How to transform negative values to logarithms?

Question

I would like to know how to transform negative values to Log(), since I have heteroskedastic data. I read that it works with the formula Log(x+1) but this doesn't work with my database and I continue getting NaNs as result. E.g. I get this Warning message (I didn't put my complete database because I think with one of my negative values is enough to show an example):

> log(-1.27+1)
[1] NaN
Warning message:
In log(-1.27 + 1) : NaNs produced
> 

Thanks in advance

UPDATE:

Here is an histogram of my data. I'm working with palaeontological time series of chemical measurements, E.g the difference between variables like Ca and Zn is too big, then I need some type of data standardization, that is why I'm testing the log() function.

This is my raw data

Answer 1

Since logarithm is only defined for positive numbers, you can't take the logarithm of negative values. However, if you are aiming at obtaining a better distribution for your data, you can apply the following transformation.

Suppose you have skewed negative data:

x <- rlnorm(n = 1e2, meanlog = 0, sdlog = 1)
x <- x - 5
plot(density(x))

then you can apply a first transformation to make your data lie in $(-1,1)$:

z <- (x - min(x)) / (max(x) - min(x)) * 2 - 1
z <- z[-min(z)]
z <- z[-max(z)]
min(z); max(z)

and finally apply the inverse hyperbolic tangent:

t <- atanh(z)
plot(density(t))

Now, your data look approximately normally distributed. This is also called Fisher transformation.

Answer 2

To transform it to a log scale, first find the log of the positive number then multiply it by its sign, the following code should do that.

transform_to_log_scale <- function(x){
    if(x==0){
        y <- 1
    } else {
        y <- (sign(x)) * (log(abs(x)))
    }
        y 
    }

Using the above example we can plot the following skewed distribution

x <- rlnorm(n = 1e2, meanlog = 0, sdlog = 1)
x <- x - 5
plot(density(x))

After using the transforming function as follows, we get a distribution that looks more 'normal'

plot(density(sapply(x,FUN=transform_logs_scale)))