[R] Correspondence analysis/optimal scaling with ordinal variable

[Jan de Leeuw]

The paper is in Statistical Science, 1998, 13, 307-336

The homals program in R (ftp://gifi.stat.ucla.edu/pub/homalsR.tar.gz)
has, in the Gifi terminology, homals and princals and overals (and
a few new extensions). It will be packaged soon, I hope.


On Thursday, October 10, 2002, at 07:02 AM, Christian Hennig wrote:

> 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/
> #######################################################################
> ich empfehle www.boag.de
>
>
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===
Jan de Leeuw; Professor and Chair, UCLA Department of Statistics;
Editor: Journal of Multivariate Analysis, Journal of Statistical  
Software
US mail: 9432 Boelter Hall, Box 951554, Los Angeles, CA 90095-1554
phone (310)-825-9550;  fax (310)-206-5658;  email: deleeuw at stat.ucla.edu
homepage: http://gifi.stat.ucla.edu
   
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