Loglinear models:

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

where y is the dependent variable; x_i, i=1,...,N are independent variables, and {a_i, 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

transforms to:

where