# Correspondence analysis - fragment of text

#### martyna

##### New Member
Hi,

Could someone please help me - I need to have a short fragment of text (half a page) about correspondence analysis checked by someone who is knowledgeable about the topic. It's in English and I want to make sure the content is correct. It shouldn't take much time.

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#### gianmarco

##### TS Contributor
If you are willing to post it here, I would not mind to read it.
While I know something about CA, that would allow people more knowledgable than me to jump in a provide further help.

cheers.
Gm

#### martyna

##### New Member
Yes, so here's the text:

The basic result of correspondence analysis is a scatter diagram – a perceptual map and set of measures that serves to assess the quality of representation of a multidimensional space on a surface. Dimensions are typically plotted to visualize the relationships among the variables. In CA, this graphical representation is called a “map”. The origin on the map corresponds to the centroid of each variable. The closer a row (column) profile’s vector location is to the origin, the closer it is to the average profile.
The algebraic basis of CA is decomposition of a matrix that represents relations between rows and columns into singular vectors and singular values (singular value decomposition). The sum of the squares of singular values equals the so-called inertia, which is chi-square calculated for a given table, divided by a sample size (n). A given singular value squared allows to assess the level of inertia specified by a given dimension. The quality of representation of the table correlations on a smaller number of dimensions allows to assess the share of inertia of a given dimension in total table inertia.

I'd like to know if it makes sense at all and if not - what is unclear or which terms are not correct. Thank you!

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#### gianmarco

##### TS Contributor
The basic result of correspondence analysis is a scatter diagram – a perceptual map and set of measures that serves to assess the quality of representation of a multidimensional space on a surface.
*I believe you may want to drop the reference to "perceptual map" and stick with scatter diagram (or scatterplot). Perceptual map is a special case of scatterplot, which is often used in marketing research. The difference is that, unlike regular CA scatterplot, in perceptual map the axes are given names according to the categories which are actually contributing to the definition of the dimensions. Unlike regular scatterplot, in perceptual maps the levels of only one of the two categorical variables are displayed.

Dimensions are typically plotted to visualize the relationships among the variables.
*
I would say that dimensions are plotted to visualize the degree of association btw levels of the 2 categ variables.

The origin on the map corresponds to the centroid of each variable
I would say that the origin of the map is called centroid, and represents the "place" where there is no difference among the profiles.

A given singular value squared allows to assess the level of inertia specified by a given dimension.
I would use "the proportion of inertia explained by a given dimension".

The quality of representation of the table correlations on a smaller number of dimensions allows to assess the share of inertia of a given dimension in total table inertia.
*
I did not quite got that, sorry.