Facet Theory
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Facet Theory
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 ''c ...
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Metatheory
A metatheory or meta-theory is a theory whose subject matter is theory itself, aiming to describe existing theory in a systematic way. In mathematics and mathematical logic, a metatheory is a mathematical theory about another mathematical theory. Meta-theoretical investigations are part of the philosophy of science. A metatheory is not applied directly to practice, but may have applications to the practice of the field it studies. The emerging field of metascience seeks to use scientific knowledge to improve the practice of science itself. Examples of metatheories Metascience Metascience is the use of scientific methodology to study science itself. Metascience seeks to increase the quality of scientific research while reducing waste. It is also known as "''research on research''" and "''the science of science''", as it uses research methods to study how research is done and where improvements can be made. Metascience concerns itself with all fields of research and has been des ...
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Data Analysis
Data analysis is a process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. Data analysis has multiple facets and approaches, encompassing diverse techniques under a variety of names, and is used in different business, science, and social science domains. In today's business world, data analysis plays a role in making decisions more scientific and helping businesses operate more effectively. Data mining is a particular data analysis technique that focuses on statistical modeling and knowledge discovery for predictive rather than purely descriptive purposes, while business intelligence covers data analysis that relies heavily on aggregation, focusing mainly on business information. In statistical applications, data analysis can be divided into descriptive statistics, exploratory data analysis (EDA), and confirmatory data analysis (CDA). EDA focuses on discovering ne ...
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Psychometrics
Psychometrics is a field of study within psychology concerned with the theory and technique of measurement. Psychometrics generally refers to specialized fields within psychology and education devoted to testing, measurement, assessment, and related activities. Psychometrics is concerned with the objective measurement of latent constructs that cannot be directly observed. Examples of latent constructs include intelligence, introversion, mental disorders, and educational achievement. The levels of individuals on nonobservable latent variables are inferred through mathematical modeling based on what is observed from individuals' responses to items on tests and scales. Practitioners are described as psychometricians, although not all who engage in psychometric research go by this title. Psychometricians usually possess specific qualifications such as degrees or certifications, and most are psychologists with advanced graduate training in psychometrics and measurement theory. I ...
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Clyde Coombs
Clyde Hamilton Coombs (July 22, 1912 – February 4, 1988) was an American psychologist specializing in the field of Psychometrics, mathematical psychology. He devised a voting system, that was hence named Coombs' method. Coombs founded the Mathematical Psychology program at the University of Michigan. His students included Amos Tversky, Robyn Dawes, and Baruch Fischhoff, all important researchers in Decision Sciences. The classic text "An Introduction to Mathematical Psychology," by Coombs, Dawes, and Tversky was a must for Michigan graduate students in Mathematical and Experimental Psychology. In 1959 he was elected as a Fellow of the American Statistical Association. The development of scaling theory by Louis Guttman and Clyde Coombs has been recognized by Science (journal), Science as one of 62 major advances in the social sciences in the period 1900-1965Deutsch, K.W., Platt, J. & Sengham, D. (1971). Conditions favoring major advances in social sciences. ''Science '' 05 Feb 1 ...
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Multidimensional Scaling
Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset. MDS is used to translate "information about the pairwise 'distances' among a set of n objects or individuals" into a configuration of n points mapped into an abstract Cartesian space. More technically, MDS refers to a set of related ordination techniques used in information visualization, in particular to display the information contained in a distance matrix. It is a form of non-linear dimensionality reduction. Given a distance matrix with the distances between each pair of objects in a set, and a chosen number of dimensions, ''N'', an MDS algorithm places each object into ''N''-dimensional space (a lower-dimensional representation) such that the between-object distances are preserved as well as possible. For ''N'' = 1, 2, and 3, the resulting points can be visualized on a scatter plot. Core theoretical contributions to MDS were made by James O. Ramsay of M ...
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Factor Analysis
Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in six observed variables mainly reflect the variations in two unobserved (underlying) variables. Factor analysis searches for such joint variations in response to unobserved latent variables. The observed variables are modelled as linear combinations of the potential factors plus "error" terms, hence factor analysis can be thought of as a special case of errors-in-variables models. Simply put, the factor loading of a variable quantifies the extent to which the variable is related to a given factor. A common rationale behind factor analytic methods is that the information gained about the interdependencies between observed variables can be used later to reduce the set of variables in a dataset. Factor analysis is commonly used in psychometrics, persona ...
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Factor Analysis
Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in six observed variables mainly reflect the variations in two unobserved (underlying) variables. Factor analysis searches for such joint variations in response to unobserved latent variables. The observed variables are modelled as linear combinations of the potential factors plus "error" terms, hence factor analysis can be thought of as a special case of errors-in-variables models. Simply put, the factor loading of a variable quantifies the extent to which the variable is related to a given factor. A common rationale behind factor analytic methods is that the information gained about the interdependencies between observed variables can be used later to reduce the set of variables in a dataset. Factor analysis is commonly used in psychometrics, persona ...
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Cluster Analysis
Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters). It is a main task of exploratory data analysis, and a common technique for statistics, statistical data analysis, used in many fields, including pattern recognition, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning. Cluster analysis itself is not one specific algorithm, but the general task to be solved. It can be achieved by various algorithms that differ significantly in their understanding of what constitutes a cluster and how to efficiently find them. Popular notions of clusters include groups with small Distance function, distances between cluster members, dense areas of the data space, intervals or particular statistical distributions. Clustering can therefore be formulated as a multi-object ...
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Distributive Justice - Multiple Scaling By POSAC
Distributive may refer to: *Distributive property, in algebra, logic and mathematics *Distributive pronoun and distributive adjective (determiner), in linguistics *Distributive case The distributive case (abbreviated ) is used on nouns for the meanings of ''per'' or ''each.'' In Hungarian it is ''-nként'' and expresses the manner when something happens to each member of a set one by one (e.g., ''fejenként'' "per head", ''e ..., in linguistics * Distributive numeral, in linguistics {{Disambiguation ...
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