Newsgroups: bit.listserv.stat-l
Date:         Mon, 12 Oct 1992 17:47:00 EDT
From:         "Philip Gallagher,(919)966-1065" <UPHILG@UNC.BITNET>
Subject:      Re: Need help with PCA

PCA with missing data and N=15
==============================

April Milliken wrote for help (her msg appended at end) with a messy
problem - of the kind that often seems to get pushed off onto students,
probably because it is so messy and lacking in a priori design
features and, apparently, a pilot study, so that the profs don't want to
fool with it.  (Can't blame them, but it sure is tough on the poor
students!)  (Can I get away with it next week?)

    With respect to eliminating implausible values:
    ===============================================
    Yuch!  You have certainly identified a sticky situation.  On
    the one hand, invalid values should not be crammed into an analysis
    just because they managed to become written down on a piece of
    paper.  On the other hand, letting the investigator go through
    the data and eliminate any values he doesn't like is wide open
    to abuse, either conscious or unconscious.
                 Late addendum:  A person who was once a good
                 friend of mine was burned very badly on
                 this issue, and I have never forgotten the
                 sorrow of the situation.  I still believe he
                 had no fraudulent intent, but, apparently, I
                 am the only one.  A career down the drain.
                 In these days when even the President of the
                 Rockefeller University can be accused, ...
                 You must be holier than Caesar's wife.
    May I offer you a
    different solution which ought to satisfy most people?  Hire
    two or three persons thoroughly familiar with the machine but
    totally unfamiliar with the substantive content of Mr. Means'
    research, and ask them to go through and flag implausible values.
    Provided there is agreement amongst them, then I would feel a lot
    less uneasy about the removal of the data.  To answer your question,
    I would keep the animal but eliminate the response.  (But only if
    machine-oriented people agreed that the machine had produced a
    bad response.)  Then I'd go out and start writing grant proposals
    to get a better machine.  By the way, (and I hope Mr Means
    understands that this is meant only as an effort to "hammer the
    ideas out on the anvil of scientific controversy"), would the
    large pH values have been systematically for or systematically
    against the null hypothesis?  I hope neither!



    With respect to the PCA analysis
    ================================

    April, I am afraid that this is the least well qualified
    answer you will get (for example, I have never done a principal
    components analysis), but I have a gut feeling here.  I suspect
    15 animals is too few to be doing a PCA, especially since there
    is a missing data problem.  I encourage you to do the best
    descriptive analyses you can, with lots of plots and charts and
    other graphics as the inspiration strikes you and your investigator.
    If there is anything especially overwhelming in the data, the
    pictures may make it clear.  Given clear pictures, you will
    certainly (I pray) uncover some kind of inferential analysis
    that will back it up well enough.  (If you can convince the editor
    and reviewers from the pictures, they will, most likely, be far
    less critical of your inferential procedure.)  You will still have
    to face up to (in print) the fact of a small N, but you will be on
    far more defensible grounds.  Perhaps others will not feel as I
    do, but I am often unhappy with complex analytical procedures in the
    presence of small numbers and missing data - all the usual weasel
    words (like Central Limit Theorem  and  balanced data, etc.) don't
    apply.

                      Good luck,
                      Phil Gallagher
                      uphilg@unc



> I need some help with a consulting problem...I lack in experience (I am a
> grad student) and so I would like to hear from "experts".
>
> I am working with a professor in animal science kindly named "Mr. Means".
> He wants to publish correct results, but he seems to have difficulties in
> understanding anything beyond one-way anovas.  Consequently, I have two
> problems:
>
> 1)  The data are biochemical results; the machine (I am told) sometimes
>     fails to give a correct result due to lack of solution (or whatever
>     excuse).  Consequently, Mr. Means went through the data and elminated
>     results that he did not feel were plausible (say a pH value that was
>     higher than the rest of the values).  If they are removed, should I
>     remove that observation on that animal, or remove the entire animal
>     (keep in mind that only 15 animals are used in the study)?
>
> 2)  This is a perfect example of needing a principal components analysis
>     in one area and repeated measures in another.  HOWEVER, this is WAY
>     beyond the comprehensive power of Mr. Means.  I ran a PCA and came up
>     with some insightful results...yet, I am at a loss as where to go
>     from here; do I push PCA with 8 variables, or do 8 different one-way
>     ANOVAs for Mr. Means?
> ...
>
> April Milliken
> Department of Biometry
> University of Nebraska-Lincoln
> BIOM030@unlvm1.unl.edu
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