# [R] Correspondence analysis/optimal scaling with ordinal variable

Christian Hennig hennig at stat.math.ethz.ch
Thu Oct 10 16:02:00 CEST 2002

```Dear Marco,

although I am not really an expert in this, it may be helpful to consider
the Wiley-book A. Gifi "Nonlinear multivariate analysis" (1990) or perhaps
the paper by Michailidis and de Leeuw about the "Gifi system":

http://citeseer.nj.nec.com/cache/papers/cs/14429/http:zSzzSzwww.stat.ucla.eduzSzpaperszSzpreprintszSz204zSz204.pdf/michailidis98gifi.pdf

The keyword should be "nonlinear principal components".
I do not know about implementations in R.

Best,
Christian

On Thu, 10 Oct 2002, Marco Saerens wrote:

> Dear R specialists,
>
> I have a multivariate statistics question that I want to submit to
> the R community (which conveys a very good statistical knowledge).
>
> I need to perform an optimal scaling based on a discrete variable and
> an ordinal variable. The discrete variable, Area, defines a
> geographical area. The ordinal variable, EducationLevel, describes
> the education level of individuals (the ordinal factors are
> "VeryLow", "Low, "Medium", "Large", "VeryLarge").
>
> I have a data set specifying, for each area (rows), the number of
> individuals in this area having a given education level (columns). It
> looks like:
>
> Area    VeryLow    Low    Medium    Large    VeryLarge
> A1         6        21      15        11         0
> A2         2         4       8        17         9
> etc
>
> Meaning that in area A1 there are 6 individuals with very low
> education level, 21 with low education level, etc.
>
> I need to compute a score for each area that reflects the education
> level in this area. This can be done by using correspondence
> analysis: The scores on the first factor represent an optimal scaling
> in a certain sense (see the book of Greenacre (1984) "Theory and
> applications of correspondence analysis" for instance). In other
> words, I have to transform my ordinal variable "EducationLevel" into
> a continuous variable "EducationScore".
>
> However, this procedure does not account for the fact that one of my
> variables (EducationLevel) is ordinal. For instance, the weights
> obtained after performing the correspondence analysis could be
> non-monotically increasing (weights used in order to compute the
> projection on the first factor).
>
> In summary, the question is:
>
> (1) Are there statistical procedures that account for the ordinal
> nature of the Level variable (so that the weights are monotically
> increasing: order constraints on the weights) ?
>
> (2) Are these procedures implemented in R or S-Plus ?
>
>
> Many Thanks !!
>
> Marco Saerens
>

--
***********************************************************************
Christian Hennig
Seminar fuer Statistik, ETH-Zentrum (LEO), CH-8092 Zuerich (current)
and Fachbereich Mathematik-SPST/ZMS, Universitaet Hamburg
hennig at stat.math.ethz.ch, http://stat.ethz.ch/~hennig/
hennig at math.uni-hamburg.de, http://www.math.uni-hamburg.de/home/hennig/
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ich empfehle www.boag.de

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