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

Jan de Leeuw deleeuw at stat.ucla.edu
Thu Oct 10 17:43:11 CEST 2002

```ftp://gifi.stat.ucla.edu/pub/homalsR.tar.gz does "correspondence
analysis" for an arbitrary number of variables (not just 2), each of
which can be treated as numerical, ordinal, or nominal. In fact, it
can do much more.

It has a nice tcl/tk interface, and the documentation is abysmal.

On Thursday, October 10, 2002, at 05:36 AM, 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
> --
>
>      """
>      ö ö
> _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
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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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```