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).

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.

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