Correspondence analysis/optimal scaling with ordinal variable
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 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._