Date: Mon, 6 May 2002 12:47:11 -0700
Reply-To: Dale McLerran <stringplayer_2@YAHOO.COM>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: Dale McLerran <stringplayer_2@YAHOO.COM>
Subject: Re: Discriminant Analysis with Categorical Explanatory Variables
In-Reply-To: <004901c1f52c$98415870$520e6a81@PEDUCT225>
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PROC DISCRIM will perform a nonparametric discriminant analysis. I
have not thought too much about discriminant analysis and MANOVA, but
in a limited case, they could be inverse procedures to one another,
right? But we could account for multiple covariates in MANOVA. We
could even account for some continuous covariates on the right hand
side of a MANOVA without having to assume anything about normality
of the covariate. We could not really invert a MANOVA in which we
accounted for some continuous covariates which are not normally
distributed and get a discriminant model, could we? In general, if
there was nonzero covariance among variables on the right hand
side of a MANOVA model, we could not invert the MANOVA to obtain a
corresponding discriminant analysis, could we?
Discriminant analysis is slightly more powerful than a logistic
regression if the assumptions of multivariate normality hold. There
may be some fields of study in which these assumptions may frequently
be true, in which case discriminant analysis would be the preferred
analytic method. Within the realm of my experience, this cannot
usually be assumed, but I can certainly appreciate that it may hold
for other fields of investigation.
I suggest generalized logits as the complimentary model to
discriminant analysis. The discriminant analysis is fully
parameterized: each linear combination has a completely different
set of coefficients. Not so the ordinal logistic regression model
fitted employing cumulative logits. Of course, if there are only two
groups, then it doesn't matter whether we assume cumulative logits
or generalized logits. The generalized logits and cumulative logits
models are the same when the response is binary.
Dale
--- Paul R Swank <Paul.R.Swank@UTH.TMC.EDU> wrote:
> Any time you do a MANOVA your are, in essence doing a discriminant
> analysis.
> Manova is often reported in the literature and I do see references to
> discriminant analysis from time to time. However, one would not do a
> MANOVA
> on a dichotomous dependent variable, which is what seemed to be
> suggested. I
> have to admit to being unaware of nonparametric discriminant
> analyses. This
> would have to be akin to nonparametric MANOVA, would it not? One
> would
> think they would be relatively restricted to small data sets. A
> generalized
> linear model with a multinomial distribution would seem to fit the
> bill,
> unless of course, the categories are ordered, in which case Susie's
> suggestion of logistic would work although that is also just a
> generalized
> linear model. I am curious as to which program in SAS does a
> nonparameteric
> discriminant analysis. Might be an interesting comparison in that.
>
> Paul R. Swank, Ph.D.
> Professor, Developmental Pediatrics
> Medical School
> UT Health Science Center at Houston
>
>
>
> -----Original Message-----
> From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU]On Behalf Of
> Dale
> McLerran
> Sent: Monday, May 06, 2002 11:40 AM
> To: SAS-L@LISTSERV.UGA.EDU
> Subject: Re: Discriminant Analysis with Categorical Explanatory
> Variables
>
>
> Paul,
>
> That is true for the classical discriminant function analysis
> problem.
> However, there are nonparametric discriminant function models which
> are specifically intended for the situation where you cannot assume
> multivariate normality. The suggestion to employ a generalized
> linear
> model is, however, a good suggestion. GLM's should be considered
> whenever one is thinking about fitting a discriminant analysis.
> Assumptions about multivariate normality will rarely be met.
> Optimality of discriminant analysis over a polytomous response model
> fitted employing generalized logits only obtains when multivariate
> normality does, indeed, hold. Because this is rarely true,
> discriminant analysis is seldom employed. Rather, as you indicate,
> a GLM (in particular a polytomous response regression model assuming
> generalized logits) is usually preferred. Discriminant analysis is,
> as far as I have seen, a rarely used analytic method.
>
> Dale
>
>
> --- Paul R Swank <Paul.R.Swank@UTH.TMC.EDU> wrote:
> > The assumption for disciminant analysis is the same as for MANOVA
> > except
> > that independents and dependents are reversed. That is multivariate
> > normality for the independents (dependents for MANOVA). You
> > technically
> > cannot do a MANOVA with categorical outcome so you technically
> can't
> > do
> > discriminanat analysis with a categorical predictor. Sounds like
> you
> > might
> > need a generalized linear model.
> >
> > Paul R. Swank, Ph.D.
> > Professor, Developmental Pediatrics
> > Medical School
> > UT Health Science Center at Houston
> >
> >
> >
> > -----Original Message-----
> > From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU]On Behalf Of
> > Frederico Zanqueta Poleto
> > Sent: Monday, May 06, 2002 10:51 AM
> > To: SAS-L@LISTSERV.UGA.EDU
> > Subject: Discriminant Analysis with Categorical Explanatory
> Variables
> >
> >
> > Hi,
> >
> > Anybody know if PROC DISCRIM can handle categorical explanatory
> > variables?
> > Have I to create dummy's?
> > If SAS can't do it, anybody know if another program has it
> > implemented?
> >
> > Sincerely,
> > --
> > Frederico Zanqueta Poleto
> > fred@poleto.com
> > --
> > "It would be possible to describe everything scientifically, but it
> > would
> > make no sense; it would be without meaning, as if you described a
> > Beethoven symphony as a variation of wave pressure." Albert
> Einstein
>
>
> =====
> ---------------------------------------
> Dale McLerran
> Fred Hutchinson Cancer Research Center
> mailto: dmclerra@fhcrc.org
> Ph: (206) 667-2926
> Fax: (206) 667-5977
> ---------------------------------------
>
> __________________________________________________
> Do You Yahoo!?
> Yahoo! Health - your guide to health and wellness
> http://health.yahoo.com
=====
---------------------------------------
Dale McLerran
Fred Hutchinson Cancer Research Center
mailto: dmclerra@fhcrc.org
Ph: (206) 667-2926
Fax: (206) 667-5977
---------------------------------------
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Do You Yahoo!?
Yahoo! Health - your guide to health and wellness
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