These models are handled basically the same as you would for three-way tables, these are just more complex in terms of the number of possible models and parameters that you could examine. Higher -way tables are going to have many more two-way, three-way and k-way associations.

Model selection strategies with Loglinear models

Log-linear models are general in a sense that do not make an explicit distinction between responses and explanatory variables. They can be used if there are more than two response variables.

• Determine if some variables are responses and some explanatory. Include associations terms for the explanatory variables in the model. Focus your model search on models that relate the responses to explanatory variables.
• If a margin is fixed by design, included the appropriate term in the loglinear model (to ensure that the marginal fitted values from the model equals to observed margin).
• Try to determine the level of complexity that is neccessary by fitting models with
  • marginal/main effects only
  • all 2-way associations
  • all 3-way associations, etc....
  • all highest-way associations.
• Try a backward elimination strategy (analogous to one discussed for logit models that we will see in the next lesson) or a stepwise procedure. Be careful in using computer aglorithms; you are better off doing likelihood ratio tests, e.g. blue collar data.

You can also look at the set of Case Studies in the Case Studies folder which is still under the development! Some of those talk about logistic regression models that we have not seen yet. However, Smoking and Stress example includes a log-linear model with more than 3 random variables.