Hello all,

I'm fitting an allometric equation that looks like a really clean fit in
the log-log space, but when I back transform the fit of the curve appears
to need an adjustment - the fitted curve appears to predict values a good
deal higher than those from the data. I included a bias correction per

Newman, M. (1993). Regression analysis of log‐transformed data: Statistical
bias and its correction. Environmental Toxicology and Chemistry. Retrieved
from http://onlinelibrary.wiley.com/doi/10.1002/etc.5620120618/abstract(page
1130)

but that doesn't seem to help much - if anything the fit looks worse. Data
and code below:



temppow<-lm(log(y)~log(x))
plot(log(y)~log(x))
plot(residuals(temppow), main="pow")
abline(temppow)
plot(y~x, main="pow")
tempsum<-summary(temppow)$adj.r.squared
tempint<-summary(temppow)$coefficients[1,1] #intercept of power function
tempslope<-summary(temppow)$coefficients[2,1] #slope of power function
tempmin<-min(x)
tempmax<-max(x)
lngth<-c(tempmin:tempmax) # vector from the minimum to the maximum values
of independent variable
prediction<-exp(tempint)*((lngth)^tempslope)*exp((summary(temppow)$sigma^2)/2)
 # exp((summary(temppow)$sigma^2)/2)  is the bias correction
#prediction<-exp(tempint+tempslope*log(lngth))*exp((summary(temppow)$sigma^2)/2)
lines(prediction)

y,x
237537.61,873
5007.148438,227
17705.77306,400
12396.64369,427
228703.4021,1173
350181.9752,1538
59967.79376,630
140322.7774,710
42650.07251,630
5382.858702,264
34405.82429,637
92261.34614,980
144927.1713,1094
362998.7355,1420
203313.6442,1070
168861.649,930
214306.5266,1040
201804.5193,1000
108426.1988,820
181651.8748,980
53675.45849,775
43068.82972,563
92393.35158,805
93305.0618,740
107308.4761,840
139056.5446,775
15411.81924,420
16104.80991,390
25629.07578,502
37121.23438,461
29711.42749,565
33400.49145,510

Any insight you could give on whether the error is somehow hidden in the
code or how the bias correction I'm using could be improved is very much
appreciated. Also if you have other suggestions, please make them. My
deadline on this is coming up soon.

Best

*Ben Caldwell *

University of California, Berkeley

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