coordinates in correpondence analysis

[Shlomo Getz]

Hello list,

What does the coordinates of a correspondence analysis map stands for?

What is the meaning of a column or row point being at the negative or
positive  part of the axis (dimension 1) etc.


--
Dr. Shlomo Getz
Head, The Institute for the Research of the Kibbutz
University of Haifa

Office: (972) 4 -8240418
Mobile: [phone]

[hidden email]

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[Kooij, A.J. van der]

It's not the positions of the points itself that are of interest in a Correspondence map, but the position of the points relative to each other (the positions of the points are only unique up to rotation and reflection of axes). If points for categories lie close to each other, this means that these categories are much alike and if points for categories lie far from each other, the categories are very different.

In a Correspondence map, with row principal normalization, the Euclidean distances between the row points approximate the Chi-square distances (weighted (with mass) distances) between the row profiles. The row scores are the weighted (with frequencies) averages of the column scores, or graphically: the row points are in the weighted centroid of the column points. The column points are proportional to the weighted centroid of the row points (proportional because first the column scores are obtained as weighted averages of the row scores and then the result is normalized so that the column scores in each dimension have weighted (with the column marginals) sum of squares equal to N, the grand total).

(With column principal normalization, the Euclidean distances between the column points approximate the Chi-square distances between the column profiles. The column points are in the weighted centroid of the row points and the row points are proportional to the weighted centroid of the columns points.)

 

Anita van der Kooij
Data Theory Group
Leiden University




________________________________

From: SPSSX(r) Discussion on behalf of Shlomo Getz
Sent: Mon 21/07/2008 18:36
To: [hidden email]
Subject: coordinates in correpondence analysis



Hello list,

What does the coordinates of a correspondence analysis map stands for?

What is the meaning of a column or row point being at the negative or
positive  part of the axis (dimension 1) etc.


--
Dr. Shlomo Getz
Head, The Institute for the Research of the Kibbutz
University of Haifa

Office: (972) 4 -8240418
Mobile: [phone]

[hidden email]

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[hidden email] (not to SPSSX-L), with no body text except the
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[Hannes Schreier]

Hi,

the meaning of the coordinates have to be extracted from the data they
represent (the contribution of the points to the dimension and the
contribution of the dimension to the points). So your question can´t be
answered in general.
Positive or negative values on the dimensions isn´t the matter in
correspondence analysis, for the interpretation the distances of the points
are relevant, so it does not matter if they have a poitive or negative
score. In fact, the directions of the dimensions could be changed (so that
postive values become negative ones), the distances would still be the same.
More important than positive or negative values is therefore that you pay
attention to same scales of your dimensions, so that the distances are
represented properly.

Greetings

Hannes Schreier

On Mon, 21 Jul 2008 19:36:42 +0300, Shlomo Getz <[hidden email]> wrote:

>Hello list,
>
>What does the coordinates of a correspondence analysis map stands for?
>
>What is the meaning of a column or row point being at the negative or
>positive  part of the axis (dimension 1) etc.
>
>
>--
>Dr. Shlomo Getz
>Head, The Institute for the Research of the Kibbutz
>University of Haifa
>
>Office: (972) 4 -8240418
>Mobile: [phone]
>
>[hidden email]
>
>=====================
>To manage your subscription to SPSSX-L, send a message to
>[hidden email] (not to SPSSX-L), with no body text except the
>command. To leave the list, send the command
>SIGNOFF SPSSX-L
>For a list of commands to manage subscriptions, send the command
>INFO REFCARD

=====================
To manage your subscription to SPSSX-L, send a message to
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