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). |