Constructs the correction-factor used when back-transforming log-transformed values.

Constructs the correction-factor used when back-transforming log-transformed values according to Sprugel (1983). Sprugel's main formula -- exp((syx^2)/2) -- is used when syx is estimated for natural log transformed data. A correction for any base is obtained by multiplying the syx term by log_e(base) to give exp(((log_e(base)*syx)^2)/2). This more general formula is implemented here (if, of course, the base is exp(1) then the general formula reduces to the original specific formula).

Usage

logbtcf(obj, base = exp(1))

Arguments

obj: An object from lm.
base: A single numeric that indicates the base of the logarithm used.

Value

A numeric value that is the correction factor according to Sprugel (1983).

References

Sprugel, D.G. 1983. Correcting for bias in log-transformed allometric equations. Ecology 64:209-210.

Author

Derek H. Ogle, DerekOgle51@gmail.com

Examples

# toy data
df <- data.frame(y=rlnorm(10),x=rlnorm(10))
df$logey <- log(df$y)
df$log10y <- log10(df$y)
df$logex <- log(df$x)
df$log10x <- log10(df$x)

# model and predictions on loge scale
lme <- lm(logey~logex,data=df)
( ploge <- predict(lme,data.frame(logex=log(10))) )
#>        1 
#> 1.691612 
( pe <- exp(ploge) )
#>        1 
#> 5.428224 
( cfe <- logbtcf(lme) )
#> [1] 1.381993
( cpe <- cfe*pe )
#>        1 
#> 7.501769 

# model and predictions on log10 scale
lm10 <- lm(log10y~log10x,data=df)
plog10 <- predict(lm10,data.frame(log10x=log10(10)))
p10 <- 10^(plog10)
( cf10 <- logbtcf(lm10,10) )
#> [1] 1.381993
( cp10 <- cf10*p10 )
#>        1 
#> 7.501769 

# cfe and cf10, cpe and cp10 should be equal
all.equal(cfe,cf10)
#> [1] TRUE
all.equal(cpe,cp10)
#> [1] TRUE