed increment data. Furthermore the increment predictions based on the data sets with smoothed increment ‘data’ exhibited a significant overestimation. This demonstrates three things. First, that fit statistics measuring deviations about smoothed height increment data are misleading and strongly biased upward. Second, that the resulting models produce biased predictions that overestimate increment, especially for trees in an intermediate to suppressed social position in the stand. Third, that measurement errors in remeasured heights on standing trees are so large that the underlying height increment signal is nearly hidden (R2 = 0.14).