A number of model-based scaling methods have
been developed that apply to asymmetric proximity
matrices. A flexible data analysis approach is proposed
that combines two psychometric
procedures-seriation and multidimensional scaling (MDS). The
method uses seriation to define an empirical ordering
of the stimuli, and then uses MDS to scale the
two separate triangles of the proximity matrix
defined by this ordering. The MDS solution contains
directed distances, which define an "extra"
dimension that would not otherwise be portrayed,
because the dimension comes from relations
between the two triangles rather than within
triangles. The method is particularly appropriate
for the analysis of proximities containing temporal
information. A major difficulty is the computational
intensity of existing seriation algorithms,
which is handled by defining a nonmetric seriation
algorithm that requires only one complete iteration.
The procedure is illustrated using a matrix of
co-citations between recent presidents of the
Psychometric Society. Index terms: asymmetric
data, cluster analysis, combinatorial data analysis,
multidimensional scaling, order analysis, proximity
data, seriation, unidimensional scaling.
Rodgers, Joseph L & Thompson, Tony D. (1992). Seriation and multidimensional scaling: A data analysis approach to scaling asymmetric proximity matrices. Applied Psychological Measurement, 16, 105-117. doi:10.1177/014662169201600201
Rodgers, Joseph Lee; Thompson, Tony D..
Seriation and multidimensional scaling: A data analysis approach to scaling asymmetric proximity matrices.
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