Research Note No. 31	
March 14, 1990
		
Sources of bias in diameter growth predictions		
by
			Lee C. Wensel and Timothy A. Robards


	Differences in the growth predictions made using the growth models 
from increment core data (Wensel, Meerschaert, and Biging, 1987) compared to 
those from the difference of two measurements 5 years apart (Wensel and 
Robards, 1989) were significant enough to suggest that there could be bias 
introduced in either the measurements or the analysis.  To investigate this 
possibility, the process used for these estimates was examined in 
considerable detail and comparisons were made to assess the source of the 
differences observed.

	This assessment was carried out in three stages.  First, the validity 
of the increment data was examined.  Second, a "period" effect was estimated 
to see how comparable the growth rates were on the same trees over the two 
periods used.  Third, an overall bias is estimated.

Stage 1, validity of data and previous analyses.
	There were 82 trees available that had both remeasurements and 
increments available for the same period.  Largely these were site index trees 
that had been bored to determine tree age;  the 5-year increment was also 
determined, however.  The discrepancy in the measurements led to a reanalysis 
of the algorithm used to backdate the initial DBH measurements.  Here it was 
discovered that the increment core data used in the 1987 estimates failed to 
account for the growth in the bark.  Since the bark factor estimated for the 
entire data set is about 0.89, this introduces a bias of about 12% ( i.e., 
((1/0.89) - 1 )100%).  Thus the DBH growth estimates in the 1987 paper 
should be increased by 12%.
Stage 2, period effects.
	A period effect can be estimated for trees where remeasurement data 
are available for the two periods in question.  For the data used in the 1987 
estimates, over two thousand trees had measurements in the two periods in 
question:  5 to 10 years prior to the initial coop measurement in 1979 and 5 
to 6 years after that date.  These are referred to as period 0 and period 1.  
Table 1 summarizes the average DBH growth for the two periods.


	Table 1.  Average 5-year diameter growth for periods 0 and 1

		Ave. DBH growth	
		Species			period 0	period 1	difference	trees	
                			(inches)	(inches)	(%)		(no.)
		ponderosa pine		0.69		0.76		10		602	
		sugar pine		1.04		1.18		13		193		
		Jeffery pine		0.78		0.87		11		18		
		incense cedar		0.93		1.09		17		454		
		Douglas-fir		0.93		1.09		17		255		
		white fir		0.96		1.10		14		504		
		red fir			0.95		0.96		1		11								
		all species		0.83		0.94		4		2037


	The differences varied some between species but species showed more 
growth in period 1 than in period 0.  Thus the 1989 estimates include a period 
effect of about 14%.

Stage 3, overall bias.
	Finally, all of the increment data were matched with the remeasurement 
data for period 1.  Simply examining the average DBH growth across all 6 of the 
major species provides the result summarized in Table 2.
 
	Table 2.  Summary of sources of bias in growth predictions
			average DBH growth (inches)				
a.	remeasurement for period 1 		0.96	
b.	increment for period 0			0.68			
c.	period 0 adjusted for bark growth	0.76			
d.	adjustment for period effect (14%)	0.87	
e.	difference				0.09

This leaves an overall estimate of the differences between the two estimation 
models, 1987 corrected for both a bark and period effect and 1989, of 0.09 
inches or 9%.  Breaking the period adjustment out by species did not change 
the overall result.

Discussion
	This simple analysis reduced the unexplained difference in the average 
DBH growth from 0.28 to 0.09 inches, a reduction of about two thirds.  Other 
possible sources of the differences may be hypothesized.  However, these 
results appear to suggest that either the 1987 estimates adjusted for bark 
growth and period effect or the 1987 models can be used to give similar 
estimates.  
	However, this does not touch the real problem in estimating tree 
growth with CACTOS.  All of the estimation and validation work has centered 
on growth estimates for 5-year intervals while planners are regularly using 
CACTOS to project for much longer periods.  Trials with cofile.410 with growth 
estimates from Wensel and Robards (1989) can easily produce basa area 
stocking levels of 600 to 800 square feet (or more!) within the projection 
period.  Certainly the growth rates that do not appear to be retarded by the 
higher stocking levels.  This is an appropriate topic to consider when 
analyzing the 1990 remeasurement data.


Literature Cited

WENSEL, LEE C., WALTER J. MEERSCHAERT, AND GREG S. BIGING.
1987. 	Tree height and diameter growth models for northern California 
        conifers.  Hilgardia 55(8):1-20


WENSEL, LEE C., and TIMOTHY A. ROBARDS. 
1989. 	Revised parameter estimates for CACTOS growth models.  Research Note 
        No. 23, Nor. Calif. For Yield Coop., Dept. of Forestry and Res. Mgt., 
        Univ. of Calif., Berkeley.  15 pages




	Lee C. Wensel is Professor, Department of Forestry and Resource 
Management, University of California.  Timothy A. Robards was Associate 
Specialist ......................