[R] Correspondence analysis/optimal scaling with ordinal variable

[Christian Hennig]

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 ?
> 
> Please, feel free to answer to "saerens at ulb.ac.be".
> 
> 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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