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Congruence Coefficient
In multivariate statistics, the congruence coefficient is an index of the similarity between factors that have been derived in a factor analysis. It was introduced in 1948 by Cyril Burt who referred to it as ''unadjusted correlation''. It is also called ''Tucker's congruence coefficient'' after Ledyard Tucker who popularized the technique. Its values range between -1 and +1. It can be used to study the similarity of extracted factors across different samples of, for example, test takers who have taken the same test.Lorenzo-Seva, U. & ten Berge, J.M.F. (2006). Tucker’s Congruence Coefficient as a Meaningful Index of Factor Similarity. ''Methodology, 2,'' 57–64.Jensen, A.R. (1998). ''The ''g'' factor: The science of mental ability''. Westport, CT: Praeger, pp. 99–100.Abdi, H. (2007)RV Coefficient and Congruence Coefficient.In Neil Salkind (Ed.), ''Encyclopedia of Measurement and Statistics.'' Thousand Oaks (CA): Sage. Definition Let ''X'' and ''Y'' be column vectors of factor lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multivariate Statistics
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical application of multivariate statistics to a particular problem may involve several types of univariate and multivariate analyses in order to understand the relationships between variables and their relevance to the problem being studied. In addition, multivariate statistics is concerned with multivariate probability distributions, in terms of both :*how these can be used to represent the distributions of observed data; :*how they can be used as part of statistical inference, particularly where several different quantities are of interest to the same analysis. Certain types of problems involving multivariate data, for example simple linear regression an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, perso ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cyril Burt
Sir Cyril Lodowic Burt, FBA (3 March 1883 – 10 October 1971) was an English educational psychologist and geneticist who also made contributions to statistics. He is known for his studies on the heritability of IQ. Shortly after he died, his studies of inheritance of intelligence were discredited after evidence emerged indicating he had falsified research data, inventing correlations in separated twins which did not exist, alongside other fabrications. Childhood and education Burt was born on 3 March 1883, the first child of Cyril Cecil Barrow Burt (b. 1857), a medical practitioner, and his wife Martha. He was born in London (some sources give his place of birth as Stratford-upon-Avon, probably because his entry in '' Who's Who'' gave his father's address as Snitterfield, Stratford; in fact the Burt family moved to Snitterfield when he was ten). Burt's father initially kept a chemist shop to support his family while he studied medicine. On qualifying, he became the assistant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ledyard Tucker
Ledyard R. Tucker (19 September 1910 – 16 August 2004) was an American mathematician who specialized in statistics and psychometrics. His Ph.D. advisor at the University of Chicago was Louis Leon Thurstone. He was a lecturer in psychology at Princeton University from 1948 to 1960, while simultaneously working at ETS. In 1960, he moved to working full-time in academia when he joined the University of Illinois. The rest of his career was spent as professor of quantitative psychology and educational psychology at UIUC until he retired in 1979. Tucker is best known for his Tucker decomposition and Tucker–Koopman–Linn model. He is credited with the invention of Angoff method. In 1957 he was elected as a Fellow of the American Statistical Association. accessed 2016-07-23. He died at his home in |
Column Vector
In linear algebra, a column vector with m elements is an m \times 1 matrix consisting of a single column of m entries, for example, \boldsymbol = \begin x_1 \\ x_2 \\ \vdots \\ x_m \end. Similarly, a row vector is a 1 \times n matrix for some n, consisting of a single row of n entries, \boldsymbol a = \begin a_1 & a_2 & \dots & a_n \end. (Throughout this article, boldface is used for both row and column vectors.) The transpose (indicated by T) of any row vector is a column vector, and the transpose of any column vector is a row vector: \begin x_1 \; x_2 \; \dots \; x_m \end^ = \begin x_1 \\ x_2 \\ \vdots \\ x_m \end and \begin x_1 \\ x_2 \\ \vdots \\ x_m \end^ = \begin x_1 \; x_2 \; \dots \; x_m \end. The set of all row vectors with ''n'' entries in a given field (such as the real numbers) forms an ''n''-dimensional vector space; similarly, the set of all column vectors with ''m'' entries forms an ''m''-dimensional vector space. The space of row vectors with ''n'' entries can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cosine Similarity
In data analysis, cosine similarity is a measure of similarity between two sequences of numbers. For defining it, the sequences are viewed as vectors in an inner product space, and the cosine similarity is defined as the cosine of the angle between them, that is, the dot product of the vectors divided by the product of their lengths. It follows that the cosine similarity does not depend on the magnitudes of the vectors, but only on their angle. The cosine similarity always belongs to the interval 1, 1 For example, two proportional vectors have a cosine similarity of 1, two orthogonal vectors have a similarity of 0, and two opposite vectors have a similarity of -1. The cosine similarity is particularly used in positive space, where the outcome is neatly bounded in ,1/math>. For example, in information retrieval and text mining, each word is assigned a different coordinate and a document is represented by the vector of the numbers of occurrences of each word in the document. C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pearson Product-moment Correlation Coefficient
In statistics, the Pearson correlation coefficient (PCC, pronounced ) ― also known as Pearson's ''r'', the Pearson product-moment correlation coefficient (PPMCC), the bivariate correlation, or colloquially simply as the correlation coefficient ― is a measure of linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of teenagers from a high school to have a Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an unrealistically perfect correlation). Naming and history It was developed by Ka ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RV Coefficient
In statistics, the RV coefficient is a multivariate generalization of the ''squared'' Pearson correlation coefficient (because the RV coefficient takes values between 0 and 1). It measures the closeness of two set of points that may each be represented in a matrix. The major approaches within statistical multivariate data analysis can all be brought into a common framework in which the RV coefficient is maximised subject to relevant constraints. Specifically, these statistical methodologies include: :* principal component analysis :* canonical correlation analysis :*multivariate regression :*statistical classification ( linear discrimination). One application of the RV coefficient is in functional neuroimaging where it can measure the similarity between two subjects' series of brain scans or between different scans of a same subject. Definitions The definition of the RV-coefficient makes use of ideas concerning the definition of scalar-valued quantities which are called th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
