R help - May 2013 - inverse for formula transformations on LHS

This is an R formula handling question. It arose in class. We were working
on the Animals data in the MASS package. In order to see a relationship,
you need to log brain and body weight.  It's a fun one for teaching
regression, if you did not try it yet.  There are outliers too!

Students wanted to make a predicted value plot in the non-logged values of
y, for comparison, and I wondered if I couldn't automate this somehow for
them.

It made me wonder how R manages formulae and if a transformation like
log(y) can be be mechanically inverted.

So we have something concrete to talk about, suppose x and y are variables
in dat, a person fits

m1 <- lm(log(y) ~ log(x), data = dat)

termplot shows log(y) on the vertical.  What if I want y on the vertical?
Similarly, predict gives values on the log(y) scale, there's no argument
like type = "untransformed".

I want my solution to be a bit general, so that it would give back
predicted y for formulae like

sqrt(y)

or

exp(y)

or

log(y + d)

or whatever other math people might throw in there.

Here's what I can tell so far about R's insides.  The formula handler
makes
a list out of the formula, I can get that from the terms object that the
model generates. The formula list has "~" as element 1, and
"log(x)"
becomes element [[2]].

Where in the R source code can I see how R "looks at" the symbol
log(y) and
discerns that there is a variable y that needs to be logged? If I could
understand that, and if R has a table of inverse functions, then maybe I
could see what to do.

If you have ideas, I'm very grateful if you share them.

pj
-- 
Paul E. Johnson
Professor, Political Science      Assoc. Director
1541 Lilac Lane, Room 504      Center for Research Methods
University of Kansas                 University of Kansas
http://pj.freefaculty.org               http://quant.ku.edu

	[[alternative HTML version deleted]]

Paul,

Inverting log(y)  is just the beginning of the problem,  after that you need to
teach predict.lm()  that E(y |x) = exp(x'betahat + .5*sigmahat^2) and then
further
lessons are required to get it to understand how to adapt its confidence and
prediction bands?  and then you need to generalize all of this to other
transformations.  Quite a project!

Best,
Roger

Roger Koenker
rkoenker at illinois.edu




On May 17, 2013, at 12:21 PM, Paul Johnson wrote:
> This is an R formula handling question. It arose in class. We were working
> on the Animals data in the MASS package. In order to see a relationship,
> you need to log brain and body weight.  It's a fun one for teaching
> regression, if you did not try it yet.  There are outliers too!
> 
> Students wanted to make a predicted value plot in the non-logged values of
> y, for comparison, and I wondered if I couldn't automate this somehow
for
> them.
> 
> It made me wonder how R manages formulae and if a transformation like
> log(y) can be be mechanically inverted.
> 
> So we have something concrete to talk about, suppose x and y are variables
> in dat, a person fits
> 
> m1 <- lm(log(y) ~ log(x), data = dat)
> 
> termplot shows log(y) on the vertical.  What if I want y on the vertical?
> Similarly, predict gives values on the log(y) scale, there's no
argument
> like type = "untransformed".
> 
> I want my solution to be a bit general, so that it would give back
> predicted y for formulae like
> 
> sqrt(y)
> 
> or
> 
> exp(y)
> 
> or
> 
> log(y + d)
> 
> or whatever other math people might throw in there.
> 
> Here's what I can tell so far about R's insides.  The formula
handler makes
> a list out of the formula, I can get that from the terms object that the
> model generates. The formula list has "~" as element 1, and
"log(x)"
> becomes element [[2]].
> 
> Where in the R source code can I see how R "looks at" the symbol
log(y) and
> discerns that there is a variable y that needs to be logged? If I could
> understand that, and if R has a table of inverse functions, then maybe I
> could see what to do.
> 
> If you have ideas, I'm very grateful if you share them.
> 
> pj
> -- 
> Paul E. Johnson
> Professor, Political Science      Assoc. Director
> 1541 Lilac Lane, Room 504      Center for Research Methods
> University of Kansas                 University of Kansas
> http://pj.freefaculty.org               http://quant.ku.edu
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at 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.

> Paul Johnson <pauljohn32 at gmail.com> wrote:
>
> m1 <- lm(log(y) ~ log(x), data = dat)
>
> termplot shows log(y) on the vertical.  What if I want y on the vertical?
plotmo in the plotmo package has an inverse.func argument,
so something like the following might work for you?

library(MASS)
library(plotmo)
log.brain <- log(Animals$brain)
log.body  <- log(Animals$body)
m2 <- lm(log.brain ~ log.body)

myplot <- function(...)
    plotmo(m2, do.par=F, nrug=-1, col.resp=2, pch=20, 
        se=1, main="",  xlab="log(body)", ...)

par(mfrow = c(2, 2))
myplot(ylab="log(brain)")
myplot(ylab="brain", inverse.func=exp)
termplot(m2, se=T, rug=T) #  for comparison