The study of how the probability of success depends on expanatory variables and grouping of materials.
The analysis of binary data also involves goodness-of-fit tests of a sample of binary variables to a theoretical distribution, as well as the study of \( { 2 \times 2 } \) contingency tables and their subsequent analysis. In the latter case we note especially independence tests between attributes, and homogeneity tests.
HISTORY
See data analysis.
MATHEMATICAL ASPECTS
Let Y be a binary random variable and \( { X_1, X_2, \ldots, X_{k} } \) be supplementary binary variables. So the dependence of Y on the variables \( { X_1, X_2, \ldots, X_{k} } \) is represented by the following models (the coefficients of which are estimated via the maximum likelihood):
- 1.
Linear model: \( { P (Y=1) } \) is expressed as a linear function (in the parameters) of X i .
- 2.
Log-linear model: \( { \log P (Y = 1) } \) is expressed as a linear function (in the parameters) of X i .
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REFERENCES
Cox, D.R., Snell, E.J.: The Analysis of Binary Data. Chapman & Hall (1989)
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© 2008 Springer-Verlag
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(2008). Analysis of Binary Data. In: The Concise Encyclopedia of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32833-1_5
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DOI: https://doi.org/10.1007/978-0-387-32833-1_5
Publisher Name: Springer, New York, NY
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