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Bonjour,

Federico Spinazzi a répondu à un message sur le forum Geostats où il est

question d'analyse discriminante et d'ADE. Comme je sais qu'il est sur ce

forum, j'ai pensé que ma question, préparée d'abord pour geostats, avait plus

sa place ici.

Dear Colleagues,

I read the answer given by federico Spinazzi to Dr. Palapa on the geostats

forum (see below).

He mentioned the ADE software as a tool for discriminant analysis. As I am

interested in using this method, I went through the example given in the ADE

documentation for the "Discrimin" module, option "Discriminant alysis/Run"

Data are from Manly, 1994 ("Multivariate statistical methods"), chapter 8.

If you follow the ADE documentation, you must run

the module "PCA:correlation matrix PCA" to standardize the data prior to using

the discriminant analysis module. It is an overall standardization, and not by

groups as suggested by Dr. Palapa.

Yet the results differ from those of Manly.

In page 113 in Manly (1994) the canonical

discriminant functions are :

Z1 = -0.0107X1 +0.0040X2 +0.0119X3 -0.0068X4

Z2 = +0.0031X1 +0.0168X2 -0.0046X3 -0.0022X4

Z3 = -0.0068X1 +0.0010X2 +0.0000X3 +0.0247X4

Z4 = +0.0126 -0.0001X2 + 0.0112X3 +0.0054X4

The results given by ADE using the ---.cnta file (containing the centered and

normed table) as input file for the discriminant analysis, are (---.difa file):

0.5261 0.1884 -0.4563 0.7372

-0.1553 1.0320 0.1221 -0.0021

-0.6627 -0.3643 -0.0798 0.7216

0.2257 -0.2466 0.9505 0.2172

If you use the "PCA: covariance matrix pca" option instead, then you get a

centered table (by column). And the results given by ADE using the ---.cpta

file (containing the centered table) as input file for the discriminant analysis,

are (---.difa file) :

-0.1079 0.0387 0.0936 0.1512

0.0316 0.2096 -0.0248 -0.0004

0.1236 -0.0680 0.0149 0.1346

-0.0706 -0.0771 -0.2973 0.0679

The value given for the first eigenvalue also differ :

Manly 1st=0.437, 2nd=0.035, 3rd=0.015, 4th=0.002

Ade standardized : 0.2983 0.0375 0.0155 0.0020

Ade centered : 0.2983 0.0375 0.0155 0.0020

I may be wrong somewhere. Yet I don't understand where. Can anyone help ?

Many thanks

L. Tito de Morais

tito@bouake.orstom.ci

******** Original messages from geostats *************

*>On Sat, 20 Jun 1998, Palapa wrote:
*

*>
*

*>> If I want to discriminate between two groups ( A and B). Each group has
*

*>> two variable X and Y ( those variables has different unit ).Between A
*

*>> and B has different mean value of X and Y. If I standardize the
*

*>> variables, each group will contain zero mean of variable X and Y. So
*

*>> the difference matrix A and B is Zero.
*

*>> "Do we have to standardize the variables before applying
*

*>> discriminant analysis ?"
*

*>>
*

*>> =palapa=
*

*>>
*

*>As far as I know (AFAIK): Malahanobis distance, used in the
*

*>classification/discrimination algorithm, take care of standardization.
*

*>Moreover, why standardize by group ? If you do such a thing, you can only
*

*>guess that the two correlation matrix will differ, else you'll get not
*

*>any difference between the two groups, but discriminant analysis won't
*

*>help in such case.
*

*>
*

*>Recall that the assumption here is that the two covariance/correlation
*

*>matrixes (spelled right ?) are equal, else you should use quadratic
*

*>discriminant analysis or, to get better results, regularized discriminant
*

*>analysis.
*

*>
*

*>To summarize: don't standardize.
*

*>
*

*>A quite good and free software (MAC and Win95/NT) for Linear Discriminat
*

*>Analysis and much more (no cross-validation):
*

*>
*

*>point to
*

*>
*

*>http://pbil.univ-lyon1.fr/
*

*>
*

*>and go to
*

*>http://pbil.univ-lyon1.fr/ADE-4/ADE-4.html
*

*>
*

*>
*

*>hope that help
*

*>
*

*>federico spinazzi
*

*>federico@syspr03.disat.unimi.it
*

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