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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 ]
A theory is κ-categorical (or categorical in κ) if it has exactly one model of cardinality κ up to isomorphism. Morley's categoricity theorem is a theorem of Michael D. Morley ( 1965 ) stating that if a first-order theory in a countable language is categorical in some uncountable cardinality , then it is categorical in all uncountable ...
In the panel data fixed effects estimator dummies are created for each of the units in cross-sectional data (e.g. firms or countries) or periods in a pooled time-series. However in such regressions either the constant term has to be removed, or one of the dummies removed making this the base category against which the others are assessed, for ...
Duality: Every statement, theorem, or definition in category theory has a dual which is essentially obtained by "reversing all the arrows". If one statement is true in a category C then its dual is true in the dual category C op. This duality, which is transparent at the level of category theory, is often obscured in applications and can lead ...
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.
The difference between the multinomial logit model and numerous other methods, models, algorithms, etc. with the same basic setup (the perceptron algorithm, support vector machines, linear discriminant analysis, etc.) is the procedure for determining (training) the optimal weights/coefficients and the way that the score is interpreted.
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 ...
In mathematics, categorification is the process of replacing set-theoretic theorems with category-theoretic analogues. Categorification, when done successfully, replaces sets with categories, functions with functors, and equations with natural isomorphisms of functors satisfying additional properties.