Height-diameter models define the general relationship between the tree height and diameter at each growth stage
of the forest stand. This paper presents generalized height-diameter models for mixed-species forest stands consisting
of Norway spruce (Picea abies Karst.), Silver fir (Abies alba L.), and European beech (Fagus sylvatica L.) from
Slovakia. The models were derived using two growth functions from the exponential family: the two-parameter Michailoff
and three-parameter Korf functions. Generalized height-diameter functions must normally be constrained
to pass through the mean stand diameter and height, and then the final growth model has only one or two parameters
to be estimated. These “free” parameters are then expressed over the quadratic mean diameter, height and stand age
and the final mathematical form of the model is obtained. The study material included 50 long-term experimental
plots located in the Western Carpathians. The plots were established 40–50 years ago and have been repeatedly
measured at 5 to 10-year intervals. The dataset includes 7,950 height measurements of spruce, 21,661 of fir and 5,794
of beech. As many as 9 regression models were derived for each species. Although the “goodness of fit” of all models
showed that they were generally well suited for the data, the best results were obtained for silver fir. The coefficient
of determination ranged from 0.946 to 0.948, RMSE (m) was in the interval 1.94–1.97 and the bias (m) was –0.031 to
0.063. Although slightly imprecise parameter estimation was established for spruce, the estimations of the regression
parameters obtained for beech were quite less precise. The coefficient of determination for beech was 0.854–0.860,
RMSE (m) 2.67–2.72, and the bias (m) ranged from –0.144 to –0.056. The majority of models using Korf’s formula
produced slightly better estimations than Michailoff’s, and it proved immaterial which estimated parameter was
fixed and which parameters were free.
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