[R] Correspondence analysis/optimal scaling with ordinal variable
Marco Saerens
saerens at isys.ucl.ac.be
Thu Oct 10 14:36:44 CEST 2002
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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