If K = IniY) - Jn(Y) were added to this model as an approximate correction for log-bias in 

 the nonnormal case, then the effect would be: 



in(Y) = K + iii(Y) + i>i (xi - xi) + C>f 2 - xo) + • • • + jb (x - x ) 



= ln(Y) - JnCY) + in(Y) + i^i (xi - x 1 ) + ••• + b^ix^ - x^) 



= ln[Y) + i?! (xi - xi) + boixo - xo) + + b (x - x ) . 



n n n 



In other words, the correction would force the model through the log of mean Y instead of the 

 mean of log Y. Therefore, Y will pass through Y when xj = x^, X2 = X2, ^ which 



appears to be the adjustment desired. Whether this is a true "mean-unbiased" estimator is 

 impossible to prove without first knowing the true distribution of IniY) . 



The correction for log bias is applied by adding it to the intercept term of the log of 

 basal area growth model. The log bias correction factors for the three equations developed 

 in this study are found in table 11. For comparative purposes, the appropriate correction 

 for normally distributed residuals (that is, ij-MSE) is also found in table 26. Notice that 

 if normality had been assumed, the correction would have been considerably larger than the one 

 not assuming normality. 



Table 26 . --Proposed correction factor and log-normal correction factor for log bias of the 



three log of basal area growth equations 



Equation Proposed factor Lognormal factor 

 type [in (mean Y) ] - [mean iri(Y)] ^-MSE 



Blackjack pine with 



even-aged data 0.300534069 0.48453144 

 Blackjack pine without 



even-aged data .324720185 .56464436 



Yellow pine .873936593 2.76746302 



66 



