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The Burt table is the symmetric matrix of all two-way cross-tabulations between the categorical variables, and has an analogy to the covariance matrix of continuous variables. Analyzing the Burt table is a more natural generalization of simple correspondence analysis , and individuals or the means of groups of individuals can be added as ...
This is a list of statistical procedures which can be used for the analysis of categorical data, also known as data on the nominal scale and as categorical variables. General tests [ edit ]
Correspondence analysis (CA) is a multivariate statistical technique proposed [1] by Herman Otto Hartley (Hirschfeld) [2] and later developed by Jean-Paul Benzécri. [3] It is conceptually similar to principal component analysis, but applies to categorical rather than continuous data.
The basic setup is the same as in logistic regression, the only difference being that the dependent variables are categorical rather than binary, i.e. there are K possible outcomes rather than just two. The following description is somewhat shortened; for more details, consult the logistic regression article.
The example above is the simplest kind of contingency table, a table in which each variable has only two levels; this is called a 2 × 2 contingency table. In principle, any number of rows and columns may be used. There may also be more than two variables, but higher order contingency tables are difficult to represent visually.
It is also known as Principal Coordinates Analysis (PCoA), Torgerson Scaling or Torgerson–Gower scaling. It takes an input matrix giving dissimilarities between pairs of items and outputs a coordinate matrix whose configuration minimizes a loss function called strain, [2] which is given by (,,...,) = (, (),) /, where denote vectors in N-dimensional space, denotes the scalar product between ...
When classification is performed by a computer, statistical methods are normally used to develop the algorithm.. Often, the individual observations are analyzed into a set of quantifiable properties, known variously as explanatory variables or features.
Elliptical distributions are defined in terms of the characteristic function of probability theory. A random vector on a Euclidean space has an elliptical distribution if its characteristic function satisfies the following functional equation (for every column-vector )