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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Facet theory | 1/8 | https://en.wikipedia.org/wiki/Facet_theory | reference | science, encyclopedia | 2026-05-05T09:54:10.375224+00:00 | kb-cron |
Facet theory is a metatheory for the multivariate behavioral sciences that posits that scientific theories and measurements can be advanced by discovering relationships between conceptual classifications of research variables and empirical partitions of data-representation spaces. For this purpose, facet theory proposes procedures for (1) Constructing or selecting variables for observation, using the mapping sentence technique (a formal definitional framework for a system of observations), and (2) Analyzing multivariate data, using data representation spaces, notably those depicting similarity measures (e.g., correlations), or partially ordered sets, derived from the data. Facet theory is characterized by its direct concern with the entire content-universe under study, containing many, possibly infinitely many, variables. Observed variables are regarded just as a sample of statistical units from the multitude of variables that make up the investigated attribute (the content-universe). Hence, Facet theory proposes techniques for sampling variables for observation from the entire content universe; and for making inferences from the sample of observed variables to the entire content universe. The sampling of variables is done with the aid of the mapping sentence technique (see Section 1); and inferences from the sample of observed variables to the entire content universe are made with respect to correspondences between conceptual classifications (of attribute-variables or of population-members) and partitions of empirical geometric representation spaces obtained in data analysis (see Sections 2 & 3). Of the many types of representation spaces that have been proposed, two stand out as especially fruitful: Faceted-SSA (Faceted Smallest Space Analysis) for structuring the investigated attribute (see Section 2); and POSAC (Partial Order Scalogram Analysis by base Coordinates) for multiple scaling measurements of the investigated attribute (see Section 3). Inasmuch as observed variables in a behavioral study form in fact but a sample from the content-universe of interest, facet theory's procedures and principles serve to avoid errors that may ensue from incidental sampling of observed variables, thus meeting the challenge of the replication crisis in psychological research and in behavioral research in general. Facet Theory was initiated by Louis Guttman and has been further developed and applied in a variety of disciplines of the behavioral sciences including psychology, sociology, and business administration.
== The mapping sentence ==
=== Definition and properties of the mapping sentence === Definition (Guttman). A mapping sentence is a verbal statement of the domain and of the range of a mapping including connectives between facets as in ordinary language. In the context of behavioral research, a mapping sentence is essentially a function whose domain consists of the respondents and of the stimuli as arguments, and whose image consists of the cartesian product of the ranges of responses to the stimuli, where each response-range is similarly ordered from high to low with respect to a concept common to all stimuli. When stimuli are classified a priori by one or more content criteria, the mapping sentence facilitates stratified sampling of the content-universe. A classification of the stimuli by their content is called a content facet; and the pre-specified set of responses to a stimulus (classifying respondents by their response to that stimulus) is called a range facet. The mapping sentence defines the system of observations to be performed. As such, the mapping sentence provides also the essential concepts in terms of which research hypotheses may be formulated.
=== An example from intelligence research === Suppose members pi of a population P are observed with respect to their success in a written verbal intelligence test. Such observations may be described as a mapping from the observed population to the set of possible scores, say, R = {1,...,10}: Pq1 → R, where q1 is the sense in which a specific score is assigned to every individual in the observed population P, i.e., q1 is "verbal intelligence" in this example. Now, one may be interested in observing also the mathematical or, more specifically, the numerical intelligence of the investigated population; and possibly also their spatial intelligence. Each of these kinds of intelligence is a "sense" in which population members pi may be mapped into a range of scores R = {1,...,10}. Thus, 'intelligence' is now differentiated into three types of materials: verbal (q1), numerical (q2) and spatial (q3). Together, P, the population, and Q = {q1, q2, q3}, the set of types of intelligence, form a cartesian product which constitutes the mapping domain. The mapping is from the set of pairs (pi, qj) to the common range of test-scores R = {1,...,10}: P × Q → R. A facet is a set that serves as a component-set of a cartesian product. Thus, P is called the population facet, Q is called a content facet, and the set of scores obtainable for each test is a range facet. The range facets of the various items (variables) need not be identical in size: they may have any finite number of scores, or categories, greater or equal to 2.
=== The Common Meaning Range (CMR) === The ranges of the items pertaining to an investigated content-universe – intelligence in this example – should all have a Common Meaning Range (CMR); that is, they must be ordered from high to low with respect to a common meaning. Following Guttman, the common meaning proposed for the ranges of intelligence-items is "correctness with respect to an objective rule". The concept of CMR is central in facet theory: It serves to define the content-universe being studied by specifying the universe of items pertaining to that content-universe. Thus, the mapping-definition of intelligence, advanced by facet theory is: "An item belongs to the universe of intelligence items if and only if its domain requires performance of a cognitive task concerning an objective rule and its range is ordered from high correctness to low correctness with respect to that rule."