R help - Sep 2011 - linear regression, log-transformation and plotting

Hello,

I've some questions concerning log-transformations and plotting of the
regression lines. So far as I know is it a problem to log-transform values
smaller than 1 (0-1). In my statistics lecture I was told to do a log(x+1)
transformation in such cases. So I provide here a small example to explain my
questions:


# Some example data for testing
a1 <-c(0.2,1.9,0.1,0.2,0.8,22,111.3,19.9,23.9,138,42.3,54.2,0.9)
b1 <-c(1.8,28.2,0.3,12.4,3.2,81.1,122.1,2.9,37.2,98.9,21,28.7,1.8)
data1  <- data.frame(a1,b1)

model <- lm(log(a1+1)~log(b1+1))


because of values less then one I did the log(x+1) transformation for running
the lm. Is that correct so far? (Just to mention: These are example data so I
haven't checked if the need a transformation at all)

Then some questions arise when it comes to plot the data. As usual I'd like
to plot the original data (not log transformed) but in a log-scale.

I tried two approaches the standard plot function and ggplot.

# Plot with ggplot
ggplot()+
geom_point(aes(b1,a1,data=data1))+
geom_abline(aes(intercept=coef(model)[1],slope=coef(model)[2]))+
scale_y_log()+
scale_x_log()

# Plot with standard plot
plot(b1,a1,log="xy")
abline(model,untf=T)
abline(model,untf=F)


1) The regression lines are different for plot vs. ggplot(transformed or
untransformed). So what is actually the correct line?

2) The regression line was calculated on basis of log(x+1), but the log scale on
my axis is just simple log (without +1). So how are such cases usually treated?
I thought about subtracting the value 1 from the intercept?

So my simple question: What is the best way to display such data with a
regression line?

Thank you
/Johannes
--

I think that you have not understood your lecturer. You can log transform
any positive number.  You can not log transform a negative number.  Adding a
constant to a negative number to make it constant before log transformation
is sometimes suggested by those who do not understand what they are doing.
 This practice is not appropriate except perhaps in some extraordinary
circumstances.

John



On Wednesday, 7 September 2011, Johannes Radinger <JRadinger@gmx.at>
wrote:
> Hello,
>
> I've some questions concerning log-transformations and plotting of the
regression lines. So far as I know is it a problem to log-transform values
smaller than 1 (0-1). In my statistics lecture I was told to do a log(x+1)
transformation in such cases. So I provide here a small example to explain
my questions:
>
>
> # Some example data for testing
> a1 <-c(0.2,1.9,0.1,0.2,0.8,22,111.3,19.9,23.9,138,42.3,54.2,0.9)
> b1 <-c(1.8,28.2,0.3,12.4,3.2,81.1,122.1,2.9,37.2,98.9,21,28.7,1.8)
> data1  <- data.frame(a1,b1)
>
> model <- lm(log(a1+1)~log(b1+1))
>
>
> because of values less then one I did the log(x+1) transformation for
running the lm. Is that correct so far? (Just to mention: These are example
data so I haven't checked if the need a transformation at
all)
>
> Then some questions arise when it comes to plot the data. As usual I'd
like to plot the original data (not log transformed) but in a
log-scale.
>
> I tried two approaches the standard plot function and ggplot.
>
> # Plot with ggplot
> ggplot()+
> geom_point(aes(b1,a1,data=data1))+
> geom_abline(aes(intercept=coef(model)[1],slope=coef(model)[2]))+
> scale_y_log()+
> scale_x_log()
>
> # Plot with standard plot
> plot(b1,a1,log="xy")
> abline(model,untf=T)
> abline(model,untf=F)
>
>
> 1) The regression lines are different for plot vs. ggplot(transformed or
untransformed). So what is actually the correct line?
>
> 2) The regression line was calculated on basis of log(x+1), but the log
scale on my axis is just simple log (without +1). So how are such cases
usually treated? I thought about subtracting the value 1 from the
intercept?
>
> So my simple question: What is the best way to display such data with a
regression line?
>
> Thank you
> /Johannes
> --
>
> ______________________________________________
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
-- 
John C Frain
Economics Department
Trinity College Dublin
Dublin 2
Ireland
www.tcd.ie/Economics/staff/frainj/home.html
mailto:frainj@tcd.ie
mailto:frainj@gmail.com

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