Asian Journal of Mathematics & Statistics1994-54182077-2068Asian Network for Scientific Information10.3923/ajms.2008.34.42PietroAmentaBiagioSimonettiEricBeh1200811Several non-iterative procedures for
performing correspondence analysis with external information have been
proposed in literature. The interpretation of the multidimensional representation
of the row and column categories may be greatly simplified if additional
information about the row and column structure are incorporated. In this
paper, a new combined approach to impose external information (as linear
constraints) in analyzing a contingency table which can be of an ordinal
nature, is showed. Linear constraints are imposed using the polynomial
approach to correspondence analysis. The classical approach to correspondence
analysis decomposes the Pearson chi-squared statistic into singular values
by partitioning the matrix of Pearson contingencies using singular value
decomposition. The polynomial approach to correspondence analysis decomposes
the same statistic by partitioning the matrix of Pearson contingencies
using orthogonal polynomials rather than singular value decomposition.
An alternative approach to partitioning the Pearson chi-squared statistic
for a two-way contingency table is essentially to combine the approach
of orthogonal polynomials for the ordered columns and singular vectors
for the unordered rows. With this mixed approach, the researcher can determine
any statistically significant sources of variation (location, dispersion
and higher order components) of the ordered columns along the a particular
axis using the simple correspondence analysis. Main aim of the present
study is to introduce external information to this approach. In our proposal
external information, such as taking into account that categories are
not equally spaced is then included directly on suitable matrices which
reflect the most important components. This approach allows for one to
overcome the problem of having to impose linear constraints at the variables
based on subjective decisions.]]>Beh, E.J.,1997Beh, E.J.,1998Beh, E.J.,1999Beh, E.J., 2001Beh, E.J., B. Simonetti and L. D'Ambra,2007Benzecri, J.P.,1980Best, D.J. and J.C.W. Rayner,1996Bockenholt, U. and I. Bocknholt,1990BĂ¶ckenholt, U. and Y. Takane,1994D'Ambra, L., R. Lombardo and P. Amenta,2002Davy, P.J., J.C.W. Rayner and E.J. Beh,2003Greenacre, M.J.,1984Hwang and Takane,2002Lebart, L., A. Morineau and K.M. Warwick,1984Lombardo, R., E.J. Beh and L. D'Ambra,2007McEwan, J.A. and P. Schlich,1992Nishisato, S.,1980Rao, R.C.,1973Takane, Y., H. Yanai and S. Mayakawa,1991