Question

Differences between log linear model and generalized log linear model.

Answer 1

The log-linear model is a specialized case of generalized linear models for Poisson-distributed data. Loglinear analysis is an extension of the two-way contingency table where the conditional relationship between two or more discrete, categorical variables is analyzed by taking the natural logarithm of the cell frequencies within a contingency table. Although log-linear models can be used to analyze the relationship between two categorical variables, they are more commonly used to evaluate multiway contingency tables that involve three or more variables. The variables investigated by log-linear models are all treated as “response variables”. In other words, no distinction is made between independent and dependent variables. Therefore, log-linear models only demonstrate an association between variables.

When given an opportunity to analyze multivariate categorical response data, it is often desirable to have at one’s disposal a broad class of models that can be used to simultaneously answer several questions about the multivariate distributions. For instance, we may wish to describe both the first-order marginal distributions and joint distributions. More generally, we may wish to simultaneously describe several different response configuration distributions; a response configuration is simply a collection of response variables. Generalized log-linear models are well suited for this simultaneous modelling.