Procedures for estimating the functional forms and their coefficients are readily 

 available in many texts on multiple linear or nonlinear regression for models with 

 continuous dependent variables such as height and diameter increment, and for crown 

 and bark dimensions . 



The mortality models require rather different statistical techniques. One possibl 

 mortality model and an estimation procedure developed especially for that model have 

 been described by Hamilton (in preparation). Examples of how these models might be 

 formulated are illustrated in a later section where the implementation of this prognosi 

 procedure is described for lodgepole pine. 



Self-Calibration of Diameter Growth Functions 



The self-calibration feature is intended to scale the diameter growth functions 

 that are contained in the program so that the predictions match the actual growth rates 

 measured on the trees in the stand to be modeled. First, the stand stocking that 

 existed at the start of the period during which growth was recorded is estimated. To 

 do this, the average basal area growth percentage is calculated for the growth -sample 

 trees of each species. Then, the current sum of diameters -squared is reduced by 

 subtracting the product of present basal area times the mean ratio of past basal area 

 increment to basal area derived from the growth -sample trees. The sum of diameters 

 is similarly reduced using the square root of the ratio. Then, the stocking at the 

 start of the period is computed from the number of trees, and the reduced sums of 

 diameters and of their squares. Trees removed or dying during the calibration period 

 are included in the prior stocking with no growth adjustment. All other stand 

 parameters are assumed to have remained constant. 



Deviations between predicted and recorded growth rates (scaled in units of the 

 logarithm of change in the square of diameter) are then sorted and the median deviation 

 calculated. The value of the median is subtracted from the constant term of the loga- 

 rithmic growth function to calibrate it. Thus, the effect is to multiply each 

 prediction by a correction factor. 



The median was selected as the location parameter for the adjustment rather than 

 the mean because it is less likely to be influenced by occasional outliers due to 

 measurement errors or abnormalities of growth (Barrodale 1968; Forsythe 1972). 



10 



