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st: RE: What multiple regression model for extreme distributions

From   "Nick Cox" <>
To   <>
Subject   st: RE: What multiple regression model for extreme distributions
Date   Tue, 2 Feb 2010 15:23:16 -0000

This kind of problem is often raised on this list. It is not easy, but
some commonly made remarks include 

1. No transformation will undo a spike in the data. A spike maps to a
spike, whatever you do with it. 

2. The assumptions made in multiple regression do not include the
response being normally distributed, as any decent text makes clear. The
assumption is at most that errors are so distributed, and even then it's
about the least important assumption made. 

3. log(y + 1) is an ad hoc transformation that many dislike on various

4. -glm- with log link does not depend on the response being positive
and circumvents #3. Neither -glm- nor its relatives purport to be a
transformation procedure that leaves anything normally distributed that
was not so previously. 

5. Much depends on how you think of the zeros, whether as a
qualitatively different group, or as in essence an extreme subset with
extremely low savings. Some people like two-part models in terms of who
or who does not save and then how much savers save. This is a
substantive or scientific matter requiring the researcher to think,
rather than to apply pre-existing formulae or programs. 

Emphatically not all that could be said.... 


muhammed abdul khalid

I have a household income survey data ( 38,000 observations), and my
problem is doing a multiple regression on saving ( independent var) to
etc( dependent var).

The problem is this : 70% of my observation for the value of saving is
zero. I had recode it to 1 and log them, but the distribution is still
extremely skewed ( mean 0.78, std dev is 2.4  min 0 max 14). The
historgam still looks like the letter L , exteremly skewed to the
right with  long tail.  Obviously, OLS is out, and I tried Poisson(
glm nbinomial) but the distribution is still not distributed normally.
The data are in order i.e no missing values etc etc. It is clean.For
some reason, lobit would not run.

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