[R] Correspondence analysis/optimal scaling with ordinal variable

[Marco Saerens]

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
-- 

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_oOO-(_)-OOo______________________________________________________________
Prof. Marco Saerens
Information Systems Research Unit (ISYS)
IAG
Université Catholique de Louvain            Tel:   +32(0)10.47.92.46.
Place des Doyens 1                          Fax:   +32(0)10.47.83.24.
B-1348 Louvain-la-Neuve                     Email: saerens at isys.ucl.ac.be
BELGIUM
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