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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 ...
As with any addition of variables to a model, the addition of dummy variables will increase the within-sample model fit (coefficient of determination), but at a cost of fewer degrees of freedom and loss of generality of the model (out of sample model fit). Too many dummy variables result in a model that does not provide any general conclusions.
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 crucial line above is the third. The second follows directly from the definition of expected value. The third line is particular to the categorical distribution, and follows from the fact that, in the categorical distribution specifically, the expected value of seeing a particular value i is directly specified by the associated parameter p ...
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 ...
For Dummies is an extensive series of instructional reference books which are intended to present non-intimidating guides for readers new to the various topics covered. The series has been a worldwide success with editions in numerous languages.
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 ...