# logbtcf: Constructs the correction-factor used when back-transforming... In FSA: Simple Fisheries Stock Assessment Methods

## Description

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

 `1` ```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).

## Author(s)

Derek H. Ogle, derek@derekogle.com

## References

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```# 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))) ) ( pe <- exp(ploge) ) ( cfe <- logbtcf(lme) ) ( cpe <- cfe*pe ) # 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) ) ( cp10 <- cf10*p10 ) # cfe and cf10, cpe and cp10 should be equal all.equal(cfe,cf10) all.equal(cpe,cp10) ```

FSA documentation built on July 17, 2021, 5:07 p.m.