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Loglinear models

Home » Glossaries » Loglinear models

Loglinear models

Loglinear models:

Loglinear models are models that postulate a linear relationship between the independent variables and the logarithm of the dependent variable, for example:



log(y) = a0 + a1 x1 + a2 x2 ... + aN xN


where y is the dependent variable; xi, i=1,...,N are independent variables, and {ai, i=0,...,N} are parameters (coefficients) of the model.


Loglinear models, for example, are widely used to analyze categorical data represented as a contingency table . In this case, the main reason to transform frequencies (counts) or probabilities to their log-values is that, provided the independent variables are not correlated with each other, the relationship between the new transformed dependent variable and the independent variables is a linear (additive) one. For example, a simple bivariate independence model for two categorical variables X and Y



pij = P(X=i) P(Y=j); i=1,...,M; j=1,...,N


transforms to:



log(pij) = liX + ljY;


where



liX = logP(X=i);
ljY = logP(Y=j).

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Courses Using This Term

Categorical Data Analysis
This course will teach you the analysis of contingency table data. Topics include tests for independence, comparing proportions as well as chi-square, exact methods, and treatment of ordered data. Both 2-way and 3-way tables are covered.
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