kb/data/en.wikipedia.org/wiki/Facet_theory-3.md

title	chunk	source	category	tags	date_saved	instance
Facet theory	4/8	https://en.wikipedia.org/wiki/Facet_theory	reference	science, encyclopedia	2026-05-05T09:54:10.375224+00:00	kb-cron

=== Principles of faceted SSA: A summary ===

1. The attribute under study is represented by a geometric space.
2. Variables of the attribute are represented as points in that space. Conversely, every point in the geometric space is a variable of the attribute. This is the Continuity Principle.
3. The observed variables, located as points in the empirical Faceted SSA map, constitute but a sample drawn from the many (possibly infinitely many) variables constituting the content universe of the attribute investigated.
4. The observed variables chosen for SSA must all belong to the same content universe. This is ensured by including in the SSA only variables whose ranges are similarly ordered with respect to a common meaning (CMR).
5. The sample of variables marked on the Faceted SSA map is used as a guide for inferring possible partitions of the SSA-attribute-map into distinct regions, each region representing a component, or subdomain, of the attribute.
6. In Facet Theory, relationships between attribute components (such as verbal intelligence and numeric intelligence as components of intelligence), are expressed in geometric terms –such as shapes and spatial orientation – rather than in algebraic terms. Just as one would describe relationships between neighboring countries in terms of their shapes and geographical orientation, not in terms of distances between them.
7. The imagery of an attribute as a continuous space, from which variables are sampled, implies that clustering of variables in SSA map has no significance: It is just an artifact of the sampling of the variables. Sampled variables that are clustered together may belong to different subdomains; just as two cities that are close together may be located in different countries. Conversely, variables that are far apart, may belong to the same sub-domain; just as two cities that are far apart may belong to the same country. What matters is the identification of distinct regions with well-defined sub-domains. Facet Theory proposes a way of transcending accidental clustering of variables by focusing on a robust and replicable aspect of the data, namely the partitionability of the attribute-space. These principles bring in new concepts, raise new questions, and opens new ways of understanding behavior. Thus, Facet Theory represents a paradigm of its own for multivariate behavioral research.

=== Complementary topics in faceted SSA === Besides analyzing a data matrix of N individuals by n variables, as discussed above, Faceted SSA is usefully employed in additional modes. Direct measures of (dis)similarity. For a given a set of objects and a similarity (or dissimilarity) measure between every pair of objects, Faceted SSA can provide a map whose regions correspond to a specified classification of the objects. For example, in a study of color perception, a sample of spectral colors, with a measure of perceived similarity between every pair of colors, yielded the radex theory of spectral color perception. In a study of community elites, a measure of distance devised between pairs of community leaders, yielded a sociometric map whose regions were interpreted from the perspective of sociological theory. Transposed data matrix. Switching the roles of individuals and variables, Faceted SSA may be applied to individuals rather than to the variables. This rarely used procedure may be justified to the extent variables evenly cover a research domain. For example, intercorrelations between members of a multidisciplinary team of experts were computed based on their human quality-of life value assessments. The resulting Faceted SSA map yielded a radex of disciplines, supporting the association between social institutions and human values.

== Multiple scaling by POSAC ==

=== Description of Partial Order Scalogram Analysis by Coordinates (POSAC) === In Facet Theory, the measurement of investigated individuals (and, by extension, of all individuals belonging to the sampled population) with respect to a multivariate attribute, is based on the following assumptions and conditions: