Newsgroups: bit.listserv.edstat-l
Date:         Thu, 16 Apr 1992 14:42:01 CST
Reply-To:     BIOM030@UNLVM.BITNET
From:         BIOM030@UNLVM.BITNET
Subject:      transformation

Recall the question I asked last week about TRANSFORMATIONS.  The
following is a list of responses I received, including the author.
I want to thank everyone who sent me their professional (and personal)
opinion.

ZOE Hayes <hayes@esseX.stfx.ca>  agreed with me on the question of
transformations.  Hope these responses help you, too.

From: pratto@lilac.stanford.edu (Felicia Pratto)
Felicia writes:

The reason to use transformations is to make your variable be distri-
buted in the way that is assumed by the statistical test you want to
use......
I think that inforamtion about your data is important.  But, if you want
to relate one variable to another using any of the linearity assumptions,
make the formulations normal.  As long as you use a transformation that
keeps the order information (i.e., what case is bigger than what case)
, you aren't going to be too misleading.

From: PLOCH@UTKVX.BITNET
Don writes:

The world doesn't come in any kind of units. We impose them by
convention, etc. If you are making counts their logs can be understood
as: 1. a multiplicative rather than a linear model, 2. Constant prop-
ortionality rather than constant difference. We have a variety of
equations for modelling physical, biological and social realities. Trans-
forming variables is often the most appropriate way to state these
equations.

Jerry Arnold  Dept of Animal Sciences   Oregon State Univ.
internet: jwa@ans.orst.edu
Jerry writes:

When using *linear* models to analyze data, we make certain assumptions
regarding the data, the distribution we associate it with and the
relationships between dependent and independent variables.  One of those
assumptions involves linearity of response.  Since the logrithmic
function transforms exponential data into a linear scale, it allows us
to apply a "linear" tool to non-linear data.

Because you have used a LT on your original data, any conclusions
based on a linear analysis of the transformed data DO apply to the
original data.  The world may not always be in log units, but it
isn't always in linear units either.
The key is that in performing the transformation, we don't change
any fundamental relationships that exist in the system being looked at.

(Please note:  Jerry is ALSO a K-Stater....we all have our loyalties to
 defend.)

From:    "Philip Gallagher,(919)966-7275"            <UPHILG@UNC>
Phil writes:
    April, here is an outsider's firmly held feeling on the matter
    (although it will probably be different tomorrow!).  Statisticians
    often introduce transformations to satisfy reasonably objective
    mathematical criteria, such as the distributions of residuals, etc.
    No one I both know and respect introduces transformations simply
    in order to get better p-values - rather the transformations
    are selected in order to create variables which better satisfy
    the (objective) requirements of the statisitical procedure(s)
    being used.  As a one-time bench scientist, I prefer to use
    these transformations only when I can find a theoretical reason
    why the process under study should follow the distribution that
    the transformation implies, say, exponential.  I cringe when
    I feel forced to introduce a transformation for which I cannot
    postulate a thoroughly reasonable physical mechanism.

    Understand, now, I can't summon a really good criticism of
    an analyst who transforms variables solely to meet distribu-
    tional requirements, and I certainly can't put up with either
    the idea of using statistical procedures without meeting the
    distributional requirements or transforming data just to get better
    p-values.  At the same time, I can't be happy with transformations
    that aren't in any way theoretically justifiable (on
    non-statistical grounds).  But, please remember that many
    times mathematical transformations that are mystifying to
    mathematically unsophisticated folks are in fact
    reasonable.

    On re-reading this I'm not sure I made the point that
    really worries me.  Here it is:  I often feel that some
    really good statisticians are seduced into making transformations
    based totally on (valid!) statistical grounds without
    adequately considering the implications that those
    transformations have for the theory of the discipline from
    which the data arise.

From: <IARSPAL@UCLAMVS.BITNET>
Tony writes:
The reasons to use transformations:
  1. The model we've got gives nonsense predictions - e.g. negative
     infant mortality rates, etc.
  2. The variances are unequal at different x values.
  3. The residuals after removing the effects I want to are not normal.

      Karl L. Wuensch, Dept. of Psychology, East Carolina Univ.
      Greenville, NC  27858-4353, PSWUENSC AT ECUVM1 (BITNET)
Karl writes:

The next time someone gives you a hard time about using nonlinear
transformations, saying that they are too far removed from the real data,
ask em to consider the implications of Fechner's law -- this law
describes the relationship between physical reality and psychological
sensation, and it specifies that it is a log function.
      Although today we know that the
function is not always a log function, it is generally nonlinear -- in
other words, our own perception of concrete reality (if you assume such
exits) is a nonlinear transformation.  So why the big fuss about
introducing another nonlinear transformation to allow our data to meet
distributional assumptions of our analytic technique?

From: Dallas E. Johnson <DEJOHNSN@KSUVM>  Kansas State University
Dallas writes:

I do not generally favor transformations, but there are times when they
may be appropriate.

Consider the model y = f(x1,x2,...,xk) + e .  One really important thing
about this model is it says that what we are observing is f(x) + or -
some noise (or error).  If we truely believe that this model is reason-
able, then I would not be in favor of transformations.  However, there
are times when some transformation of y, say g(y), is more likely to have
an additive error structure, that is, g(y)=f(x1,x2,...,xk) + e for some
f.  If g(y) is more likely to have an additive error structure, I would
favor doing an analysis on g(y).  This is because our analysis techniques
are based on normally distributed errors with an additive error structure
(least squares estimates) and maximum likelihood estimates are identical
when the errors are additive and normally distributed).  One example of
a case where transformations might be required is when counting insect
populations.  Insects are likely to increase in number at an exponential
rate since each insect can produce many many eggs and it does not take
too long for the eggs to hatch, and for the new insects to become adults
and lay their own eggs.  Quite often then the errors for insect counts
tend to be multiplicative rather than additive.  That is, a reasonable
model might be y = f(x) times e.  If this is so, then the log of y would
have an additive error structure.  log(y) = h(x) + e* where
h(x)=log(f(x) and e* = log(e). In these kinds of situations transforming
will be important particularly if we are fitting models by the method of
least squares.  I hope this helps.  Statistics don't lie, but liars do
statistics!



      More to come...
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